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The integers y and z are both positive. Is yz a multiple of 500?

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The integers y and z are both positive. Is yz a multiple of 500?  [#permalink]

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New post 15 Jun 2015, 09:27
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Difficulty:

  75% (hard)

Question Stats:

55% (02:30) correct 45% (02:20) wrong based on 105 sessions

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The integers y and z are both positive. Is yz a multiple of 500?

(1) yz is a multiple of 25 and z is a multiple of 20.

(2) y^2 is a multiple of 10 and z^2 is a multiple of 5.
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Re: The integers y and z are both positive. Is yz a multiple of 500?  [#permalink]

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New post 15 Jun 2015, 10:06
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Gmatdecoder wrote:
The integers y and z are both positive. Is yz a multiple of 500?

(1) yz is a multiple of 25 and z is a multiple of 20.

(2) y^2 is a multiple of 10 and z^2 is a multiple of 5.


Question : Is yz a multiple of 500?

Statement 1: yz is a multiple of 25 and z is a multiple of 20

Case 1: z= 20 and y= 5 i.e. yz=100 but NOT a multiple of 500

Case 2: z= 100 and y= 5 i.e. yz=500 i.e. a multiple of 500

NOT SUFFICIENT

Statement 2: y^2 is a multiple of 10 and z^2 is a multiple of 5

i.e. y is a multiple of 10 (because y is an Integer and y^2 is a multiple of 10)
AND
z is a multiple of 5 (because z is an Integer and z^2 is a multiple of 5)

i.e. yz is a multiple of 10 and 5 individually
i.e. yz is a multiple of 50 but we can't say whether it's a multiple of 500 or NOT

Hence, NOT SUFFICIENT

Combining the two statements:

Case 1: z= 20 and y= 10 i.e. yz=100 but NOT a multiple of 500

Case 2: z= 100 and y= 10 i.e. yz=1000 i.e. a multiple of 500

NOT SUFFICIENT

Answer: option
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Re: The integers y and z are both positive. Is yz a multiple of 500?  [#permalink]

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New post 16 Jun 2015, 02:38
Nice Question. Took me time but yes the answer is E.

I primarily tried always to negate the given criteria by picking the numbers, worked well.

the only doubt I have is, can this be a 600 level questions, i mean considering the difficulty range.


Gmatdecoder wrote:
The integers y and z are both positive. Is yz a multiple of 500?

(1) yz is a multiple of 25 and z is a multiple of 20.

(2) y^2 is a multiple of 10 and z^2 is a multiple of 5.

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Re: The integers y and z are both positive. Is yz a multiple of 500?  [#permalink]

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New post 16 Jun 2015, 02:55
shriramvelamuri wrote:
Nice Question. Took me time but yes the answer is E.

I primarily tried always to negate the given criteria by picking the numbers, worked well.

the only doubt I have is, can this be a 600 level questions, i mean considering the difficulty range.


Gmatdecoder wrote:
The integers y and z are both positive. Is yz a multiple of 500?

(1) yz is a multiple of 25 and z is a multiple of 20.

(2) y^2 is a multiple of 10 and z^2 is a multiple of 5.


I would call it a 650 level question because neither it's that easy that it should be 600 level nor it's so difficult to be called a 700 level.
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Re: The integers y and z are both positive. Is yz a multiple of 500?  [#permalink]

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New post 31 Dec 2018, 04:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The integers y and z are both positive. Is yz a multiple of 500?   [#permalink] 31 Dec 2018, 04:24
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