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

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If t and x are integers, what is the value of x? [#permalink]

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

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

(2) x>0 and t>0
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Apr 2017, 06:32, edited 3 times in total.
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Re: If t and x are integers, what is the value of x? [#permalink]

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New post 07 Apr 2016, 09:14
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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 y 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 y is a positive multiple of 3. Not sufficient.

Answer: E.

Hope it's clear.
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Re: If t and x are integers, what is the value of x? [#permalink]

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New post 07 Apr 2016, 09:33
Bunuel wrote:
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 y 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 y is a positive multiple of 3. Not sufficient.

Answer: E.

Hope it's clear.


Thanks. Great explanation.

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

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New post 15 Apr 2016, 01:30
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

Bunuel wrote:
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 y 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 y is a positive multiple of 3. Not sufficient.

Answer: E.

Hope it's clear.

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

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New post 15 Apr 2016, 01:43
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prateek720 wrote:
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

Bunuel wrote:
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 y 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 y is a positive multiple of 3. Not sufficient.

Answer: E.

Hope it's clear.


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

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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

Bunuel wrote:
prateek720 wrote:
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

Bunuel wrote:
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 y 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 y is a positive multiple of 3. Not sufficient.

Answer: E.

Hope it's clear.


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

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New post 15 May 2016, 23:06
TurgCorp wrote:
If t and x are integers, what is the value of x?

(1) \(\frac{x^2}{t^2} = \frac{4}{9}\)
(2) x>0 and t>0


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

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

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New post 12 Jun 2017, 10:42
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.

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

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New post 12 Jun 2017, 12:39
Nathanlambson wrote:
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 14 Dec 2017, 16:56
surupab wrote:
If t and x are integers, what is the value of x?

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

(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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Re: If t and x are integers, what is the value of x? [#permalink]

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New post 16 Dec 2017, 23:26
surupab wrote:
If t and x are integers, what is the value of x?

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

(2) x>0 and t>0



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.
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Re: If t and x are integers, what is the value of x?   [#permalink] 16 Dec 2017, 23:26
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