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Nine Consecutive Integers

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Nine Consecutive Integers

by carlos.lara.7 » Thu Sep 15, 2016 4:06 pm
Is the smallest of nine consecutive integers an even number?

(1) The product of the integers is even. (2) The sum of the integers is zero.

A - statement (1), BY ITSELF is sufficient to answer the question but statement (2) by itself is not sufficient to answer the question

B - statement (2), BY ITSELF is sufficient to answer the question but statement (1) by itself is not sufficient to answer the question

C - BOTH statement (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement BY ITSELF is sufficient to answer the question

D - EACH statement BY ITSELF is sufficient to answer the question

E - the two statements, even when taken TOGETHER, are NOT sufficient to answer the question
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by [email protected] » Thu Sep 15, 2016 4:47 pm
Hi carlos.lara.7,

This question is based on a couple of Number Properties. We're told that we're dealing with 9 CONSECUTIVE INTEGERS. We're asked if the smallest of the integers is even. This is a YES/NO question.

1) The product of the integers is even.

For the product of a group of integers to be even, at least one of the integers MUST be even.

IF the integers are....
1, 2, 3, 4, 5, 6, 7, 8, 9
Then the answer to the question is 1

IF the integers are....
0, 1, 2, 3, 4, 5, 6, 7, 8
Then the answer to the question is 0
Fact 1 is INSUFFICIENT

2) The sum of the integers is zero.

For the SUM of a group of consecutive integers to be 0, the integers must be "balanced around" the number 0. Since we're dealing with 9 consecutive integers, they MUST be...

-4, -3, -2, -1, 0, 1, 2, 3, 4
and the answer to the question is -4
Fact 2 is SUFFICIENT

Final Answer: B

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by Matt@VeritasPrep » Fri Sep 16, 2016 1:46 pm
S1:

This is a totally worthless statement! Any time you have even TWO consecutive integers, one of them will be even, which will force the product to be even. So this doesn't tell us anything we didn't already know: as soon as we know we have NINE consecutive integers, the product must be even.

Since S1 does nothing, the answer is B or E.

S2:

Let's call the integers x, x + 1, x + 2, ..., x + 8.

Their sum would be x + (x + 1) + ... + (x + 8), or 9x + 36. If 9x + 36 = 0, x = -4. Sufficient! So B.
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by Jay@ManhattanReview » Tue Dec 20, 2016 5:57 am
carlos.lara.7 wrote:Is the smallest of nine consecutive integers an even number?

(1) The product of the integers is even.

(2) The sum of the integers is zero.
We have to deduce whether the smallest of nine consecutive integers is an even number. We need a unique answer: either YES or NO.

S1: The product of few integers is even if at least ONE integer is even.

Case 1: If the consecutive nine integers start from an ODD integer, the next one would be an EVEN integer, making the product EVEN. Smallest integer is ODD. Still, there could be many cases within Case 1, we cannot get the unique value of the smallest consecutive integer.

Case 2: If the consecutive nine integers start from an EVEN integer, making the product EVEN. Smallest integer is EVEN. As with Case 1, there could be many cases within Case 2, we cannot get the unique value of the smallest consecutive integer.

No unique value. Insufficient!

S2: We are given that the sum of the integers is zero.

Since the number of consecutive integers is ODD (9), there must be an integer that is 0; and to keep the sum = 0, the sum of integers greater than 0 must be equal the sum of integers less than 0.

So the nine consecutive integers would be: {-4, -3, -2, -1, 0, 1, 2, 3, 4}.

The smallest of these = -4. A unique answer. Sufficient!

OA: B

-Jay

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by Scott@TargetTestPrep » Tue Jan 03, 2017 4:24 pm
carlos.lara.7 wrote:Is the smallest of nine consecutive integers an even number?

(1) The product of the integers is even.

(2) The sum of the integers is zero.
We have a set of 9 consecutive integers and must determine whether the first integer is an even number.

Statement One Alone:

The product of the integers is even.

We know that the product of a set of integers is even if one of the integers is even. Since there are 9 consecutive integers, at least one of them will be even. Thus, the product of these 9 integers will always be even regardless of whether the first integer is odd or even.

For instance, the set could be 1 to 8, inclusive, in which the first number is odd, or 2 to 9, inclusive, in which the first number is even. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The sum of the integers is zero.

Since we have a set of consecutive integers, in order for the sum to equal zero, we need to have 4 numbers below zero, 4 numbers above zero, and one number equal to zero. Thus, the only possible numbers are:

-4, -3, -2, -1, 0, 1, 2, 3, 4

We see that the smallest number is -4, which is even. Statement two alone is sufficient.

Answer: B

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