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Math Expert V
Joined: 02 Sep 2009
Posts: 64133
How many positive integers less than 60 are equal to the product of a  [#permalink]

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Difficulty:   15% (low)

Question Stats: 77% (01:12) correct 23% (01:40) wrong based on 221 sessions

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How many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?

A. 4
B. 5
C. 9
D. 10
E. 11

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Re: How many positive integers less than 60 are equal to the product of a  [#permalink]

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Number of positive multiples of 5 less than 60 = 11
5*1=5
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5*7=35
5*8=40
5*9=45
5*10=50
5*11=55

Only 5 of the above are a product of a positive multiple of 5 and an even number - 10,20,30,40,50

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How many positive integers less than 60 are equal to the product of a  [#permalink]

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1
let's say 5q is the multiple of 5, 2p the even number
hence, the integer will be of the form 10qp, only 10 20 30 40 and 50 are of this form and less than 60.

Originally posted by LuisP on 03 Dec 2015, 09:24.
Last edited by LuisP on 05 Dec 2015, 05:46, edited 1 time in total.
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How many positive integers less than 60 are equal to the product of a  [#permalink]

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Bunuel wrote:
How many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?

Quote:
positive integers less than 60.............product of a positive multiple of 5 and an even number
is 5k

k = {2,4,6,8 ......} (Since numbers are even )

k = {2m} (Since numbers are even )

Hence 5k = 5(2m)

Or, 5 k =10m

So, We have to find numbers which are multiples of 10

Hence the numbers are - { 10, 20 , 30 , 40 , 50 } Only 5 numbers..

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Intern  Joined: 06 May 2015
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Re: How many positive integers less than 60 are equal to the product of a  [#permalink]

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I think the answer is D
"product of positive multiples of 5 and an even number"
5x2, 5x4, 5x6,5x8, 5x10
10x2, 10x4
15x2
20x2
25x2

10,15,20 and 25 are also positive multiples of 5.
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Re: How many positive integers less than 60 are equal to the product of a  [#permalink]

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I disagree with those saying the answer is B. In my opinion, answer is D.

Multiple of 5 are: 5, 10, 15, 20, 25, ...

In this case, we have the following fulfilling the conditions:

1. 5*2
2. 5*4
3. 5*6
4. 5*8
5. 5*10
6. 10*2
7. 10*4
8. 15*2
9. 20*2
10. 25*2
Intern  Joined: 04 Sep 2015
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Re: How many positive integers less than 60 are equal to the product of a  [#permalink]

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vp101 wrote:
I disagree with those saying the answer is B. In my opinion, answer is D.

Multiple of 5 are: 5, 10, 15, 20, 25, ...

In this case, we have the following fulfilling the conditions:

1. 5*2
2. 5*4
3. 5*6
4. 5*8
5. 5*10
6. 10*2
7. 10*4
8. 15*2
9. 20*2
10. 25*2

I came up with the same answer!
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Re: How many positive integers less than 60 are equal to the product of a  [#permalink]

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I guess u will be repeating numbers ... And so u will get 10 ... When u remove the repeats ... U get only 5 now... Hence B...
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Re: How many positive integers less than 60 are equal to the product of a  [#permalink]

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Hi vp101 and Condon,

GMAT questions are always carefully worded, so you have to make sure that you answer the question that is ASKED.

We're asked for the number of positive integers that are less than 60 AND even multiples of 5. If you check your lists, you'll see that you included a number of your integers TWICE.

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Re: How many positive integers less than 60 are equal to the product of a  [#permalink]

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Bunuel wrote:
How many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?

A. 4
B. 5
C. 9
D. 10
E. 11

We should note that “the product of a positive multiple of 5 and an even number” is the same thing as “an even multiple of 5”. The positive integers less than 60 that are also even multiples of 5 are 10, 20, 30, 40, and 50, so there are 5 integers.

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GMAT 1: 600 Q46 V27 Re: How many positive integers less than 60 are equal to the product of a  [#permalink]

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Bunuel wrote:
How many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?

A. 4
B. 5
C. 9
D. 10
E. 11

You need to multiply 5 with least positive even integer and see what is the result.
We get 10
Next would be 5*4=20.
next would be 30,40,50.
60 does not qualify as the question states less than 60.

Hence 5.
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Re: How many positive integers less than 60 are equal to the product of a  [#permalink]

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Bunuel wrote:
How many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?

A. 4
B. 5
C. 9
D. 10
E. 11

Asked: How many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?

Positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number = {10,20,30,40,50} = 5 numbers

IMO B
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Re: How many positive integers less than 60 are equal to the product of a  [#permalink]

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Bunuel wrote:
How many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?

A. 4
B. 5
C. 9
D. 10
E. 11

The way I arrived at the solution. Since the question says that positive integers < 60 when 5 multiplied by an even number.

Thus
5x2 = 10
5x4= 20
5x6 = 30
5x8 = 40
5x10 = 50
5x12 = 60 < filter reached.

Thus there are 5 integers less than 60 when 5 is multiplied by an even number. Re: How many positive integers less than 60 are equal to the product of a   [#permalink] 03 Apr 2020, 06:51

# How many positive integers less than 60 are equal to the product of a   