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If x is an integer such that 79 < x < 86, what is the value of x?

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by BTGmoderatorDC » Mon Jan 27, 2020 5:30 pm
If x is an integer such that 79 < x < 86, what is the value of x?

I. If x were divided by 4, the remainder would be 1
II. If x - 1 were divided by 3, the remainder would be 2



OA C

Source: e-GMAT
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Re: If x is an integer such that 79 < x < 86, what is the value of x?

by Jay@ManhattanReview » Mon Jan 27, 2020 9:49 pm
BTGmoderatorDC wrote: ↑
Mon Jan 27, 2020 5:30 pm
 If x is an integer such that 79 < x < 86, what is the value of x?

I. If x were divided by 4, the remainder would be 1
II. If x - 1 were divided by 3, the remainder would be 2

OA C

Source: e-GMAT
Given that 79 < x < 86, x is one among 80, 81, 82, 83, 84 and 85.

Let's take each statement one by one.

I. If x were divided by 4, the remainder would be 1.

x can be 81 or 85. No unique value of x. Insufficient.

II. If x – 1 were divided by 3, the remainder would be 2.

Given that x is one among 80, 81, 82, 83, 84 and 85, (x – 1) would be one among 79, 80, 81, 82, 83, and 84. Since (x – 1) when divided by 3 leaves the remainder 2, (x – 1) can be either 80 or 83. Thus, x can be 81 or 84. No unique value of x. Insufficient.

(1) and (2) together

Only one value of x is common in both statements, and i.e. x = 81. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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