If 500 is the multiple of 100 that is closest to X and 400 is the multiple of 100 that is closest to Y, then which multiple of 100 is closest to X+Y

1) X<500

2) Y<400



Help please!

Hi,


Lets understand the problem first:-

When 500 is the multiple of 100 closest to x , we get the following equation:-
451 < =x <= 550
(if x goes beyond that, then 500 wouldn't remain its multiple, consider a case when x = 551, in this case closest multiple of 100 is 600 since 600 - 551 = 49 which is less than 551 - 500 = 51)

similarly, when 400 is the multiple of 100
y = 351 < =y <= 450
( As said above)



(1) x < 500 , which means 451 <=x <= 499, which is clearly not sufficient in itself

(2) y < 400, which means 351 <= y <= 399 , which is clearly not sufficient in itself


Combining (1) and (2),

x+y 802 <= x+y <= 898 , Clearly, we cannot come to unique solution, since closest multiple can be 800 or 900.


Hence (E) , Please let me know if thats correct

thanks.

OA: E

What exactly does 500 is the multiple of 100 that is closest to X mean?

Is it saying that:

100(X) is less then or equal to 500....so X=4.51------>5.49

100(Y) is less then or equal to 400....so Y=3.51------>4.49

??????


I guess it would make sense that the answer is E because it doesn't specify that X and Y are integers. But if it said that X&Y are integers would the answer be X+Y = 9 ???

"500 is the multiple of 100 that is closest to X"
means
"500 is closer to X than is any other multiple of 100"
which means
450 < X < 550

"400 is the multiple of 100 that is closest to Y"
means
"400 is closer to Y than is any other multiple of 100"
which means
350 < Y < 450

let's look at both statements together:
if both statements are true, then we have 450 < X < 500 and 350 < Y < 400.
in order to investigate the range of possibilities, look near the low end of the range and then look near the high end of the range.
low end:
if X = 451 and Y = 351, then X + Y = 802, which is closer to 800 than to other multiples of 100.
if X = 499 and Y = 399, then X + Y = 898, which is closer to 900 than to other multiples of 100.
(notice that if you're slow at arithmetic, you needn't calculate these exact values; 451 + 351 is approx 450 + 350, which is obviously closer to 800 than to other hundreds, and 499 + 399 ~ 500 + 400, which is obviously close to 900)

this gives two different answers to the problem, so both statements together are still insufficient.

answer = e