Problem Solving

Hi emdadul28,

This question can be solved by TESTing VALUES.

We're told that when R is divided by 5, the remainder is 2.

Let's TEST.... R = 7

7/5 = 1 r 2

We're asked for the remainder when (7)(R) is divided by 5....

(7)(R) = (7)(7)/5 = 49/5 = 9 r 4

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

emdadul28 wrote:When an integer r is divided by 5 , the remainder is 2. if the product of 7 and r is divided by 5, what would the remainder be?

a. 1
b. 2
c. 3
d. 4
e. 5

Ans: d.

Hi emdadul28,

While the most efficient approach is by assuming a suitable value of r, here is the conceptual approach.

Say r = 5n + 2; where n is a non-negatibe integer.

Thus, 7r = 35n + 14 = 35n + 10 + 4

Remainder when (35n + 10 + 4) is divided by 5 equals to 4 since 35n and 10 are divisible by 5.

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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emdadul28 wrote:When an integer r is divided by 5 , the remainder is 2. If the product of 7 and r is divided by 5, what would the remainder be?

a. 1
b. 2
c. 3
d. 4
e. 5

There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

When an integer r is divided by 5 , the remainder is 2
So, r = 5k + 2 for some integer k

If the product of 7 and r is divided by 5, what would the remainder be?
7r = 7(5k + 2)
= 35k + 14
= 35k + 10 + 2
= 5(7k + 2) + 2
= 5(some integer) + 2

This tells us that 7r is 2 greater than some multiple of 5
So, if we divide 7r by 5, the remainder will be 2

Answer: B

Cheers,
Brent

emdadul28 wrote:When an integer r is divided by 5 , the remainder is 2. if the product of 7 and r is divided by 5, what would the remainder be?

a. 1
b. 2
c. 3
d. 4
e. 5

We are given that when an integer r is divided by 5, the remainder is 2. Thus:

r/5 = Q + 2/5

r = 5Q + 2

So 7r = 7(5Q + 2) = 35Q + 14.

The remainder of (35Q + 14)/5 = 35Q/5 + 14/5.

Since 35Q/5 has a remainder of zero and 14/5 has a remainder of 4, the remainder of 7r/5 is 4.

Answer: D