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y is an integer. What is the smallest possible value of y?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Nov 11, 2016 6:23 am
NandishSS wrote:y is an integer. What is the least possible value of y?

(1) y is negative.

(2) |y| < 10
Target question: What is the least possible value of y?

Given: y is an integer

Statement 1: y is negative
Since negative values go on indefinitely, there's no way to identify the smallest value of y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |y| < 10
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then -k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

So, from rule #1, we can write: -10 < y < 10
Since we're told that y is an integer, the least possible value of y is -9
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

RELATED VIDEO
- Inequalities and absolute value: https://www.gmatprepnow.com/module/gmat ... /video/985
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by Jay@ManhattanReview » Thu Jan 05, 2017 10:36 pm
NandishSS wrote:y is an integer. What is the smallest possible value of y?

(1) y is negative.

(2) |y| < 10
We need the smallest possible value of y.

It is clear that statement 1 itself is not sufficient as y may have any value under the Sun.

Statement 2: |y| < 10 => -10 < y < 10.

Since y is an integer, the smallest value of y = -9 and the largest value = 9. Sufficient.

Statement 1 is deliberately put to distract you. There is no need of it. Set of y: {-9, -8, -7, ..., 7, 8, 9}. The smallest value among these is -9.

Answer: B

Hope this helps!

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by melguy » Tue Jan 10, 2017 8:07 am
Statement 1

Clearly insufficient.

Statement 2

|y| < 10 means y < 10 and y > -10

-10 < y < 10 (Therefore -9 is the smallest value).

Sufficient

Answer B
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by Danny@GMATAcademy » Tue Jan 10, 2017 8:53 am
Absolute value can be thought of as 'distance from zero.' Statement number 2 is saying that y is less than 10 away from zero.

This means that if we were to draw the possible values of y on the number line, we'd get a closed segment (it wouldn't continue forever in either direction).

A closed segment for possible values will have a lowest possible value. So statement two is sufficient. No calculation necessary.
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by [email protected] » Tue Jan 10, 2017 2:55 pm
Hi NandishSS,

In this prompt, we're told that Y is an INTEGER. We're asked for the smallest possible value of Y.

1) Y is negative.

This Fact doesn't provide much additional information. Y could potentially be ANY negative integer, but we don't know the smallest possible value.
Fact 1 is INSUFFICIENT.

2) |Y| < 10

Since we know that Y is an integer, this Fact limits the range of possible values (every integer value from -9 to +9, inclusive). Thus, we now know the smallest possible value for Y is -9.
Fact 2 is SUFFICIENT.

Final Answer: B

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