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Retired Moderator V
Joined: 27 Oct 2017
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what is the value of xy? 1) y is the smallest prime number.  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 30% (01:18) correct 70% (00:56) wrong based on 62 sessions

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GMATbuster's Weekly Quant Quiz#9 Ques 8

what is the value of xy?
1) y is the smallest prime number.
2) $$3^x * 5^y = 75$$

_________________

Originally posted by gmatbusters on 17 Nov 2018, 10:17.
Last edited by gmatbusters on 20 Nov 2018, 08:59, edited 2 times in total.
Typo in statement 1 removed
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1272
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: what is the value of xy? 1) y is the smallest prime number.  [#permalink]

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3

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

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

gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#9 Ques 8

what is the value of xy?
1) y is the smallest prime number.
2) $$3^x * 5^y = 75$$

_________________
##### General Discussion
Manager  P
Joined: 09 Jun 2018
Posts: 185
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
Re: what is the value of xy? 1) y is the smallest prime number.  [#permalink]

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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
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Manager  G
Joined: 13 Nov 2018
Posts: 128
Location: India
GMAT 1: 700 Q51 V32 Re: what is the value of xy? 1) y is the smallest prime number.  [#permalink]

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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
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Posts: 26
Re: what is the value of xy? 1) y is the smallest prime number.  [#permalink]

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1
A) Not sufficient
If X =2, Y=3, then XY=6
If X=2,Y=5, then XY=10

B)75=3*(5^2)
So, X=1,Y=2
XY=2
SUFFICIENT
IMO:OPTION B
Manager  P
Joined: 09 Jun 2018
Posts: 185
Location: United States
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Re: what is the value of xy? 1) y is the smallest prime number.  [#permalink]

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gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#9 Ques 8

what is the value of xy?
1) x and y are prime numbers.
2) $$3^x * 5^y = 75$$

gmatbusters: Can you please confirm the OA for this question, please? It says C, but I feel B is the right answer...
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Manager  S
Joined: 17 Jul 2017
Posts: 201
Re: what is the value of xy? 1) y is the smallest prime number.  [#permalink]

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1
gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#9 Ques 8

what is the value of xy?
1) x and y are prime numbers.
2) $$3^x * 5^y = 75$$

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

Originally posted by vanam52923 on 19 Nov 2018, 08:28.
Last edited by vanam52923 on 19 Nov 2018, 08:49, edited 1 time in total.
Manager  S
Joined: 17 Jul 2017
Posts: 201
Re: what is the value of xy? 1) y is the smallest prime number.  [#permalink]

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gmatbusters wrote:

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

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

gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#9 Ques 8

what is the value of xy?
1) y is the smallest prime number.
2) $$3^x * 5^y = 75$$

gmatbusters
IS my logic correct?

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
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1272
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: what is the value of xy? 1) y is the smallest prime number.  [#permalink]

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1
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.

vanam52923 wrote:
gmatbusters wrote:

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

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

gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#9 Ques 8

what is the value of xy?
1) y is the smallest prime number.
2) $$3^x * 5^y = 75$$

gmatbusters
IS my logic correct?

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

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Posts: 2341
Re: what is the value of xy? 1) y is the smallest prime number.  [#permalink]

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sowmiyav wrote:
A) Not sufficient
If X =2, Y=3, then XY=6
If X=2,Y=5, then XY=10

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

Take care that the question does not state x & y are integers. Do not assume that. It is trap common trap. Re: what is the value of xy? 1) y is the smallest prime number.   [#permalink] 19 Nov 2018, 09:02
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