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# How many positive integers are there from 0 to 1000 that leave a

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General GMAT Forum Moderator
Joined: 15 Jan 2018
Posts: 671
Concentration: General Management, Finance
GMAT 1: 720 Q50 V37
How many positive integers are there from 0 to 1000 that leave a  [#permalink]

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28 Nov 2019, 01:43
2
00:00

Difficulty:

65% (hard)

Question Stats:

44% (02:35) correct 56% (02:19) wrong based on 16 sessions

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How many positive integers are there from 0 to 1000 that leave a remainder of 3 on division by 7 and a remainder of 2 on division by 4?

A. 32
B. 36
C. 24
D. 19
E. 67
Intern
Joined: 06 Nov 2014
Posts: 20
Location: Viet Nam
GMAT 1: 720 Q50 V36
GMAT 2: 740 Q50 V40
GPA: 3.67
Re: How many positive integers are there from 0 to 1000 that leave a  [#permalink]

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28 Nov 2019, 03:20
1
I would like to tell you my guessing strategy:
With the divisor pair (7;4), the pattern is repeated each 28 no matter the remainder mentioned in the problem.

1000/28 is slightly less than 36, then 2 possible answers are A and B.
- If the first qualified number is 28, surely we need to pick A.
- However, the first qualified number is 10, which is less than 28. Therefore, the answer should be B.
VP
Joined: 07 Dec 2014
Posts: 1217
How many positive integers are there from 0 to 1000 that leave a  [#permalink]

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29 Nov 2019, 11:59
DisciplinedPrep wrote:
How many positive integers are there from 0 to 1000 that leave a remainder of 3 on division by 7 and a remainder of 2 on division by 4?

A. 32
B. 36
C. 24
D. 19
E. 67

note least value of compliant integers=10
10+(7*4)=38
let number of compliant integers=x
10+28x<1000
x=35
1+35=36
B
How many positive integers are there from 0 to 1000 that leave a   [#permalink] 29 Nov 2019, 11:59
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