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What is the median of 3 consecutive integers?

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Math Revolution GMAT Instructor
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What is the median of 3 consecutive integers? [#permalink]

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New post 28 May 2018, 01:07
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (00:47) correct 39% (00:54) wrong based on 57 sessions

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[GMAT math practice question]

What is the median of 3 consecutive integers?

1) The product of the integers is 0
2) The sum of the integers is equal to their product

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Re: What is the median of 3 consecutive integers? [#permalink]

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New post 28 May 2018, 02:04
From option A, we will get (-1,0,1), (-2,-1,0),(0,1,2) from option B, we will get (-1,0,1),(1,2,3),(-3,-2,-1). Combining A and B we will get only one option i.e. - 1,0,1

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Re: What is the median of 3 consecutive integers? [#permalink]

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New post 30 May 2018, 01:23
=>

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.

Let the 3 consecutive integers be n – 1, n and n + 1.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on its own first.

Condition 1)
Since the product of the three integers is 0, one of the integers must be 0. There are three possible lists of consecutive integers:
( -2, -1, 0 ), ( -1, 0, 1) and ( 0, 1, 2 ).
The medians of these lists are -1, 0 and 1.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
Since the sum of the integers is equal to their product, there are three possible lists of consecutive integers:
(-3, -2, -1), ( -1, 0, 1) and ( 1, 2, 3).
The medians of these lists are -2, 0 and 2.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
(-1, 0, 1) is the unique list of three consecutive integers that satisfies both conditions 1) & 2).
Both conditions together are sufficient.

Therefore, C is the answer.

Answer: C

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: What is the median of 3 consecutive integers? [#permalink]

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New post 31 May 2018, 16:20
MathRevolution wrote:
[GMAT math practice question]

What is the median of 3 consecutive integers?

1) The product of the integers is 0
2) The sum of the integers is equal to their product


We need to determine the median of 3 consecutive integers, which will be the integer in the middle of the 3 integers.

Statement One Alone:

The product of the integers is 0.

All we know is that 0 is one of the integers; however, we cannot determine the median since the three integers could be {0, 1, 2} or {-2, -1, 0}. Statement one alone is not sufficient.

Statement Two Alone:

The sum of the integers is equal to their product.

If the sum of 3 consecutive integers is equal to their product, then the three integers can only be one of the following 3 sets: {-3, -2, -1}, {-1, 0, 1} and {1, 2, 3}. . Since we we have more than one possible set, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using our two statements we see that the only set of three consecutive integers possible is {-1, 0, 1}.So the median is zero.

Answer: C
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Re: What is the median of 3 consecutive integers?   [#permalink] 31 May 2018, 16:20
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