Hello,
For the question below, I derived that statement 1 is sufficient to show that x is a multiple of y, but am not sure how to think through statement 2. Any help would be much appreciated.
Thanks!
GMATPrep Q: NEed help with second statement
This topic has expert replies
- nandinitaneja
- Junior | Next Rank: 30 Posts
- Posts: 17
- Joined: Tue Feb 11, 2014 12:34 pm
-
- Master | Next Rank: 500 Posts
- Posts: 379
- Joined: Tue Sep 30, 2008 7:17 am
- Location: NY
- Thanked: 28 times
- Followed by:11 members
(1)
y(3y + 7) = x
-- since y times some integer** is x, it follows that x is a multiple of y.
(** we know that 3y + 7 is an integer, because y is an integer)
sufficient
(2)
x(x - 1) is a multiple of y
-- could mean any of 3 things:
possibility a) x is a multiple of y
possibility b) x - 1 is a multiple of y
possibility c) neither x nor x - 1 is a multiple of y, but together they contain all the prime factors of y (e.g., x = 3, x - 1 = 2, y = 6)
insufficient, because we don't know whether it's possibility (a) or not
ANS A.
y(3y + 7) = x
-- since y times some integer** is x, it follows that x is a multiple of y.
(** we know that 3y + 7 is an integer, because y is an integer)
sufficient
(2)
x(x - 1) is a multiple of y
-- could mean any of 3 things:
possibility a) x is a multiple of y
possibility b) x - 1 is a multiple of y
possibility c) neither x nor x - 1 is a multiple of y, but together they contain all the prime factors of y (e.g., x = 3, x - 1 = 2, y = 6)
insufficient, because we don't know whether it's possibility (a) or not
ANS A.
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: Is x a multiple of y?If x and y are integers greater than 1, is x a multiple of y?
(1) 3y² + 7y = x
(2) x² - x is a multiple of y
Asking whether x is a multiple of y is the same as asking whether x = (y)(some integer)
For example, 12 is a multiple of 3 because 12 = (3)(4)
So, let's rephrase the question as...
REPHRASED target question: Does x = (y)(some integer)?
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: 3y² + 7y = x
Factor to get x = y(3y + 7)
If y is an integer, then (3y + 7) must be an integer
In other words: x = y(some integer)
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: x² - x is a multiple of y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 4 and y = 2 (this satisfies statement 2 because x² - x = 12, and 12 is a multiple of 2). In this case, x IS a multiple of y
Case b: x = 5 and y = 2 (this satisfies statement 2 because x² - x = 20, and 20 is a multiple of 2). In this case, x is NOT a multiple of y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
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 nandinitaneja,
This DS question is a great "concept" question. With some Number Property knowledge and a bit of TESTing VALUES, you can get to the answer without doing too much work.
We're told that X and Y are both INTEGERS GREATER THAN 1. We're asked if X is a multiple of Y. This is a YES/NO question.
Fact 1: 3Y² + 7Y = X
There's a great Number Property rule that applies here: If a multiple of some number is added to another multiple of the same number, then the total will ALSO be a multiple of that original number.
For example...
4 is a multiple of 2
8 is a multiple of 2
So....4+8 = 12 is a multiple of 2
We know that Y is an INTEGER....
3Y² is a multiple of Y
7Y is a multiple of Y
So... 3Y² + 7Y is a multiple of Y
Since X = 3Y² + 7Y, we know that X MUST be a multiple of Y. The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
Fact 2: X² - X is a multiple of Y
Here, let's TEST Values....
If X = 4
4² - 4 = 12
12 is a multiple of Y, so Y could be 2, 3, 4 or 6
If Y = 2, then the answer to the question is YES
If Y = 3, then the answer to the question is NO
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This DS question is a great "concept" question. With some Number Property knowledge and a bit of TESTing VALUES, you can get to the answer without doing too much work.
We're told that X and Y are both INTEGERS GREATER THAN 1. We're asked if X is a multiple of Y. This is a YES/NO question.
Fact 1: 3Y² + 7Y = X
There's a great Number Property rule that applies here: If a multiple of some number is added to another multiple of the same number, then the total will ALSO be a multiple of that original number.
For example...
4 is a multiple of 2
8 is a multiple of 2
So....4+8 = 12 is a multiple of 2
We know that Y is an INTEGER....
3Y² is a multiple of Y
7Y is a multiple of Y
So... 3Y² + 7Y is a multiple of Y
Since X = 3Y² + 7Y, we know that X MUST be a multiple of Y. The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
Fact 2: X² - X is a multiple of Y
Here, let's TEST Values....
If X = 4
4² - 4 = 12
12 is a multiple of Y, so Y could be 2, 3, 4 or 6
If Y = 2, then the answer to the question is YES
If Y = 3, then the answer to the question is NO
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
- Jim@StratusPrep
- MBA Admissions Consultant
- Posts: 2279
- Joined: Fri Nov 11, 2011 7:51 am
- Location: New York
- Thanked: 660 times
- Followed by:266 members
- GMAT Score:770
I like to think of these as a fraction. This means that
(x^2 - x)/y is an integer.
Factoring you get this:
x(x-1)/y is an integer
You could plug numbers here, but generally speaking y could divide into x which would give you a 'yes' or y could divide into x-1 which would give you a 'no'
(x^2 - x)/y is an integer.
Factoring you get this:
x(x-1)/y is an integer
You could plug numbers here, but generally speaking y could divide into x which would give you a 'yes' or y could divide into x-1 which would give you a 'no'
GMAT Answers provides a world class adaptive learning platform.
-- Push button course navigation to simplify planning
-- Daily assignments to fit your exam timeline
-- Organized review that is tailored based on your abiility
-- 1,000s of unique GMAT questions
-- 100s of handwritten 'digital flip books' for OG questions
-- 100% Free Trial and less than $20 per month after.
-- Free GMAT Quantitative Review
-- Push button course navigation to simplify planning
-- Daily assignments to fit your exam timeline
-- Organized review that is tailored based on your abiility
-- 1,000s of unique GMAT questions
-- 100s of handwritten 'digital flip books' for OG questions
-- 100% Free Trial and less than $20 per month after.
-- Free GMAT Quantitative Review