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What is the median of 3 consecutive integers?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the median of 3 consecutive integers?  [#permalink]

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28 May 2018, 00:07
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Difficulty:

45% (medium)

Question Stats:

71% (01:21) correct 29% (01:26) wrong based on 98 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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28 May 2018, 01:04
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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30 May 2018, 00:23
=>

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.

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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31 May 2018, 15:20
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.

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Joined: 18 Apr 2018
Posts: 98
Re: What is the median of 3 consecutive integers?  [#permalink]

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30 Jun 2018, 07:47
MathRevolution wrote:
=>

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.

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.

Hi I really love your variable approach to DS questions however I have a question about your explanation. Is it right to always assume that consecutive integers always mean numbers with a different of 1 e.g 1,2,3. Can't it mean 2,4,8 as well on DS questions?

Also, if it were that this question was asking for the 1st consecutive integer in the sequence, would E be the right answer?

Also, In condition 1
(N+1)(n) (n-1) = 0 will always give N=0 Couldnt this make Come 1 sufficient?

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Intern
Joined: 08 Oct 2017
Posts: 25
Re: What is the median of 3 consecutive integers?  [#permalink]

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30 Jun 2018, 08:07
Analyze statement 1) The product of the integers is 0 - one of the digit has to be 0 - possible sets are
(0,1,2)
(-1,0,1)
(-2,-1,0)
We can't tell what is median for sure.

2) The sum of the integers is equal to their product
possible sets
(1,2,3), (-1,0,1)...
Still cant tell medium for sure...

Now use statement 1 and statement 2 together.... Set will be
(-1, 0, 1) --- Product of all = 0, Sum of numbers = Product of numbers

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

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30 Jun 2018, 08:38
1
Kem12 wrote:
Hi I really love your variable approach to DS questions however I have a question about your explanation. Is it right to always assume that consecutive integers always mean numbers with a different of 1 e.g 1,2,3. Can't it mean 2,4,8 as well on DS questions?

Also, if it were that this question was asking for the 1st consecutive integer in the sequence, would E be the right answer?

Also, In condition 1
(N+1)(n) (n-1) = 0 will always give N=0 Couldnt this make Come 1 sufficient?

Posted from my mobile device

Hy.. consecutive integers means difference of 1.. consecutive integers will always be like -2,-1,0,1,2....

2,4,8 are consecutive even integers and not consecutive integers..

Also since we were able to find the complete set of three integers, we can easily find the first integer.

You said (n+1)(n)(n-1)=0 will always give n=0

even when n= 1 this equation is true and even with n=-1 this equation is true. So 1 is not sufficient.
Manager
Joined: 18 Apr 2018
Posts: 98
Re: What is the median of 3 consecutive integers?  [#permalink]

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30 Jun 2018, 08:43
Antreev wrote:
Kem12 wrote:
Hi I really love your variable approach to DS questions however I have a question about your explanation. Is it right to always assume that consecutive integers always mean numbers with a different of 1 e.g 1,2,3. Can't it mean 2,4,8 as well on DS questions?

Also, if it were that this question was asking for the 1st consecutive integer in the sequence, would E be the right answer?

Also, In condition 1
(N+1)(n) (n-1) = 0 will always give N=0 Couldnt this make Come 1 sufficient?

Posted from my mobile device

Hy.. consecutive integers means difference of 1.. consecutive integers will always be like -2,-1,0,1,2....

2,4,8 are consecutive even integers and not consecutive integers..

Also since we were able to find the complete set of three integers, we can easily find the first integer.

You said (n+1)(n)(n-1)=0 will always give n=0

even when n= 1 this equation is true and even with n=-1 this equation is true. So 1 is not sufficient.

Thanks so much, brilliant explanation. Totally cleared my doubts.
Re: What is the median of 3 consecutive integers? &nbs [#permalink] 30 Jun 2018, 08:43
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