Based on the given information, we can form the following Venn-diagram for ease of understanding:&nbsp;<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/1_R7e1Mg7.png" alt="1">The conditions help us to further bifurcate the individuals based on their expertise.Mridangam: A and B (condition 1); one out of F and G&nbsp;(condition 3)Tabla: one out of&nbsp;A and B (condition 1); F and G (condition 3); D (condition 2)Ghatam: D (condition 2)Based on condition 4, we infer that 'I' and 'J' are either experts in Ghatam or Mridangam. However, condition 5 adds that 'I' is not an expert in Mridangam. This helps us definitively zero-in on 'I' as an expert in Ghatam. Since 'I' is a Ghatam expert, J is an expert in Mridangam and 'H' is an expert in Tabla [based on conditions 4 and 5]. Thus, we can depict our understanding so far as follows:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Slot20120LRDI202020202.png" alt="Slot 1 LRDI 2020 2">Mridangam&nbsp;[total: 5] -&nbsp;A and B (condition 1); one out of F and G (condition 3); J (condition 4 and 5); one out of C and E {remaining experts}Tabla&nbsp;[total: 6] -&nbsp;one out of A and B (condition 1); F and G (condition 3); D (condition 2); H&nbsp;(condition 4 and 5);&nbsp;one out of C and E {remaining experts}&nbsp;Ghatam&nbsp;[total: 2] - D (condition 2); I (condition 4 and 5)Thus, we observe that&nbsp;H&nbsp;is definitely an expert&nbsp;in tabla but not in either mridangam or ghatam. Hence, Option C is the correct answer.

Based on the given information, we can form the following Venn-diagram for ease of understanding:&nbsp;<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/1_isU9l6N.png" alt="1">The conditions help us to further bifurcate the individuals based on their expertise.Mridangam: A and B (condition 1); one out of F and G&nbsp;(condition 3)Tabla: one out of&nbsp;A and B (condition 1); F and G (condition 3); D (condition 2)Ghatam: D (condition 2)Based on condition 4, we infer that 'I' and 'J' are either experts in Ghatam or Mridangam. However, condition 5 adds that 'I' is not an expert in Mridangam. This helps us definitively zero-in on 'I' as an expert in Ghatam. Since 'I' is a Ghatam expert, J is an expert in Mridangam and 'H' is an expert in Tabla [based on conditions 4 and 5]. Thus, we can depict our understanding so far as follows:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Slot20120LRDI202020202.png" alt="Slot 1 LRDI 2020 2">Mridangam&nbsp;[total: 5] -&nbsp;A and B (condition 1); one out of F and G (condition 3); J (condition 4 and 5); one out of C and E {remaining experts}Tabla&nbsp;[total: 6] -&nbsp;one out of A and B (condition 1); F and G (condition 3); D (condition 2); H&nbsp;(condition 4 and 5);&nbsp;one out of C and E {remaining experts}&nbsp;Ghatam&nbsp;[total: 2] - D (condition 2); I (condition 4 and 5)If C is an expert in Mridangam, E has to be an expert in Tabla. Additionally, if F is not an expert in Mridangam, he has to be an expert only in Tabla while G will be an expert in both Tabla and Mridangam.Tabla&nbsp;[total: 6] - one out of A and B (condition 1); F and G (condition 3); D (condition 2); H (condition 4 and 5);&nbsp;E {based on the condition given in the question}Of these experts, A, B and G are experts of Mridangam and D is an expert of Ghatam as well. Thus, excluding these, we have&nbsp;&nbsp;F, H and E who are the experts solely in Tabla. Thus, Option A is the correct answer.

Based on the given information, we can form the following Venn-diagram for ease of understanding:&nbsp;<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/1_nUK4Mqk.png" alt="1">The conditions help us to further bifurcate the individuals based on their expertise.Mridangam: A and B (condition 1); one out of F and G&nbsp;(condition 3)Tabla: one out of&nbsp;A and B (condition 1); F and G (condition 3); D (condition 2)Ghatam: D (condition 2)Based on condition 4, we infer that 'I' and 'J' are either experts in Ghatam or Mridangam. However, condition 5 adds that 'I' is not an expert in Mridangam. This helps us definitively zero-in on 'I' as an expert in Ghatam. Since 'I' is a Ghatam expert, J is an expert in Mridangam and 'H' is an expert in Tabla [based on conditions 4 and 5]. Thus, we can depict our understanding so far as follows:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Slot20120LRDI202020202.png" alt="Slot 1 LRDI 2020 2">Mridangam&nbsp;[total: 5] -&nbsp;A and B (condition 1); one out of F and G (condition 3); J (condition 4 and 5); one out of C and E {remaining experts}Tabla&nbsp;[total: 6] -&nbsp;one out of A and B (condition 1); F and G (condition 3); D (condition 2); H&nbsp;(condition 4 and 5);&nbsp;one out of C and E {remaining experts}&nbsp;Ghatam&nbsp;[total: 2] - D (condition 2); I (condition 4 and 5)Thus, we observe that&nbsp;J&nbsp;is definitely an expert in mridangam but not in either tabla or ghatam. Hence, Option B is the correct answer.

Based on the given information, we can form the following Venn-diagram for ease of understanding:&nbsp;<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/1_zim8mDB.png" alt="1">The conditions help us to further bifurcate the individuals based on their expertise.Mridangam: A and B (condition 1); one out of F and G&nbsp;(condition 3)Tabla: one out of&nbsp;A and B (condition 1); F and G (condition 3); D (condition 2)Ghatam: D (condition 2)Based on condition 4, we infer that 'I' and 'J' are either experts in Ghatam or Mridangam. However, condition 5 adds that 'I' is not an expert in Mridangam. This helps us definitively zero-in on 'I' as an expert in Ghatam. Since 'I' is a Ghatam expert, J is an expert in Mridangam and 'H' is an expert in Tabla [based on conditions 4 and 5]. Thus, we can depict our understanding so far as follows:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Slot20120LRDI202020202.png" alt="Slot 1 LRDI 2020 2">Mridangam&nbsp;[total: 5] -&nbsp;A and B (condition 1); one out of F and G (condition 3); J (condition 4 and 5); one out of C and E {remaining experts}Tabla&nbsp;[total: 6] -&nbsp;one out of A and B (condition 1); F and G (condition 3); D (condition 2); H&nbsp;(condition 4 and 5);&nbsp;one out of C and E {remaining experts}&nbsp;Ghatam&nbsp;[total: 2] - D (condition 2); I (condition 4 and 5)We observe that the pair&nbsp;C and E&nbsp;cannot have any musician who is an expert in both tabla and mridangam but not in ghatam. Hence, Option C is the correct answer.

Of the 1000 subjects, only 500 have been considered for the treatment. This constitutes our sample set. Thus the four drugs- A, B, C and D have been administered to this set of 500 individuals, while the rest 500 have been given the placebo.&nbsp;Based on the given information, we can then draw the following 4-set Venn diagram:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/1_1oQhxTM.png" alt="1">We can solve for the number of patients who were administered the drugs A, B and D excluding C by putting in the values for set A. The required value = 250 - (25+20+30+40+20+50+35) =&nbsp;30.&nbsp;Based on condition&nbsp;(c), we know that&nbsp;100 patients were treated with exactly three types of medicines.&nbsp;Thus, we can fill the slot for the number of patients who were administered only B, C and D excluding A by 100 - (40+20+30) =&nbsp;10.&nbsp;&nbsp;Similarly, based on condition&nbsp;(f), we know that the candidates who were administered only dug B are 75 - (25+20+10) =&nbsp;20. Post this, we can easily calculate the number of people administered with only drugs B and C by 210 - (30+20+40+50+10+20+20) =&nbsp;20. We can fill in the above values to obtain the following diagram:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/2_JCRMAxi.png" alt="2">The sum of all the values should add up to 500. On solving for 'x' [which represents the number of people who were administered drugs B and D only], we obtain x =&nbsp;150.&nbsp;The final representation would appear as follows:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Slot20120LRDI202020205_7Ki12MV.png" alt="Slot 1 LRDI 2020 5">Based on the above, the number of&nbsp;patients who were treated with medicine type B is equal to&nbsp;340.

Of the 1000 subjects, only 500 have been considered for the treatment. This constitutes our sample set. Thus the four drugs- A, B, C and D have been administered to this set of 500 individuals, while the rest 500 have been given the placebo.&nbsp;Based on the given information, we can then draw the following 4-set Venn diagram:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/1_r2ISE3D.png" alt="1">We can solve for the number of patients who were administered the drugs A, B and D excluding C by putting in the values for set A. The required value = 250 - (25+20+30+40+20+50+35) =&nbsp;30.&nbsp;Based on condition&nbsp;(c), we know that&nbsp;100 patients were treated with exactly three types of medicines.&nbsp;Thus, we can fill the slot for the number of patients who were administered only B, C and D excluding A by 100 - (40+20+30) =&nbsp;10.&nbsp;&nbsp;Similarly, based on condition&nbsp;(f), we know that the candidates who were administered only dug B are 75 - (25+20+10) =&nbsp;20. Post this, we can easily calculate the number of people administered with only drugs B and C by 210 - (30+20+40+50+10+20+20) =&nbsp;20. We can fill in the above values to obtain the following diagram:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/2_fMW1bQH.png" alt="2">The sum of all the values should add up to 500. On solving for 'x' [which represents the number of people who were administered drugs B and D only], we obtain x =&nbsp;150.&nbsp;The final representation would appear as follows:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Slot20120LRDI202020205_7Ki12MV.png" alt="Slot 1 LRDI 2020 5">The number of patients who were treated with medicine types B, C and D, but not type A was:&nbsp;10.

Let the&nbsp;number of schools with exactly three of the facilities was the same irrespective of which three were considered be x.Number of schools with none of the facilities be 'n' from 1, n=80.&nbsp;Number of schools with only F1 and F2 be 'b'Number of schools with only F1 and F3 be 'c'Number of schools with only F1 and F4 be 'd'From the information given in the question we will get the following Venn diagram.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_dVRclfE.png" alt="image">From 5, b+141+3x=313 =&gt; b+3x=172....(i)From 8, b+x+40+x=162 =&gt; b+2x=122....(ii)(ii)-(i) gives x=50 =&gt; b=22From 9, 237+3x+c+d=279+3x=d =&gt; c=42Total number of schools =600 =&gt; 313+25+c+x+d+26+24+20+80=600 =&gt; d=20.The final table looks like:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_gagYEXB.png" alt="image">The total number of schools having facilities F4 and F2= 45+50+50+40=185.

Let the&nbsp;number of schools with exactly three of the facilities was the same irrespective of which three were considered be x.Number of schools with none of the facilities be 'n' from 1, n=80.&nbsp;Number of schools with only F1 and F2 be 'b'Number of schools with only F1 and F3 be 'c'Number of schools with only F1 and F4 be 'd'From the information given in the question we will get the following Venn diagram.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_dVRclfE.png" alt="image">From 5, b+141+3x=313 =&gt; b+3x=172....(i)From 8, b+x+40+x=162 =&gt; b+2x=122....(ii)(ii)-(i) gives x=50 =&gt; b=22From 9, 237+3x+c+d=279+3x=d =&gt; c=42Total number of schools =600 =&gt; 313+25+c+x+d+26+24+20+80=600 =&gt; d=20.The final table looks like:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_gagYEXB.png" alt="image">The total number of schools with exactly three of the four facilities= 4x=200.

Let the&nbsp;number of schools with exactly three of the facilities was the same irrespective of which three were considered be x.Number of schools with none of the facilities be 'n' from 1, n=80.&nbsp;Number of schools with only F1 and F2 be 'b'Number of schools with only F1 and F3 be 'c'Number of schools with only F1 and F4 be 'd'From the information given in the question we will get the following Venn diagram.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_dVRclfE.png" alt="image">From 5, b+141+3x=313 =&gt; b+3x=172....(i)From 8, b+x+40+x=162 =&gt; b+2x=122....(ii)(ii)-(i) gives x=50 =&gt; b=22From 9, 237+3x+c+d=279+3x=d =&gt; c=42Total number of schools =600 =&gt; 313+25+c+x+d+26+24+20+80=600 =&gt; d=20.The final table looks like:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_gagYEXB.png" alt="image">The total number of schools having only F1 and F4=20.

Let the&nbsp;number of schools with exactly three of the facilities was the same irrespective of which three were considered be x.Number of schools with none of the facilities be 'n' from 1, n=80.&nbsp;Number of schools with only F1 and F2 be 'b'Number of schools with only F1 and F3 be 'c'Number of schools with only F1 and F4 be 'd'From the information given in the question we will get the following Venn diagram.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_dVRclfE.png" alt="image">From 5, b+141+3x=313 =&gt; b+3x=172....(i)From 8, b+x+40+x=162 =&gt; b+2x=122....(ii)(ii)-(i) gives x=50 =&gt; b=22From 9, 237+3x+c+d=279+3x=d =&gt; c=42Total number of schools =600 =&gt; 313+25+c+x+d+26+24+20+80=600 =&gt; d=20.The final table looks like:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_gagYEXB.png" alt="image">The total number of schools having only F1 and F3= c=42

No. of girls = 15Let the no. of boys be xNo. of singers = 6No of boys who are singers = 4Therefore, no of girls who are singers = 2No of dancers = 10No of boys who are dancers = 6Therefore, no. of girls who are dancers = 4No. of boys who are neither singers nor dancers = x-10No. of girls who are neither singers nor dancers = 9<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_153039.png">Now we fill the above table,using statements 1 and 2, we get the following table<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_162402.png">Let the number of girls who are interested in attending a 2-day event be a and the number of girls who are dancers and are interested in 2-day event be b.Now using statements 3 and 4, we get<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_163600.png">2≤0.18x−4≤66≤0.18x≤100.18x should be integer for which x should be a multiple of 50, and 0.18x lies between 6 and 10; therefore, the only possible value of x is 50.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_164325.png">From statement 5, we can say that,4+ 0.4a - b = 5+b +1or, 0.4a = 2+2bor, a = 5(1+b)a should be a multiple of 5 as b is a whole number. So possible values of a can be 5, 10 or 15. Now, as the maximum value of b can be 4 and the maximum value of 0.4a-b can be 2, so the only possible value of a satisfying the conditions above is 5. If a= 5 then b=1.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_165113.png">

No. of girls = 15Let the no. of boys be xNo. of singers = 6No of boys who are singers = 4Therefore, no of girls who are singers = 2No of dancers = 10No of boys who are dancers = 6Therefore, no. of girls who are dancers = 4No. of boys who are neither singers nor dancers = x-10No. of girls who are neither singers nor dancers = 9<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_153039.png">Now we fill the above table,using statements 1 and 2, we get the following table<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_162402.png">Let the number of girls who are interested in attending a 2-day event be a and the number of girls who are dancers and are interested in 2-day event be b.Now using statements 3 and 4, we get<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_163600.png">2≤0.18x−4≤66≤0.18x≤100.18x should be integer for which x should be a multiple of 50, and 0.18x lies between 6 and 10; therefore, the only possible value of x is 50.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_164325.png">From statement 5, we can say that,4+ 0.4a - b = 5+b +1or, 0.4a = 2+2bor, a = 5(1+b)a should be a multiple of 5 as b is a whole number. So possible values of a can be 5, 10 or 15. Now, as the maximum value of b can be 4 and the maximum value of 0.4a-b can be 2, so the only possible value of a satisfying the conditions above is 5. If a= 5 then b=1.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_165113.png">Total students interested in 2-day event = 30+5 = 35Total students = 15 + 50 = 65Fraction =&nbsp;$\frac{35}{65} = \frac{7}{13}$

No. of girls = 15Let the no. of boys be xNo. of singers = 6No of boys who are singers = 4Therefore, no of girls who are singers = 2No of dancers = 10No of boys who are dancers = 6Therefore, no. of girls who are dancers = 4No. of boys who are neither singers nor dancers = x-10No. of girls who are neither singers nor dancers = 9<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_153039.png">Now we fill the above table,using statements 1 and 2, we get the following table<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_162402.png">Let the number of girls who are interested in attending a 2-day event be a and the number of girls who are dancers and are interested in 2-day event be b.Now using statements 3 and 4, we get<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_163600.png">2≤0.18x−4≤66≤0.18x≤100.18x should be integer for which x should be a multiple of 50, and 0.18x lies between 6 and 10; therefore, the only possible value of x is 50.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_164325.png">From statement 5, we can say that,4+ 0.4a - b = 5+b +1or, 0.4a = 2+2bor, a = 5(1+b)a should be a multiple of 5 as b is a whole number. So possible values of a can be 5, 10 or 15. Now, as the maximum value of b can be 4 and the maximum value of 0.4a-b can be 2, so the only possible value of a satisfying the conditions above is 5. If a= 5 then b=1.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_165113.png">

No. of girls = 15Let the no. of boys be xNo. of singers = 6No of boys who are singers = 4Therefore, no of girls who are singers = 2No of dancers = 10No of boys who are dancers = 6Therefore, no. of girls who are dancers = 4No. of boys who are neither singers nor dancers = x-10No. of girls who are neither singers nor dancers = 9<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_153039.png">Now we fill the above table,using statements 1 and 2, we get the following table<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_162402.png">Let the number of girls who are interested in attending a 2-day event be a and the number of girls who are dancers and are interested in 2-day event be b.Now using statements 3 and 4, we get<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_163600.png">2≤0.18x−4≤66≤0.18x≤100.18x should be integer for which x should be a multiple of 50, and 0.18x lies between 6 and 10; therefore, the only possible value of x is 50.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_164325.png">From statement 5, we can say that,4+ 0.4a - b = 5+b +1or, 0.4a = 2+2bor, a = 5(1+b)a should be a multiple of 5 as b is a whole number. So possible values of a can be 5, 10 or 15. Now, as the maximum value of b can be 4 and the maximum value of 0.4a-b can be 2, so the only possible value of a satisfying the conditions above is 5. If a= 5 then b=1.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_165113.png">

No. of girls = 15Let the no. of boys be xNo. of singers = 6No of boys who are singers = 4Therefore, no of girls who are singers = 2No of dancers = 10No of boys who are dancers = 6Therefore, no. of girls who are dancers = 4No. of boys who are neither singers nor dancers = x-10No. of girls who are neither singers nor dancers = 9<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_153039.png">Now we fill the above table,using statements 1 and 2, we get the following table<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_162402.png">Let the number of girls who are interested in attending a 2-day event be a and the number of girls who are dancers and are interested in 2-day event be b.Now using statements 3 and 4, we get<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_163600.png">2≤0.18x−4≤66≤0.18x≤100.18x should be integer for which x should be a multiple of 50, and 0.18x lies between 6 and 10; therefore, the only possible value of x is 50.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_164325.png">From statement 5, we can say that,4+ 0.4a - b = 5+b +1or, 0.4a = 2+2bor, a = 5(1+b)a should be a multiple of 5 as b is a whole number. So possible values of a can be 5, 10 or 15. Now, as the maximum value of b can be 4 and the maximum value of 0.4a-b can be 2, so the only possible value of a satisfying the conditions above is 5. If a= 5 then b=1.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/Screenshot_20221221_165113.png">

It is given that the total number of products supermarket sells is 320.cosmetic + nutrition = foreign + domestic = FDA + EU = 320 productsIn statement 1, it is given that the number of foreign products is equal to the number of domestic products.Foreign products = Domestic products = 320/2 = 160<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_Ze3gnUJ.png">In statement 2, it is given that half of the domestic products were FDA approved cosmetic products, i.e. domestic, cosmetic and FDA = 80In statement 4, it is given that there were 140 nutrition products, half of them were foreign products. This implies remaining half are domestic.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_GnGyV1U.png">In statement 5, it is given that there are 200 FDA approved products out of which 70 are foreign products and 120 are cosmetic products.If 70 are foreign products, remaining 130 should be domestic products. In domestic products, FDA approved cosmetic products are 80. This implies FDA approved nutrition products are 130-80, i.e. 50.There are 120 FDA approved cosmetic products.Domestic, cosmetic and FDA approved = 80This implies, Foreign, cosmetic and FDA approved is 120-80, i.e. 40.There are 70 FDA approved foreign products.This implies Foreign, nutrition and FDA approved is 70-40, i.e. 30.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_kNjMage.png">Domestic and Cosmetic = 90Domestic, comestic and FDA approved = 80This implies, Domestic, cosmetic and FDA not approved is 90-80, i.e. 10.Therefore, (domestic, cosmetic and only EU) = 10Similarly, we get (domestic, nutrition and only EU) = 70-50 = 20<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_kHDNBoz.png">In the question, it is given that&nbsp;50 nutrition products did not have EU approval.&nbsp;In Foreign products, there are 30 nutrition products which do not have EU approval. This implies 20 nutrition products do not have EU(have only FDA)&nbsp;approval in domestic products.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_sDP2uu7.png">It is given, d = 20c = 50 - 20 = 30It is given, a + c = 60a = 60 - 30 = 30b = 80 - 30 = 50<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_ZZmI5pI.png">Therefore,&nbsp;the number of&nbsp;domestic cosmetic products did not have EU(only FDA) approval is 50.

It is given that the total number of products supermarket sells is 320.cosmetic + nutrition = foreign + domestic = FDA + EU = 320 productsIn statement 1, it is given that the number of foreign products is equal to the number of domestic products.Foreign products = Domestic products = 320/2 = 160<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_Ze3gnUJ.png">In statement 2, it is given that half of the domestic products were FDA approved cosmetic products, i.e. domestic, cosmetic and FDA = 80In statement 4, it is given that there were 140 nutrition products, half of them were foreign products. This implies remaining half are domestic.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_GnGyV1U.png">In statement 5, it is given that there are 200 FDA approved products out of which 70 are foreign products and 120 are cosmetic products.If 70 are foreign products, remaining 130 should be domestic products. In domestic products, FDA approved cosmetic products are 80. This implies FDA approved nutrition products are 130-80, i.e. 50.There are 120 FDA approved cosmetic products.Domestic, cosmetic and FDA approved = 80This implies, Foreign, cosmetic and FDA approved is 120-80, i.e. 40.There are 70 FDA approved foreign products.This implies Foreign, nutrition and FDA approved is 70-40, i.e. 30.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_kNjMage.png">Domestic and Cosmetic = 90Domestic, comestic and FDA approved = 80This implies, Domestic, cosmetic and FDA not approved is 90-80, i.e. 10.Therefore, (domestic, cosmetic and only EU) = 10Similarly, we get (domestic, nutrition and only EU) = 70-50 = 20<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_kHDNBoz.png">The number of foreign, cosmetic and FDA approved products is 40.The answer is 40.

It is given that the total number of products supermarket sells is 320.cosmetic + nutrition = foreign + domestic = FDA + EU = 320 productsIn statement 1, it is given that the number of foreign products is equal to the number of domestic products.Foreign products = Domestic products = 320/2 = 160<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_Ze3gnUJ.png">In statement 2, it is given that half of the domestic products were FDA approved cosmetic products, i.e. domestic, cosmetic and FDA = 80In statement 4, it is given that there were 140 nutrition products, half of them were foreign products. This implies remaining half are domestic.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_GnGyV1U.png">In statement 5, it is given that there are 200 FDA approved products out of which 70 are foreign products and 120 are cosmetic products.If 70 are foreign products, remaining 130 should be domestic products. In domestic products, FDA approved cosmetic products are 80. This implies FDA approved nutrition products are 130-80, i.e. 50.There are 120 FDA approved cosmetic products.Domestic, cosmetic and FDA approved = 80This implies, Foreign, cosmetic and FDA approved is 120-80, i.e. 40.There are 70 FDA approved foreign products.This implies Foreign, nutrition and FDA approved is 70-40, i.e. 30.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_kNjMage.png">Domestic and Cosmetic = 90Domestic, comestic and FDA approved = 80This implies, Domestic, cosmetic and FDA not approved is 90-80, i.e. 10.Therefore, (domestic, cosmetic and only EU) = 10Similarly, we get (domestic, nutrition and only EU) = 70-50 = 20<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_kHDNBoz.png">The number of cosmetic products which do not have FDA approval = domestic only EU + foreign EU = 10 + 50 = 60The answer is option D.

It is given that the total number of products supermarket sells is 320.cosmetic + nutrition = foreign + domestic = FDA + EU = 320 productsIn statement 1, it is given that the number of foreign products is equal to the number of domestic products.Foreign products = Domestic products = 320/2 = 160<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_Ze3gnUJ.png">In statement 2, it is given that half of the domestic products were FDA approved cosmetic products, i.e. domestic, cosmetic and FDA = 80In statement 4, it is given that there were 140 nutrition products, half of them were foreign products. This implies remaining half are domestic.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_GnGyV1U.png">In statement 5, it is given that there are 200 FDA approved products out of which 70 are foreign products and 120 are cosmetic products.If 70 are foreign products, remaining 130 should be domestic products. In domestic products, FDA approved cosmetic products are 80. This implies FDA approved nutrition products are 130-80, i.e. 50.There are 120 FDA approved cosmetic products.Domestic, cosmetic and FDA approved = 80This implies, Foreign, cosmetic and FDA approved is 120-80, i.e. 40.There are 70 FDA approved foreign products.This implies Foreign, nutrition and FDA approved is 70-40, i.e. 30.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_kNjMage.png">Domestic and Cosmetic = 90Domestic, comestic and FDA approved = 80This implies, Domestic, cosmetic and FDA not approved is 90-80, i.e. 10.Therefore, (domestic, cosmetic and only EU) = 10Similarly, we get (domestic, nutrition and only EU) = 70-50 = 20<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_kHDNBoz.png">In the question, it is given that&nbsp;70 cosmetic products did not have EU approval.In foreign, 40 cosmetic products did not have EU approval. This implies 30 cosmetic products should have only FDA approval in domestic products.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_pWu23us.png">According to the above statement, b = 30a = 80 - 30 = 50Given, a + c = 60c = 60 - 50 = 10<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_YLk7ZrH.png">Therefore, the number of&nbsp;nutrition products which had both the approvals is 10.The answer is option A.

It is given that the total number of products supermarket sells is 320.cosmetic + nutrition = foreign + domestic = FDA + EU = 320 productsIn statement 1, it is given that the number of foreign products is equal to the number of domestic products.Foreign products = Domestic products = 320/2 = 160<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_Ze3gnUJ.png">In statement 2, it is given that half of the domestic products were FDA approved cosmetic products, i.e. domestic, cosmetic and FDA = 80In statement 4, it is given that there were 140 nutrition products, half of them were foreign products. This implies remaining half are domestic.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_GnGyV1U.png">In statement 5, it is given that there are 200 FDA approved products out of which 70 are foreign products and 120 are cosmetic products.If 70 are foreign products, remaining 130 should be domestic products. In domestic products, FDA approved cosmetic products are 80. This implies FDA approved nutrition products are 130-80, i.e. 50.There are 120 FDA approved cosmetic products.Domestic, cosmetic and FDA approved = 80This implies, Foreign, cosmetic and FDA approved is 120-80, i.e. 40.There are 70 FDA approved foreign products.This implies Foreign, nutrition and FDA approved is 70-40, i.e. 30.<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_kNjMage.png">Domestic and Cosmetic = 90Domestic, comestic and FDA approved = 80This implies, Domestic, cosmetic and FDA not approved is 90-80, i.e. 10.Therefore, (domestic, cosmetic and only EU) = 10Similarly, we get (domestic, nutrition and only EU) = 70-50 = 20<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_kHDNBoz.png">In statement 3, it is given that the number of domestic products which have both the approvals = 60<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_8PaN6wF.png">In the question, it is given that a + c = 60To find the minimum value of a, we need to maximise c.Maximum value c can take is 50Therefore, minimum value of a is 60-50, i.e. 10.To find the maximum value of a, we need to minimise c.Maximum value c can take is 0.Therefore, maximum value of a is 60-0, i.e. 60.a is minimum:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_AtisA66.png">a is maximum:<img src="https://lightyellow-stork-291267.hostingersite.com/wp-content/uploads/2025/11/image_9pPsLlV.png">Therefore, the number of domestic cosmetic products that had both the approvals is at least 10 and at most 60.The answer is option A.

CAT DILR Venn Diagrams Questions

Instructions

Question 1.

Question 2.

Question 3.

Question 4.

Instructions

Question 5.

Question 6.

Instructions

Question 7.

Question 8.

Question 9.

Question 10.

Instructions

Question 11.

Question 12.

Question 13.

Question 14.

Question 15.

Instructions

Question 16.

Question 17.

Question 18.

Question 19.

Question 20.

Free CAT DILR Questions

CAT DILR Venn Diagrams Questions

Instructions

Question 1.

<div><p>Who among the following is DEFINITELY an expert in tabla but not in either mridangam or ghatam?</p></div>

Question 2.

<div><p>If C is an expert in mridangam and F is not, then which are the three musicians who are experts in tabla but not in either mridangam or ghatam?</p></div>

Question 3.

<div><p>Who among the following is DEFINITELY an expert in mridangam but not in either tabla or ghatam?</p></div>

Question 4.

<div><p>Which of the following pairs CANNOT have any musician who is an expert in both tabla and mridangam but not in ghatam?</p></div>

Instructions

Question 5.

<div><p>How many patients were treated with medicine type B?</p></div>

Question 6.

<div><p>The number of patients who were treated with medicine types B, C and D, but not type A was:</p></div>

Instructions

Question 7.

<div><p>What was the number of schools having facilities F2 and F4?</p></div>

Question 8.

<div><p>What was the total number of schools having exactly three of the four facilities?</p></div>

Question 9.

<div><p>What was the number of schools having only facilities F1 and F4?</p></div>

Question 10.

<div><p>What was the number of schools having only facilities F1 and F3?</p></div>

Instructions

Question 11.

<div><p>What BEST can be concluded about the number of male dancers who are interested in attending a 1-day event?</p></div>

Question 12.

<div><p>What fraction of the class are interested in attending a 2-day event?</p></div>

Question 13.

<div><p>How many female dancers are interested in attending a 2-day event?</p></div>

Question 14.

<div><p>How many boys are there in the class?</p></div>

Question 15.

<div><p>Which of the following can be determined from the given information?<br><br>I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers.<br>II. The number of female dancers who are interested in attending a 1-day event.</p></div>

Instructions

Question 16.

<div><p>If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?</p></div>

Question 17.

<div><p>How many foreign products were FDA approved cosmetic products?</p></div>

Question 18.

<div><p>How many cosmetic products did not have FDA approval?</p></div>

Question 19.

<div><p>If 70 cosmetic products did not have EU approval, then how many nutrition products had both the approvals?</p></div>

Question 20.

<div><p>Which among the following options best represents the number of domestic cosmetic products that had both the approvals?</p></div>

Free CAT DILR Questions