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.
When an integer r is divided by 5 ,
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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
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
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Hi emdadul28,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.
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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There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"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
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
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We are given that when an integer r is divided by 5, the remainder is 2. Thus: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
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
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