Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer

Question

Is x an integer ?
 
(1) 2x + 1 is an integer
(2) 5x – 1 is an integer

Luckisnoexcuse · Answer

(1) x = 1/2 or 1
not sufficient

(2) x=1/5 or 1
not sufficient

on combining
only integer value of x satisfies
C

pushpitkc · Answer

1. 2x + 1 is an integer
x can be 1 or  \frac{1}{2} . In both the cases, 2x + 1 is an integer, 
but x=1 is an integer but x =  \frac{1}{2}  is not an integer. Insufficient
2. 5x – 1 is an integer
x can be 1 or  \frac{1}{5} . In both the cases, 5x - 1 is an integer, 
but x=1 is an integer but x =  \frac{1}{5}  is not an integer. Insufficient

On combining the information from both the statements,
x has to be an integer (Sufficient) (Option C)

Arsh4MBA · Answer

Hello  pushpitkc  , I understand combining 1 & 2 helps to conclude if its an integer or not ?
But how are we sure its an integer. Can you throw some light?

pushpitkc · Answer

Hi  Arsh4MBA ,

On combining the information on both the statements,
the only option when both the expression 2x + 1 and 5x - 1 are integers is when x is an integer

If x is a fraction, the fraction has to have both 2 and 5 in its denominator.
The minimum such value of x is  \frac{1}{(2*5)} , but neither of the expressions will yield an integer

Hope that helps!

Arsh4MBA · Answer

Yes It helps. Thanks a lot !!

MooneeyTunes · Answer

On combining; I added the 2 equations, which gave me 7x = int. In this case x can be an integer or can be 1/7 as well? Not sure, where I made a mistake. Can someone please explain?

Mo2men · Answer

When you added the 2 equations, you CONCLUDED mistakenly that x could be integer or fraction. But you need to do so in light of the original 2 equations. Let's see how.

7x =Integer ........Let's see if x =1/7

Does it make both statements correct if x=1/7..........Answer is No......So x is not fraction. it is Only integer.

Let me offer another way:
Multiply statement 1 by 2: 4x+2=Integer.

Subtract statesmen 1 from modified of statement 1

5x - 1= Integer
4x + 4 = Integer
................................Subtract

x - 5 = Integer ..........x =integer........So we isolated definitive answer of x.

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 1 variable: Let the original condition in a DS question contain 1 variable. Now, 1 variable would generally require 1 equation for us to be able to solve for the value of the variable. We know that each condition would usually give us an equation and Since we need 1 equation to match the numbers of variables and equations in the original condition, the logical answer is D. The answer could be A, B, or D, but the default answer will be D.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find whether 'x' is an integer.

Second and the third step of Variable Approach: From the original condition, we have 1 variable (x).To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Let’s take a look at each condition.

Condition(1) tells us that 2x + 1 is an integer.

=> For x = 1: 2(1) + 1 = 3[integer] - is 'x' an integer - YES

=> For x = \(\frac{1}{2}\): 2(\(\frac{1}{2}\)) + 1 = 2[integer] - is 'x' an integer - NO

Since the answer is not unique YES or NO, condition(1) is notsufficient by CMT 1.

Condition(2) tells us that 5x -1 is an integer.

=> For x = 1: 5(1) - 1 = 4[integer] - is 'x' an integer - YES

=> For x = \(\frac{1}{5}\): 5(\(\frac{1}{5}\)) - 1 = 0[integer] - is 'x' an integer - NO

Since the answer is not unique YES or NO, condition(2) is not sufficient by CMT 1.

Let’s take a look at both conditions together.

=> from condition (1) and (2) we will have x = integer values satisfying both.

Since the answer will be unique YES , both conditions together are sufficient by CMT 1.

So, C is the correct answer.

Answer: C

Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer

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GMAT Data Sufficiency (DS) Questions

Is x an integer ? (1) 2x + 1 is an integer (2) 5x – 1 is an integer

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards