Is y a multiple of 15?

Hi 282552,

DS questions often include a 'test of your thoroughness' - in real simple terms, "do you see more than just the obvious possibilities?"

Here, we're asked if Y is a multiple of 15. This is a YES/NO question. Before you begin working on the two Facts, ask yourself this:

"Do we know ANYTHING about the value of Y?"

Starting off, the answer is NO - there are NO restrictions on the value of Y.... So Y could be positive, negative, zero, a fraction, a square root, some crazy repeating decimal, etc. Most Test Takers only think about the 'obvious' possibilities (positive integers), but you MUST consider the alternatives if you want to make sure that you're choosing the correct answer.

In Fact 1, we're told that Y^2 is a multiple of 15, but that does NOT mean that Y is a multiple of 15. Be thorough with your thinking, look for alternatives, ask yourself if there's anything else that's possible....and you'd be surprised how easy it can be to find those other possibilities.

GMAT assassins aren't born, they're made,
Rich

ques asks
is y =0,15,30,etc

statement 1: y*y=0,15,...15*15...
no when 15
yes when 15*15

statement 2: sqrt y=0,15...
yes always

B is sufficient

You must provide the OA from the beginning.
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Test It

Statement 1 - Y = 15 ....yes
Y is equal to Sqrt15------No insufficient

Statement 2 Sqrt of Y is a multiple of 15, that means that the prime factors of Y contain the prime factors of 15
Sufficient

1. y^2 is a multiple of 15

let y^2= 30= 15*2

y= \sqrt{15*2} which is definitely not a multiple of 15

let y^2= 225= 15*15

then y= \sqrt{225} = 15 (multiple of 15)

hence this statement is not sufficient

2. \sqrt{y} is a multiple of 15

let \sqrt{y}= 30

then y= 30^2= 15^2 * 2^2

this is definitely a multiple of 15

Hence second statement is sufficient.

Answer B

since we are not explicitly told that y must be an integer, 1 is insufficient, because y might be sqrt(15), which is not a multiple of 15.

statement 2 alone says that sqrt(y)=multiple of 15. so y must be a multiple of 15 as well.

(1) y^2 is a multiple of 15
what is y= 15 ^1/2. In this case y is not a multiple of 15 but y^2 is.

(2) The square root of y is a multiple of 15.
let's say square root of y = 15 (minimum value)
so y = 225 (minimum value)

All values >15 with y^1/2 being multiple of 15, y will be multiple of 15

B is the answer
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Statement 1: INSUFFICIENT
Y square= 0, 15, 30
So, Y= 0, Square Root 15, Square Root 30.
Here 0 is a multiple of 15 but
Square Root 15 is NOT a multiple of 15.

Statement 2: Sufficient
SQRT (Y) = O, 15,30,.....15xp
So Y =0,15^2,(2x15)^2..(15xp)^2
So y is always a multiple of 15.

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