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If t and x are integers, what is the value of x?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sun May 21, 2017 8:43 am
NandishSS wrote:If t and x are integers, what is the value of x?

(1) x²/t² = 4/9

(2) x > 0 and t > 0
Target question: What is the value of x?

Given: t and x are integers

Statement 1: x²/t² = 4/9
Let's TEST some values.
There are several values of x and t that satisfy statement 1. Here are two:
Case a: x = 2 and t = 3. Notice that x²/t² = 2²/3² = 4/9. In this case x = 2
Case b: x = 20 and t = 30. Notice that x²/t² = 20²/30² = 400/900 = 4/9. In this case x = 20
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > 0 and t > 0
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of x and t that satisfy BOTH statements. Here are two:
Case a: x = 2 and t = 3. Notice that x²/t² = 2²/3² = 4/9. In this case x = 2
Case b: x = 20 and t = 30. Notice that x²/t² = 20²/30² = 400/900 = 4/9. In this case x = 20
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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by [email protected] » Sun May 21, 2017 10:30 am
Hi NandishSS,

This DS question is ultimately testing the 'thoroughness' of your thinking (as the math behind this question isn't that complex). You can solve it by TESTing VALUES.

We're told that T and X are INTEGERS. We're asked for the value of X.

1) (X^2)/(T^2) = 4/9

With Fact 1, you might immediately see that X and T could be positive OR negative.

IF... X = 2, T = 3 then the answer to the question is 2
IF... X = -2, T = -3 then the answer to the question is -2
Fact 1 is INSUFFICIENT

2) X > 0 and T > 0

This Fact tells us nothing about the specific values of either variable.
Fact 2 is INSUFFICIENT

Combined, you might be tempted to assume that X = 2, Y = 3 is the "only" option... but you have to remember that fractions can be reduced... so are 2 and 3 really the "only" pair of values that will fit that equation? If we multiplied both the numerators and denominators of the two fractions by the same perfect square, then we could "reduce" that perfect square out....

For example...
(X^2)/(T^2) = 4/9 = 16/36
X = 4, T = 9 and the answer to the question is 4

We now have two different values of X.
Combined, INSUFFICIENT

Final Answer: E

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by GMATGuruNY » Sun May 21, 2017 10:42 am
NandishSS wrote:If t and x are integers, what is the value of x?

(1) x^2/t^2 = 4/9

(2) x>0 and t>0
Statement 1: x²/t² = 4/9
Since the question stem asks for the value of x, ISOLATE X:
x² = (4/9)t²
x = ±(2/3)t.

Case 1: t=3
Here, it's possible that x = (2/3)(3) = 2.
Case 2: t=6
Here, it's possible that x = (2/3)(6) = 4.
Since x can be different values, INSUFFICIENT.

Cases 1 and 2 satisfy BOTH STATEMENTS.
Since each case yields a different possible value for x, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by ceilidh.erickson » Sun May 21, 2017 3:37 pm
NandishSS wrote:If t and x are integers, what is the value of x?

(1) x^2/t^2 = 4/9

(2) x>0 and t>0

OA:E

Source:GMATPrep EP1
If you found yourself thinking, "wait, how is it not x =2 and y = 3???" then you were falling for a trap: not considering other possibilities.

Here's a good general rule: if there is one easy, obvious solution that comes to mind - that 6th grader would easily have come up with - there's probably something more complicated going on. Be skeptical, and push to find other solutions.

On the GMAT, if it feels too easy... it probably is!
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by Jeff@TargetTestPrep » Fri May 26, 2017 10:44 am
NandishSS wrote:If t and x are integers, what is the value of x?

(1) x^2/t^2 = 4/9

(2) x>0 and t>0
We are given that t and x are integers and need to determine the value of x.

Statement One Alone:

(x^2)/(t^2) = 4/9

Taking the square root of both sides of the equation, we have:

x/t = |2|/|3|

Cross multiplying, we have:

|3|x = |2|t

We see that we do not have enough information to determine x. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x>0 and t>0

Since the information in statement two does not provide any information regarding the value of x, statement two is not sufficient to answer the question.

Statements One and Two Together:

Using the information in statements one and two, we do not have enough information to answer the question. For example, x = 2 and t = 3, or x = 4 and t = 6.

Answer: E
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