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

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

(1) x^2/t^2 = 4/9 --> take the square root: \(|\frac{x}{t}|=\frac{2}{3}\) --> x is a multiple of 2 and t is a multiple of 3. Not sufficient.

(2) x > 0 and t > 0. Clearly not sufficient.


(1)+(2) Since from (2) both x and t are positive then from (1) \(\frac{x}{t}=\frac{2}{3}\): x is a positive multiple of 2 and t is a positive multiple of 3. Not sufficient.

Answer: E.

Hope it's clear.
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From \(|\frac{x}{t}|=\frac{2}{3}\) we can have x=+/-2 and y=+/-3, OR x=+/-4 and y=+/-6, OR x=+/-6 and y=+/-9, ...
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Thanks. Great explanation.

Hi Bunuel,

Could you please tell that how x and t will be multiple of 2 and 3.

If x^2 = 4 then x can be +-2 whereas y^2 =+-3

I am not able to figure out how x will be multiple 2. Pls help

Thank you for your help and quick response. I deleted my post as I did figure out about the multiples before your reply. X and t are in ratio rather than values. This is the mistake I made.

Thank you

Statement 1: [m]\frac{x^2}{t^2} = \frac{4}{9}
Hence x/t = 2/3 or -2/3
We cannot deduce the value of x.
INSUFFICIENT

Statement 2: x>0 and t>0
clearly INSUFFICIENT

Combining both statements:
We know that x/t = 2/3
Still we cannot find the value of x.
INSUFFICIENT

Correct Option: E

Is X not equal to 2 because it is in the fraction 2/3? I'm having a hard time wrapping my head around why x does not equal 2 and y does not equal 3.

(1)+(2) Since from (2) both x and t are positive then from (1) \(\frac{x}{t}=\frac{2}{3}\): x is a positive multiple of 2 and y is a positive multiple of 3. We can have x=+/-2 and y=+/-3, OR x=+/-4 and y=+/-6, OR x=+/-6 and y=+/-9, ... Not sufficient.
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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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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.


Since we have 2 variables (t and x) and 0 equations, C is most likely to be the answer and so we should consider 1) & 2) first.

Conditions 1) and 2):

We have a bunch of cases satisfying both conditions together.
x = 2, t = 3
x = 4, t = 6

Thus both conditions together are not sufficient.

Therefore, E is the answer.

Normally, in problems which require 2 or more additional 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.

During the GMATPREP practice exam, I thought this problem was easy and chose "C", thinking the answer is x = 2.

How am I supposed to tell that we're looking for multiples? Where does it hint that?

The question asks to find the value of x.

At the end we get that \(\frac{x}{t}=\frac{2}{3}\). The ratio is not enough to determine single numerical value of x: it could be 2, 4, 6, ...
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Hello Bunuel, I don't seem to understand why the answer is not C because x/t = 2/3

A similar question below in which the official answer is D rather than B
What is the value of w^(−2)?

(1) w^(−1) = 1/2
(2) w^3 = 8

Please help me with my confusion

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

Cheers,
Brent

The algebraic approach was fastest on this one:

Statement 1.
\(\frac{x^2}{t^2}= \frac{4}{9}\)

if x> 0 and t>0 then one result could be \(\frac{x}{t} = \frac{2}{3}\)
but we don't know know the signs so we could have\(\frac{x}{t} = \frac{2}{-3}\)or \(\frac{-2}{3}\) or a bunch of other solutions

Statement 2.
x> 0 t>0
Insufficient as we aren't told anything about the value of x, specifically.

Combined
A lot of people, including myself, fell for the trap that \(\frac{x}{t} = \frac{2}{3}\) and that x must be 2

This is incorrect.

Lets work with x>0 and t>0

\(\frac{x^2}{t^2} = \frac{4}{9}\)
\(9x^2 = 4t^2\)
\(x^2 = \frac{4t^2}{9}\)x = \(\sqrt{\frac{4t^2}{9}}\)
\(x = \frac{2t}{3}\)

We do not know what t is, therefore we CANNOT conclude a value for x

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