If we consider statement a then 2 possibilities occur , the champion&nbsp;may or may not receive bye and the answer for both possibilities would be different. If we consider both statements a &amp; b together we can find the exact answer to the question.

Using only statement A, we cannot say anything because the player might have received the bye in any round and the total number of players differs if the round in which the player got a bye changes. Using only statement B, we cannot saty anything because there might be players who received a bye in other rounds. Using both the statements, we know that only 1 player got a bye in the whole tournament and that happened in round 3. If the number of players were between 65 and 128, then the number of rounds is 7. =&gt; In the fourth round there would be 16 people. One person got a bye here =&gt; 31 people in round 3 =&gt; 62 people in round 2 =&gt; 124 people in round 1. Hence, we can ansswer the question using both the statements together.

Let w1 and w2 be average of both the groups respectively. Since average of whole class is 45. $\frac{50*w1+50*w2}{100} = 45$ =&gt; w1 + w2 = 90 And if we consider case A we have w2-w1 = 1. From the two equations average weight can be found out. Further using the equations deduced from given condition which are : $\frac{50*w1-l+h}{50} = w2$ and $\frac{50*w2+l-h}{50} = w1$ where l and h is weight of poonam and deepak respectively. However, both of the above equations are effectively the same. Hence we have two equations and 3 unknowns, thus we cannot find the weights by using statement I alone. If we consider statement B, then we can get another equation. So we will have 3 equations and then we can solve them for the 3 variables. So both the equations are required to answer the question.

Using statement A alone, we can determine the inner volume of the tank to be at least 4/3 $\pi$ (125-64) = 256 $m^3$. But we do not know if it is more than 400 $m^3$. So, using statement A alone, we cannot determine the answer. Using statement B alone, volume of tank = 30000 kg / 3gm/cc = $10^7 * 10^{-6}$ &nbsp;= 10 $m^3$ So, inner volume = 4/3 $\pi$ 125 - 10 &gt; 400 $m^3$ So, using statement B alone, we can answer the question

We know that the $x^2 + y^2 + z^2$ will be minimum when x = y = z = 89/3 Since that is not an integer, we can consider integer values that are closest to 89/3 Let x = y = 30 and z = 29 =&gt; $x^2 + y^2 + z^2$ = 2641 If x = y = 29 and z = 31,$x^2 + y^2 + z^2$ = 2643 So, the minimum is 2641 So, the question can be answered using statment 1 alone Using statement 2 alone, we cannot answer the question. Option a)

If the side of the square is x cm, then the maximum length of OM is $\sqrt2x$ The minimum length of OL is x. So, OM can never be 2 times OL So, using statement A alone, we can conclude that Rahim is unable to draw the square. Using statement B alone, we cannot answer the question. So, option a) is the correct answer.

No. of athletes which are top academic performers: 10 According to statement a)&nbsp;Sixty per cent of the top academic performers were not athletes &nbsp;so 40% of top academic performers are athletes which we know is 10. So total no. of top academic performers are 25.&nbsp; Hence statement a is alone to answer the question. while we cant deduce anything from statement b .

From the information given in the question, D has a better rank than E and B has a better rank than C. Also, C = 4 or 5. From statement A, A = 5 =&gt; C = 4. But we do not know if D or B is number 1. From statement B, B = 3 or 4. Again, we cannot determine the number 1 rank precisely. By using both the statements together, we know C = 4, A = 5, B = 3 and D has a better rank than E. So, D = 1 and E = 2. Therefore, the question can be answered by using both the statements together. Hence, option D.

Let the total number of employees be 100k. Number of males = 30k. Number of females = 70k. Number of female engineers = 7k. From statement A, number of male engineers = 25k - 7k = 18k. From statement B, number of male engineers = (6/5)*7k. Therefore, percentage of male engineers can be calculated. So, the question can be answered by either statement alone.

From statement A, we know that the club scored four goals in the second half but we do not know the number of goals scored by the opposition. So, we cannot answer the question. From statement B, we know that the opposition scored 4 goals in the match but we do not know the number of goals scored by Mahindra and Mahindra club. So, we cannot answer the question. Using both the statements, we know that the opposition scored 4 goals in the match and Mahindra and Mahindra scored 4 goals in the second half. But, we do not know if the score was 3-0 or 4-1 at the end of first half. If it was 4-1, then Mahindra and Mahindra would win the match after the second half. But if the score was 3-0 at the end of first half, the match would end in a draw after the second half. Therefore, the question cannot be answered even by using both the statements together.

Statement B is redundant. We already know that M has 5 siblings from the question. From statement A alone, we know that F has 2 brothers and M has 2 brothers and 3 sisters.

Considering statement&nbsp;A. The game ended normally. &nbsp;Here we know that last 2 results were heads and the person receives 100 Rs. and since there was overall loss of 50 Rs we can calculate no. of matches which ended in tails or non consecutive heads . hence , statement a is sufficient to answer. Considering statement&nbsp;B. The total number of tails obtained in the game was 138. So we know person lost here rs.138 and we can add any no. of single heads in between those tails such that the overall loss will be 50Rs. Hence this statement is also sufficient to answer.

Considering statements a we can deduce that she got letter S in her 21st purchase in previous 20 puchase she had either A, O or P . Hence statement a is not enough to answer. If we consider statement b we will know that out of 20 purchases 18 are vowel so 2 purchases contained letter P . So both statements are necessary to answer the question.

Let the distance be x. Time taken by A is T, so time taken by B is T+60 and time taken by C is T+90. From statement A, we know that the ratio of speeds of A and C is x:(x-375) = x/T : x/(T+90) We have only 1 equation and 2 unknows. We need the second statement to find the values. So, the question can be answered by using both the statements together.

CAT Data Sufficiency

Instructions

Question 1.

Question 2.

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Question 3.

Question 4.

Question 5.

Question 6.

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Question 7.

Question 8.

Question 9.

Question 10.

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Question 11.

Question 12.

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Question 14.

Free CAT Quant Questions

CAT Data Sufficiency

Instructions

Question 1.

<div>What is the number of Matches played by the champion?<br />A. The entry list for the tournament consists of 83 players?<br />B. The champion received one bye.</div>

Question 2.

<div>If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n?<br />A. Exactly one player received a bye in the entire tournament.<br />B. One player received a bye while moving on to the fourth round from the third round.</div>

Instructions

<div>Instructions <br />Directions for the following four questions: Each question is followed by two statements A and B. Indicate your responses based on data sufficiency</div>

Question 3.

Question 4.

Question 5.

<div>Consider integers x, y and z. What is the minimum possible value of $x^2 + y^2 + z^2$?<br />A: x + y + z = 89<br />B: Among x, y, z two are equal.</div>

Question 6.

<div>Rahim plans to draw a square JKLM with a point O on the side JK but is not successful. Why is Rahim unable to draw the square?<br />A: The length of OM is twice that of OL.<br />B: The length of OM is 4 cm</div>

Instructions

<div>Instructions <br />Directions for the following four questions:<br />Each question is followed by two statements, A and B. Answer each question using the following instructions:</div>

Question 7.

Question 8.

Question 9.

Question 10.

<div>In a football match, at the half-time, Mahindra and Mahindra Club was trailing by three goals. Did it win the match?<br />A. In the second-half Mahindra and Mahindra Club scored four goals.<br />B. The opponent scored four goals in the match.</div>

Instructions

<div>Instructions <br />For the following questions answer them individually</div>

Question 11.

<div>F and M are father and mother of S, respectively. S has four uncles and three aunts. F has two siblings. The siblings of F and M are unmarried. How many brothers does M have?<br />A. F has two brothers.<br />B. M has five siblings.</div>

Question 12.

Question 13.

Question 14.

Free CAT Quant Questions