If Q and T are integers, what is the value of Q?

Question

(1)  Q = \frac{2T}{7} .

(2)  T+\frac{7}{2} =\frac{7(Q+2)}{4}

Nightfury14 · Accepted Answer

Statement 1) Insufficient.
Statement 2) 8T+28 = 14Q+28 => 8T= 14Q => Q=4T/7 .. Insufficient

Together Statement 1) & 2) Q=2T/7 & Q=4T/7, More over Q & T are Integers.
this is possible only if T=0 and hence Q=0.

Choice C) is the answer. Statement 1) & 2) together are sufficient to ans the question.

Good luck
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14101992 · Answer

Statement 1:
Q=2T/7 -----> 7Q=2T
so, Q can be 2 and T can be 7 or Q can be 4 and T can be 14.
So, Statement 1 doesn't satisfy.
A and D out.
Statement 2:
T+7/2 =7(Q+2)/4 -----> 4T+14=7Q+14 -----> 4T=7Q
so, Q can be 4 and T can be 7 or Q can be 8 and T can be 14.
So, Statement 2 also doesn't satisfy.

Combining 1 and 2:
2T=7Q and 4T=7Q. This can be true only if T=0 and Q=0.
So, we know Q=0.
Hence, we get an answer for Q.
Answer is C.

OptimusPrepJanielle · Answer

Statement 1: Q = 2T/7
We do not know anything about T.
INSUFFICIENT

Statement 2: T+7/2 =7(Q+2)/4
On solving,
T + 7/2 = 7Q/4 + 7/2
T = 7Q/4
We do not know anything about T.
INSUFFICIENT

Combining both statements: 
Q = 2T/7 and Q = 4T/7
Hence 2T/7 = 4T/7
This can be true for T = 0 only.

Hence Q = 0
SUFFICIENT

Correct Option: C

Kinshook · Answer

Asked: If Q and T are integers, what is the value of Q?

(1)  Q = \frac{2T}{7} .
7Q = 2T
Since T is unknown
NOT SUFFICIENT

(2)  T+\frac{7}{2} =\frac{7(Q+2)}{4} 
4T + 14 = 7Q + 14
4T = 7Q
Since T is unknown
NOT SUFFICIENT

(1) + (2) 
(1)  Q = \frac{2T}{7} .
7Q = 2T
(2)  T+\frac{7}{2} =\frac{7(Q+2)}{4} 
4T + 14 = 7Q + 14
4T = 7Q
7Q = 2T = 4T; T=0=Q
SUFFICIENT

IMO C

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 2 variables (Q and T) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) We have 7Q = 2T from condition 1) and 4T + 14 = 7Q +14 or 7Q = 4T. Thus we have 2T = 7Q = 4T = 0 and T=Q=0. Since both conditions together yield a unique solution, they are sufficient. Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B. Condition 1) Q=2,T=7 and Q=4,T=14 are possible solutions. Since condition 1) does not yield a unique solution, it is not sufficient. Condition 2) Q=T=0 and Q=4,T=7 are possible solutions. Since condition 2) does not yield a unique solution, it is not sufficient. Therefore, C is the answer. Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

deepak.brijendra · Answer

This is possible when Q & T are infinite also.

If Q and T are integers, what is the value of Q?

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If Q and T are integers, what is the value of Q?

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