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Number Properties Question (Kaplan Math Workbook-Q.No. 19.)

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Number Properties Question (Kaplan Math Workbook-Q.No. 19.) [#permalink] New post 15 Jul 2013, 09:11
Q.How many Positive Integers less than 60 are equal to the product of a positive multiple of 5 and an even number ?

Ans. Positive multiples of 5 are 10,20,30,40,50,60.......
Therefore, according to question....

Positive integer less than 60 = (Positive multiple of 5 * even no.)
Let us first take 10 as positive multiple of 5
therefore.....
P = 10* even no.
(taking smallest even no.2)
P = 10*2 = 20 ( which is less than 60) - 1
taking next even no. 4
P = 10* 4 = 40 ( less than 60) - 2
and now 6
P = 10*6 = 60 (not less than 60)

now next multiple is 20
P = 20* 2 = 40 ( less than 60) - 3
P = 20* 3 = 60 ( not less than 60 )
next multiple 40
P = 30*2=60 ( not less than 60)

Therefore we got only 3 numbers less than 60 which satisfy the condition.

But in question the options are as follows
1. 4
2. 5
3. 9
4. 10
5. 11

Can anybody explain why ????
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Re: Number Properties Question (Kaplan Math Workbook-Q.No. 19.) [#permalink] New post 15 Jul 2013, 12:14
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You have all the math worked out that you need to, the question makes the answer quite difficult to figure out.

If you split up the question into 2 parts it may make more sense.

You have the second half of the question figured out. (the product of a positive multiple of 5 and an even number)
10,20,30,40,50,60

The first half asks how many positive integers are less than 60.
answer? 59. 1,2,3,4,5,6 etc...

How many of those positive integers are equal to the product of a positive multiple of 5 and an even number?
10,20,30,40,50

(60 doesn't count, the first part asks for numbers less than 60)

Thus, the answer is B. (5)
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Re: Number Properties Question (Kaplan Math Workbook-Q.No. 19.) [#permalink] New post 05 Mar 2014, 01:54
Schreined wrote:
You have all the math worked out that you need to, the question makes the answer quite difficult to figure out.

If you split up the question into 2 parts it may make more sense.

You have the second half of the question figured out. (the product of a positive multiple of 5 and an even number)
10,20,30,40,50,60

The first half asks how many positive integers are less than 60.
answer? 59. 1,2,3,4,5,6 etc...

How many of those positive integers are equal to the product of a positive multiple of 5 and an even number?
10,20,30,40,50

(60 doesn't count, the first part asks for numbers less than 60)

Thus, the answer is B. (5)
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Number Properties Question (Kaplan Math Workbook-Q.No. 19.)

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