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a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
 07 Jan 2013, 06:59
Question Stats:
76% (02:14) correct
23% (01:17) wrong based on 2 sessions
a, b, c, and d are positive integers. If the remainder is 9 when a is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d? (A) 20 (B) 19 (C) 18 (D) 16 (E) 15
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Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
07 Jan 2013, 07:21
When a is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.
b + d cannot be 15, hence E is the answer.
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Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
09 Jan 2013, 16:12
a/b gives reminder 9, hence b\geq{10} c/d gives reminder 5, hence d\geq{6}Add above inequalities: (b+d)\geq{16}Among the answer choices, the only value that does NOT satisfy above constraint is 15. Hence choice(E) is the answer.
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Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
10 Jan 2013, 04:15
PraPon wrote: a/b gives reminder 9, hence b\geq{10}
c/d gives reminder 5, hence d\geq{6}[/m]
Add above inequalities:
[m](b+d)\geq{16}
Among the answer choices, the only value that does NOT satisfy above constraint is 15.
Hence choice(E) is the answer. Hi can u please explain highlighted part? I missing sumthing here..
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Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
10 Jan 2013, 04:31
bhavinshah5685 wrote: PraPon wrote: a/b gives reminder 9, hence b\geq{10}
c/d gives reminder 5, hence d\geq{6}[/m]
Add above inequalities:
[m](b+d)\geq{16}
Among the answer choices, the only value that does NOT satisfy above constraint is 15.
Hence choice(E) is the answer. Hi can u please explain highlighted part? I missing sumthing here.. For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since 15 = 6*2 + 3. Notice that 0\leq{r}<x means that remainder is a non-negative integer and always less than divisor.For more check Remainders chapter of Math Book: remainders-144665.htmla, b, c, and d are positive integers. If the remainder is 9 when a is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?(A) 20 (B) 19 (C) 18 (D) 16 (E) 15 According to the above, since the remainder is 9 when a is divided by b, then b (divisor) must be greater than 9 (remainder). So, the least value of b is 10. Similarly, since he remainder is 5 when c is divided by d, then d must be greater than 5. So, the least value of d is 6. Hence, the least value of b + d is 10 + 6 = 16. Therefore 15 (option E) is NOT a possible value for b + d. Answer: E. Hope it's clear.
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Re: a, b, c, and d are positive integers. If the remainder is 9
[#permalink]
10 Jan 2013, 04:31
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