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a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
07 Jan 2013, 05:59

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Difficulty:

25% (low)

Question Stats:

77% (02:20) correct
23% (01:51) wrong based on 91 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?

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
07 Jan 2013, 06:21

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.

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..

If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y =divisor*quotient+remainder= xq + r and 0\leq{r}<x.

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.

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

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.

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
06 Apr 2014, 09:27

what if a = 1 and b= 9...then wouldn't 1/9 still have a remainder of 9? doesn't the rule that b must be greater than or equal to 10 not hold in this case?

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
06 Apr 2014, 09:39

Expert's post

HCalum11 wrote:

what if a = 1 and b= 9...then wouldn't 1/9 still have a remainder of 9? doesn't the rule that b must be greater than or equal to 10 not hold in this case?

Posted from my mobile device

No.

Let me ask you a question: how many leftover apples would you have if you had 1 apple and wanted to distribute in 9 baskets evenly? Each basket would get 0 apples and 1 apple would be leftover (remainder).

When a divisor is more than dividend, then the remainder equals to the dividend, for example: 3 divided by 4 yields the reminder of 3: 3=4*0+3; 9 divided by 14 yields the reminder of 9: 9=14*0+9; 1 divided by 9 yields the reminder of 1: 1=9*0+1.