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When Q is divided by W, the quotient is R and the remainder

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by Brent@GMATPrepNow » Fri Oct 26, 2018 5:11 am
AAPL wrote:Magoosh

When Q is divided by W, the quotient is R and the remainder is E. Which of the following expressions is equal to E?

A. RW + Q
B. RW - Q
C. Q - RW
D. QW - R
E. Q/(RW)

OA C.
-----ASIDE-----------------------
There's a nice rule that says, "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
-------------------------------------

GIVEN: When Q is divided by W, the quotient is R and the remainder is E.
So, we can write: Q = WR + E

Which of the following expressions is equal to E?
Take: Q = WR + E
Subtract WR from both sides to get: Q - WR =E

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Fri Oct 26, 2018 6:32 am
AAPL wrote:Magoosh

When Q is divided by W, the quotient is R and the remainder is E. Which of the following expressions is equal to E?

A. RW + Q
B. RW - Q
C. Q - RW
D. QW - R
E. Q/(RW)
Brent´s nice explanation is (part of) the so-called Division Algorithm.
I would like to add that the remainder is always a non-negative integer less than the divisor. (In GMAT´s scope, the divisor is always a positive integer.)
(In our case, 0 <= E < W.)

Let´s explore a particular case, that will serve as yet another example... and also as an alternate solution!

When 5 (Q) is divided by 3 (W), the quotient is 1 (R) and the remainder is 2 (E):
5 = 1*3 + 2 (Note that 2 is a non-negative integer less than 3).

Considering the particular case suggested, our FOCUS (in this case, the TARGET) is: 2

(A) 1*3+5 NO
(B) 1*3-5 NO
(C) 5-1*3 YES (this is a survivor)
(D) 5*3-1 NO
(E) 5/(1*3) NO

The ONLY survivor obtained must be associated with the right (general) answer.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Scott@TargetTestPrep » Tue Oct 30, 2018 10:24 am
AAPL wrote:Magoosh

When Q is divided by W, the quotient is R and the remainder is E. Which of the following expressions is equal to E?

A. RW + Q
B. RW - Q
C. Q - RW
D. QW - R
E. Q/(RW)
We are given that:

Q/W = R + E/W

Multiply the equation by W, we have:

Q = RW + E

Q - RW = E

Answer: C

Scott Woodbury-Stewart
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