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If a, b, and c are consecutive integers and a<b<c, is a an even number

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If a, b, and c are consecutive integers and a<b<c, is a an even number  [#permalink]

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New post 12 Jul 2018, 01:08
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[GMAT math practice question]

If \(a, b,\) and \(c\) are consecutive integers and \(a<b<c,\) is \(a\) an even number?

1) \(ac\) is a multiple of \(8\).
2) \(abc\) is a multiple of \(8\).

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Re: If a, b, and c are consecutive integers and a<b<c, is a an even number  [#permalink]

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New post 12 Jul 2018, 02:09
a,b and c are consecutive integers and a<b<c

= > b = a+1 and c = a+2

Statement 1

ac is a multiple of 8

=> a(a+2) is even

=> \(a^2 + 2a\) is even

=> \(a^2\) = even - 2a

=> \(a^2\) = even - even

=> a is even

Statement 1 sufficient

Statement 2

abc is even

=> \(a(a+1)(a+2)\) is even

=> \((a^2+a)(a+2)\) is even

=> \(a^3+3a^2+2a\) is even

=> \(a^3+3a^2\) is even

=> \(a^2(a+3)\) is even

=> a can be even or odd

Statement 2 is not sufficient

Hence option A
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Re: If a, b, and c are consecutive integers and a<b<c, is a an even number  [#permalink]

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New post 12 Jul 2018, 04:16
MathRevolution wrote:
[GMAT math practice question]

If \(a, b,\) and \(c\) are consecutive integers and \(a<b<c,\) is \(a\) an even number?

1) \(ac\) is a multiple of \(8\).
2) \(abc\) is a multiple of \(8\).



Given a,b,c are consecutive integers & a<b<c
Hence if a - odd, b - even & c - odd
or if a - even, b - odd & c - even

Question: is a an even number?


Statement 1: ac = 8k

Hence a*c has atleast three 2's. Therefore a has to be even number >=2

Statement 1 is Sufficient.


Statement 2: abc = 8k
if a - even then we know c is even & hence abc = 8k....we get YES
e.g. a = 2, b = 3, c = 4
if a - odd then we can have b as even with three 2's & hence abc = 8k....we get NO
e.g. a = 7, b =8, c = 9

Statement 2 is not sufficient


Answer A.



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Re: If a, b, and c are consecutive integers and a<b<c, is a an even number  [#permalink]

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New post 13 Jul 2018, 03:43
MathRevolution wrote:
[GMAT math practice question]

If \(a, b,\) and \(c\) are consecutive integers and \(a<b<c,\) is \(a\) an even number?

1) \(ac\) is a multiple of \(8\).
2) \(abc\) is a multiple of \(8\).


Case 1: \(a\), \(b\) and \(c\) are EVEN-ODD-EVEN
Case 2: \(a\), \(b\) and \(c\) are ODD-EVEN-ODD

Statement 1:
Here, Case 2 is not possible: if \(a\) and \(c\) are both odd, then \(ac\) will be odd and thus not a multiple of 8.
Since only Case 1 is possible, \(a\) must be even.
SUFFICIENT.

Statement 2:
Case 1 is possible if \(a\), \(b\) and \(c\) are 2, 3, and 4.
Case 2 is possible if \(a\), \(b\) and \(c\) are 7, 8, and 9.
Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.


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Re: If a, b, and c are consecutive integers and a<b<c, is a an even number  [#permalink]

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New post 15 Jul 2018, 18:12
=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The statement that a is an even integer is equivalent to the statement that ac is a multiple of 8: if a and c are two consecutive even integers, then one of them is a multiple of 4.
Thus, condition 1) is sufficient.

Condition 2)
If a = 2, b = 3, c = 4, then ac = 8, and the answer is “yes”.
If a = 7, b = 8, c = 9, then ac = 7*9, and the answer is “no”.
Since we don’t have a unique answer, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
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Re: If a, b, and c are consecutive integers and a<b<c, is a an even number &nbs [#permalink] 15 Jul 2018, 18:12
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