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How many more integers between 552 and 652 are divisible by 3 than are

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How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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18 Feb 2019, 02:02
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95% (hard)

Question Stats:

30% (02:04) correct 70% (02:03) wrong based on 93 sessions

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How many more integers between 552 and 652 are divisible by 3 than are divisible by 4 ?

A. 1
B. 6
C. 8
D. 9
E. 12

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Re: How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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27 Feb 2019, 02:34
3
2
Total number of integers = (652-552)+1 = 101.
652 and 552 are not included. So, 101-2 = 99 integers.
Divisible by 3 = 99/3 = 33.
Divisible by 4 = 99/4 = 24. (The 25th divisible number would be 652, but it's not included, hence 24).

33-24 = 9. Answer is D.
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How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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18 Feb 2019, 02:11
Bunuel wrote:
How many more integers between 552 and 652 are divisible by 3 than are divisible by 4 ?

A. 1
B. 6
C. 8
D. 9
E. 12

from 552 to 652
no of integers divisible by 3 are range 185 to 217 i.e 32 integers
and similarly for 4 are in range 139 to 162 i.e 23 integers
so no overlap integers 32-23 = 9
IMO D
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Re: How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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19 Feb 2019, 02:06
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Re: How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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19 Feb 2019, 02:11
kavitabajpayee07 wrote:

kavitabajpayee07
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Re: How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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19 Feb 2019, 02:21
2
It is C
Total factors of 3 are 34: 552 itself plus 33 more in next 100 integers from 553-652
Total factors of 4 are 26: 552 itself plus 25 more in next 100 integers from 553-652

So 34-26 giving 8 as answer

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Re: How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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19 Feb 2019, 02:30
1
VGOEL1234 wrote:
It is C
Total factors of 3 are 34: 552 itself plus 33 more in next 100 integers from 553-652
Total factors of 4 are 26: 552 itself plus 25 more in next 100 integers from 553-652

So 34-26 giving 8 as answer

Posted from my mobile device

VGOEL1234
How many more integers between 552 and 652 are divisible by 3 than are divisible by 4

you seem to have included 552 & 652 as well

solution would be
no of integers divisible by 3 would be factors from 185 to 217 i.e 32 integers
and similarly for 4 factors are 139 to 162 i.e 23 integers
so overlap integers 32-23 = 9 ; which are not divisible by 4
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Re: How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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27 Feb 2019, 08:25
Archit3110, can you explain your process, I am confused!

no of integers divisible by 3 are range 185 to 217 i.e 32 integers
and similarly for 4 are in range 139 to 162 i.e 23 integers
so no overlap integers 32-23 = 9

How are you getting the ranges?
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Re: How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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27 Feb 2019, 09:43
1
smlprkh:
question is to find out how many more integers between 552 and 652 are divisible by 3 than are divisible by 4 ?
in short we need to determine the total no of integers which are divisible by 3 but not by 4

since we need to find integer values between not inclusive from 552 to 652 so factor of 3 which divides integer after 552 is 185 similary 217 *3=651 which is last integer before 652
so the total no of integers divisible by 3 are in range 185 to 217 i.e " 217-185"= 32 integers ;

similarly we can determine the value of total integers divisible by 4 between 552 to 652 ; 4*139 = 556 and 162 *4 = 158
so integers range for no divisible by 4 are in range 139 to 162 i.e " 162-129" = 23 integers

so no overlap integers 32-23 = 9

hope this helps..

smlprkh wrote:
Archit3110, can you explain your process, I am confused!

no of integers divisible by 3 are range 185 to 217 i.e 32 integers
and similarly for 4 are in range 139 to 162 i.e 23 integers
so no overlap integers 32-23 = 9

How are you getting the ranges?
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How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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27 Feb 2019, 11:28
Bunuel sir, If the question mentions whether the numbers 552 and 652 should be included or not will help solve the confusion whether to include those numbers or not. TIA

And does GMAT explicitly mention whether the numbers are inclusive or exclusive?
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Re: How many more integers between 552 and 652 are divisible by 3 than are  [#permalink]

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04 Mar 2019, 08:47
Bunuel wrote:
How many more integers between 552 and 652 are divisible by 3 than are divisible by 4 ?

A. 1
B. 6
C. 8
D. 9
E. 12

The number of multiples of 4 between 552 and 652 is:

(648 - 556)/4 + 1 = 24

The number of multiples of 3 between 552 and 652 is:

(651 - 555)/3 + 1 = 33

So there are 33 - 24 = 9 more multiples of 3 than multiples of 4 between 552 and 652.

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Re: How many more integers between 552 and 652 are divisible by 3 than are   [#permalink] 04 Mar 2019, 08:47
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