If x/16 = 1,199.625

Question

If  \frac{x}{16}=1,199.625  and  \frac{y}{25}=29.12,  what is the sum of the remainders when  x  and  y  are divided by  24  and  15 , respectively?

A. 18
B. 20
C. 24
D. 26
E. 28

ankushsambare · Answer

x / 16 = 1199.625
So, x = 1199.625 × 16 = 19194
Now divide 19194 by 24:
24 × 799 = 19176
Remainder = 19194 − 19176 = 18
So remainder of x ÷ 24 = 18
y / 25 = 29.12
So, y = 29.12 × 25 = 728
Now divide 728 by 15:
15 × 48 = 720
Remainder = 728 − 720 = 8
So remainder of y ÷ 15 = 8
Sum of remainders = 18 + 8 = 26
 Answer: D. 26

Ved257 · Answer

This question requires alot of calculation, is there a faster way of doing this?

Edskore · Answer

Yes, there's a cleaner way to do each part. The trick is working from a nearby round number rather than brute-forcing the division.

For x: x = 16 * 1199.625 = 19194. Now you need x mod 24. Instead of dividing 19194 by 24 from scratch, notice that 19200 = 800 * 24 exactly (since 800 * 24 = 19200). So 19194 = 19200 - 6, and the remainder is 24 - 6 = 18. Done in about 5 seconds.

For y: y = 25 * 29.12 = 728. You need y mod 15. Notice 720 = 48 * 15 exactly. So 728 = 720 + 8, remainder = 8.

Sum = 18 + 8 = 26. Answer D.

The general move here: once you have your big number, ask "what's the nearest multiple of the divisor that I can compute quickly?" Usually a round number like 800 or 48 jumps out faster than dividing directly. Remainders on the GMAT almost always come out cleanly this way — the question writers set the numbers so that the nearest multiple isn't hard to find.

kevincan · Answer

Welcome to Gmatclub ! Whenever you see a solution with lots of calculations , it’s great to ask whether there is a faster way!

GMATcracker101 · Answer

The way I have solved this is -

x/16 * p = x/24 - p = 2/3 hence 1199.625 * 2/3 = 799.75 ----> 0.75 * 24 = 18

y/25 * q = y/15 - q = 5/3 hence 29.12 * 5/3 = 48.533 -----> 0.533 * 15 = 7.99 take as approv 8

So remainder when x is divided by 24 = 18

and remainder when y is divided by 15 = 8

Hence, answer is D. 26.

kevincan · Answer

1199.625 = 1200 -3/8
29.12 = 30 -22/25

Adamz · Answer

Just take (1200 - 0.375) and (30 - 0.88) and solve them separately.

MrMaxMan · Answer

Here's another way to think about it!
x/16 = 1199.625 = (1200-1)+(5/8), x=16(1200-1) + 10
x/24 = (16/24 = 2/3)(1200-1) + 10/24 = 800 - 16/24 + 10/24 = 800 - 6/24 = 799 + 18/24

Remember X/Y = Q + R/Y

x/24 = 799 + 18/24, so our remainder is 18.
Do the same for y/25

y/25 = 29.12 = (30-1) + 3/25, y = 25(30-1) + 3
y/15 = (25(30) - 25 + 3)/15 = 25(2) - 22/15 = 50 - 22/15 = 48 + 30/15 - 22/15 = 48 + 8/15
The remainder is 8

Add the remainders:
18 + 8 = 26
Wow there it is! Maybe no the fastest way of doing things, but it uses basic rules to make a difficult problem more digestible.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=89333 --- Harsha GMAT-Club-Forum-dkskyuw5.png

If x/16 = 1,199.625

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If x/16 = 1,199.625

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