a, b, c, d are positive integers. When a is divided by b, the remainde

Question

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

chetan2u · Accepted Answer

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

ScottTargetTestPrep · Answer

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.

Answer: D

chetan2u · Answer

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

Kinshook · Answer

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

Archit3110 · Answer

a = 9 m b= 8 and c=11 d=6
so d>5 answer values 69 has factor 3*23 ; not sufficient
IMO D

MathRevolution · Answer

a is divided by b, the remainder is 7

Therefore b ≥ 8

c is divided by d, the remainder is 5

Therefore d ≥ 6

Option D: 69 = 3 * 23

Answer D

BrushMyQuant · Answer

a, b, c, d are positive integers. When a is divided by b, the remainder is 7.

Theory: Divisor > Remainder

=> b > 7
=> b  ≥ 8

When c is divided by d, the remainder is 5.

=> d > 5
=> d  ≥ 6

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

=> b * d  ≥  8*6
=>  bd  ≥ 48, b ≥ 8, d ≥ 6 and b and d have to an integer

A. 48 
=> b = 8, d = 6 =>   POSSIBLE

B. 56 
=> b = 8, d = 7 =>   POSSIBLE

C. 63 
=> b = 9, d = 7 =>   POSSIBLE

D. 69  
=> b = 23, d = 3 =>   NOT POSSIBLE    as d < 5 
 (we don't need to check further, but i am solving to complete the solution)

E. 140  
=> b = 20, d = 7 =>   POSSIBLE

So,  Answer will be D 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

bumpbot · Answer

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a, b, c, d are positive integers. When a is divided by b, the remainde

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