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a, b, c, d are positive integers. When a is divided by b, the remainde  [#permalink]

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a, b, c, d are positive integers. When a is divided by b, the remainder is 7. When c is divided by d, the remainder is 5. Which of the following cannot be the value of the product b x d?

A. 48
B. 56
C. 63
D. 69
E. 140

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Math Expert V
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Posts: 7839
Re: a, b, c, d are positive integers. When a is divided by b, the remainde  [#permalink]

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nkmungila wrote:
a, b, c, d are positive integers. When a is divided by b, the remainder is 7. When c is divided by d, the remainder is 5. Which of
the following cannot be the value of the product b x d?

A. 48
B. 56
C. 63
D. 69
E. 140

Hi....
Remainders should tell us that b>7 and d>5...
So what can we say about the products..
1) minimum value 8*6=48
2) atleast two factors above 5, one out of which above 7..

Let's see the choices
A) 48-6*8... Ok
B) 56 - 7*8...ok
C) 63 - 7*9... Ok
D) 69 - 3*23... No other possibilities.. Answer
E) 140 - 7*20... Ok

D
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Re: a, b, c, d are positive integers. When a is divided by b, the remainde  [#permalink]

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nkmungila wrote:
a, b, c, d are positive integers. When a is divided by b, the remainder is 7. When c is divided by d, the remainder is 5. Which of
the following cannot be the value of the product b x d?

A. 48
B. 56
C. 63
D. 69
E. 140

Recall that the remainder must be less than the divisor; thus, b must be greater than 7 since “when a is divided by b, the remainder is 7.” Similarly, d must be greater than 5 since “when c is divided by d, the remainder is 5.” Since b and d are positive integers, b ≥ 8 and d ≥ 6.

Next we can factor each answer choice. If the number can be factored into two numbers such that one of them is at least 8 and the other is at least 6, then it can be a value of b x d. However, if the number can’t be factored in the way described above, then it CANNOT be a value of b x d and that is the number we are looking for.

A. 48 = 8 x 6 (Yes)
B. 56 = 8 x 7 (Yes)
C. 63 = 9 x 7 (Yes)
D. 69 = 1 x 69 = 3 x 23 (No)
E. 140 = 20 x 7 (Yes)

Since 69 can only be factored as 1 x 69 or 2 x 23, we don’t have one factor ≥ 8 and the other ≥ 6, so 69 can’t be a value of b x d.

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Math Expert V
Joined: 02 Aug 2009
Posts: 7839
Re: a, b, c, d are positive integers. When a is divided by b, the remainde  [#permalink]

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pushpitkc wrote:
a,b,c,d are positive integers. When a is divided by b, the remainder is 7. When c is divded by d,
the remainder is 5. Which of the following cannot be the value of the product b * d?

A. 48
B. 56
C. 63
D. 69
E. 140

Source: Experts Global

Hi..

The Q is to do more with factors than anything else..

What message can you take from remainders-
b>7 and d>5

Let's see if the choices can be converted to factors that fit in
48=8*6...yes
56=8*7...yes
63=9*7...yes
69=23*3 or 1*69....NO
140=14*10...yes

Ans D..69
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Re: a, b, c, d are positive integers. When a is divided by b, the remainde  [#permalink]

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nkmungila wrote:
a, b, c, d are positive integers. When a is divided by b, the remainder is 7. When c is divided by d, the remainder is 5. Which of the following cannot be the value of the product b x d?

A. 48
B. 56
C. 63
D. 69
E. 140

Given:
1. a, b, c, d are positive integers.
2. When a is divided by b, the remainder is 7.
3. When c is divided by d, the remainder is 5.

Asked: Which of the following cannot be the value of the product b x d?

a = 7 mod b => b>7 => b>=8
c = 5 mod d => d>5 => d>=6

39 = 13*3 But none of b or d may be = 3

IMO D
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Re: a, b, c, d are positive integers. When a is divided by b, the remainde  [#permalink]

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nkmungila wrote:
a, b, c, d are positive integers. When a is divided by b, the remainder is 7. When c is divided by d, the remainder is 5. Which of the following cannot be the value of the product b x d?

A. 48
B. 56
C. 63
D. 69
E. 140

a = 9 m b= 8 and c=11 d=6
so d>5 answer values 69 has factor 3*23 ; not sufficient
IMO D
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If you liked my solution then please give Kudos. Kudos encourage active discussions. Re: a, b, c, d are positive integers. When a is divided by b, the remainde   [#permalink] 25 Aug 2019, 11:27
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