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# 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?  [#permalink]

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23 Jun 2016, 02:04
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62% (01:40) correct 38% (01:38) wrong based on 112 sessions

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

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

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

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Re: If Q and T are integers, what is the value of Q?  [#permalink]

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23 Jun 2016, 02:36
1
Bunuel wrote:
If Q and T are integers, what is the value of Q?

(1) Q = 2T/7.
(2) T+7/2 =7(Q+2)/4

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.

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Re: If Q and T are integers, what is the value of Q?  [#permalink]

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23 Jun 2016, 02:47
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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.
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Re: If Q and T are integers, what is the value of Q?  [#permalink]

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23 Jun 2016, 04:19
1
Bunuel wrote:
If Q and T are integers, what is the value of Q?

(1) Q = 2T/7.
(2) T+7/2 =7(Q+2)/4

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
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Re: If Q and T are integers, what is the value of Q?  [#permalink]

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19 Oct 2017, 20:19
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Re: If Q and T are integers, what is the value of Q? &nbs [#permalink] 19 Oct 2017, 20:19
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