GRE® Quant Practice Q4

Quantitative Comparison | Remainder Theorem

The GRE maths sample Quantitative Comparison question given below is from the topic number properties. It tests the concept of Remainders.

Question 4: When a positive integer x is divided by 12, the remainder is 5.

Quantity A Quantity B
Remainder when 2x is divided by 12. Remainder when 3x is divided by 12.

  1. Quantity A is greater
  2. Quantity B is greater
  3. The two quantities are equal
  4. Cannot be determined

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Explanatory Answer | GRE Quantitative Comparison Question 4

Given Data

When x gets divided by 12, it leaves a remainder of 5.
Let q be the quotient.
So, \\frac{x}{12}) = q with a remainder of 5.
→ x = 12q + 5

Quantity 1: 2x = 2(12q + 5) → 2x = 24q + 10
Quantity 2: 3x = 3(12q + 5) → 3x = 36q + 15


Step 1 of solving this GRE question : Evaluate Quantity A

Remainder when 2x is divided by 12. i.e., remainder when 24q + 10 is divided by 12.

24 is divisible by 12. So, 24q is also divisible by 12.
Therefore, the remainder when 24q is divided by 12 is 'zero'.
So, the remainder when 24q + 10 is divided by 12 is the remainder when 10 is divided by 12.
Remainder when 10 is divided by 12 is 10.
Quantity A is 10.


Step 2 of solving this GRE question : Evaluate Quantity B

Remainder when 3x is divided by 12. i.e., remainder when 36q + 15 is divided by 12.

36 is divisible by 12. So, 36q is also divisible by 12.
Therefore, the remainder when 36q is divided by 12 is 'zero'.
So, the remainder when 36q + 15 is divided by 12 is the remainder when 15 is divided by 12.
Remainder when 15 is divided by 12 is 3.
Quantity B is 3.


Step 3 of solving this GRE question : The Comparison

Quantity A: Remainder when 2x is divided by 12 = 10
Quantity B: Remainder when 3x is divided by 12 = 3
Quantity A > Quantity B

Choice A is the correct answer



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