what is the value of xy? 1) y is the smallest prime number.

Question

GMATbuster's Weekly Quant Quiz#9 Ques 8 
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what is the value of xy?
1) y is the smallest prime number.
2)  3^x * 5^y = 75

nkin · Answer

Stmt 1: We can take any two prime numbers, 2*3 = 6, 3*5 = 15, hence, not sufficient.

Stmt 2: Prime factorization of 75 = 3^1 * 5^2, hence x = 1, y = 2, xy = 2, Sufficient.

Hence Option B

gmatdordie · Answer

We need value of xy

1. x and y are prime numbers
Prime numbers -{2,3,5,7,...}
so x and y can be {(2,3) ,(3,5), (5,7)..}
so the product of xy can be 6 or 15 or 35 so A is not sufficient

2. B says

3x∗5y=75

which can be re written as

3^x *5^y=3^1*5^2

so x=1, y=2
so xy=2

which gives us 1 answer , hence B is suffient

Hence :OA:B

sowmiyav · Answer

A) Not sufficient
If X =2, Y=3, then XY=6
If X=2,Y=5, then XY=10
No unique answer

B)75=3*(5^2)
So, X=1,Y=2
XY=2
SUFFICIENT
  IMO:OPTION B

nkin · Answer

gmatbusters : Can you please confirm the OA for this question, please? It says C, but I feel B is the right answer...

vanam52923 · Answer

Answer must be C.

1) 
y is smallest prime.
so xy can be anything.
2*2=4
3*7=21

So insufficient.

2)3^x * 5^y=75

3^x * 5^y=3^1*5^2

so xy=1*2=2

or

3^x*5^y=3^1*(-5)^2 * 5^0
so xy=1*0=0(note y is power of 5 not -5)

So insufficient

Combine

since y is smallest prime so it cannot be 0 so y=2 nly

3^x * 5^y=3^1*5^2

so xy=1*2=2

So C

GMATBusters · Answer

Official explanation:

what is the value of xy?
 
Notice that we are not told that the x and y are integers.

1) y is the smallest prime number. No other info available.
Clearly  not sufficient.

2)  3^x * 5^y = 75 
a) Now (x,y) can be (1,2) : xy = 2

b) 3^3 =27
3^4 = 81

Hence  there exists a number 3<x<4 such that 3^x = 75 
5^y will be 1 or y will be zero in this case. : xy = 0.

not sufficient.

Combining 1 & 2 
we get (x,y) can be (1,2) : xy = 2.  Sufficient

Answer C

(Learning: for every positive number a and b, there exists a number x such that a^x = b)

For question based on same concept, click   here

vanam52923 · Answer

gmatbusters 
IS my logic correct?
Answer must be C.

1) 
y is smallest prime.
so xy can be anything.
2*2=4
3*7=21

So insufficient.

2)3^x * 5^y=75

3^x * 5^y=3^1*5^2

so xy=1*2=2

or

3^x*5^y=3^1*(-5)^2 * 5^0
so xy=1*0=0(note y is power of 5 not -5)

So insufficient

Combine

since y is smallest prime so it cannot be 0 so y=2 nly

3^x * 5^y=3^1*5^2

so xy=1*2=2

So C

GMATBusters · Answer

hi

"3^x*5^y=3^1*(-5)^2 * 5^0"

You can  not  introduce any other term (-5)^2 in the statement 2

Hence, the explanation is not right.

Mo2men · Answer

Take care that the question does not state x & y are integers. Do not assume that. It is trap common trap.

bumpbot · Answer

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what is the value of xy? 1) y is the smallest prime number.

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