y is an integer. What is the smallest possible value of y?
(1) y is negative.
(2) |y| < 10
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
y is an integer. What is the smallest possible value of y?
This topic has expert replies
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: What is the least possible value of y?NandishSS wrote:y is an integer. What is the least possible value of y?
(1) y is negative.
(2) |y| < 10
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
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
We need the smallest possible value of y.NandishSS wrote:y is an integer. What is the smallest possible value of y?
(1) y is negative.
(2) |y| < 10
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!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Beijing | Auckland | Milan | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
-
melguy
- Master | Next Rank: 500 Posts
- Posts: 335
- Joined: Mon Mar 21, 2011 11:31 pm
- Location: Australia / India
- Thanked: 37 times
- Followed by:2 members
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
Clearly insufficient.
Statement 2
|y| < 10 means y < 10 and y > -10
-10 < y < 10 (Therefore -9 is the smallest value).
Sufficient
Answer B
-
Danny@GMATAcademy
- Junior | Next Rank: 30 Posts
- Posts: 23
- Joined: Tue Jun 28, 2016 6:39 am
- Thanked: 8 times
- Followed by:3 members
- GMAT Score:780
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.
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.
Email: [email protected]
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
