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GMAT Quant Strategy: Plugging In
he easiest way to solve quant questions is often by plugging in numbers. This is particularly true of questions that include the words “must be”.
Look at the following example from The Economist GMAT Tutor's question bank:
If x and y are positive integers, and (4x)/(3y) is an integer, which of the following must be true?
I) x is a multiple of 4
II) y is a multiple of 3
III) x·y is a multiple of 3
A) I only
B) II only
C) III only
D) I and II only
E) I, II and III
You must plug in numbers that make (4x)/(3y) an integer. The obvious thing to do is to make x = 3 and y = 4. You immediately know that statements I and II do not have to be true. Therefore, C is the only possible answer.
However, let’s imagine the question was more difficult and had a “none of the above” option. What would happen now?
We would have to prove that statement III must be true. It is useful to consider how we would do that.
An important rule to remember is that if a fraction is an integer, each element of the denominator must be present in the numerator. This means that, in this case, the numerator must be divisible by 3, and by y. We can make the following conclusions:
In this way we have proved that statement III must be true.
An important thing to remember from this question is that plugging in numbers can get you to the right answer very quickly. Secondly, for a fraction to be an integer, the numerator must be divisible by each element of the denominator.
Originally posted in Economist GMAT Blog
he easiest way to solve quant questions is often by plugging in numbers. This is particularly true of questions that include the words “must be”.
Look at the following example from The Economist GMAT Tutor's question bank:
If x and y are positive integers, and (4x)/(3y) is an integer, which of the following must be true?
I) x is a multiple of 4
II) y is a multiple of 3
III) x·y is a multiple of 3
A) I only
B) II only
C) III only
D) I and II only
E) I, II and III
You must plug in numbers that make (4x)/(3y) an integer. The obvious thing to do is to make x = 3 and y = 4. You immediately know that statements I and II do not have to be true. Therefore, C is the only possible answer.
However, let’s imagine the question was more difficult and had a “none of the above” option. What would happen now?
We would have to prove that statement III must be true. It is useful to consider how we would do that.
An important rule to remember is that if a fraction is an integer, each element of the denominator must be present in the numerator. This means that, in this case, the numerator must be divisible by 3, and by y. We can make the following conclusions:
- 4x is divisible by 3 and by y.
- 4 is not divisible by 3. Therefore, x is.
- If x is divisible by 3, x·y is also divisible by 3.
In this way we have proved that statement III must be true.
An important thing to remember from this question is that plugging in numbers can get you to the right answer very quickly. Secondly, for a fraction to be an integer, the numerator must be divisible by each element of the denominator.
Originally posted in Economist GMAT Blog
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