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

1. X < 500

2. Y < 400

Please provide the steps so I can follow.

is the answer E?

I think so. But do you have a solution?

Per the stem:
Range of X: 449<X<550
Range of Y: 349<X<450

By 1: Say X=499
Now if Y = 449 then nearest multiple of 100 to X+Y will be: 900

Say X=449 Now if Y = 350 then nearest multiple of 100 to X+Y will be: 800

Similarly you can prove that it is E

you have the right idea, and you'll get the right answer to this problem with this method, but you're making a MAJOR faux pas here: you're assuming that x and y have to be integers.
do not assume that numbers are integers, EVER, unless (a) you're explicitly told that they are OR (b) the problem implies that this is the case.
by (b) i'm referring to certain word problems whose solutions must be whole numbers just because of the nature of the subject. for instance, if a problem calls for the numbers of girls and boys in a classroom, then those have to be integers, even if the problem doesn't happen to say so (you can't have, say, 2.3 girls).

since the numbers don't have to be integers, you have
1. 450 < x < 550 (excluding BOTH endpoints) - note that x could be 450.00001 or 549.99999
2. 350 < y < 450 (again excluding both endpoints)

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also, watch your <'s and <'s. in your writeup, you wrote a condition (449 < x < 550) that prohibits x from being 449, but then you turned around and plugged in 449 for x. don't contradict your own rephrases!

hi,

please explain me the meaning of the statement "500 is the multiple of 100 that is closest to X"
i am unable to get this ..


thanks..

this means that, of all multiples of 100, 500 comes closest to x.
in other words, 500 is closer to x than is 100, 200, 300, 400, or 600, 700, 800, ...
if you think about this for a sec, you'll realize that it means x has to be strictly between 450 and 550.

if you're still having trouble with the language/wording of the statement, then concoct a similar but simpler analogy statement, such as "mccarran is the airport that is closest to my house".
this statement works the same way. it's a bit more difficult to parse, but you just have to realize that "multiple of 100" should be treated as if it were a single word.

Hi Ron,

That is great explanation... really fruitful just before my exam.

Thanks
Nishad

glad it helped

Can anybody please explain me why the range of X is defined between 449 and 549.

As per the explanation X is closest to 500 than any other multiple of 100. In that case I guess the range of X can be 401 to 599 also.

Please explain !!

Actually, X is defined as the range from 450 to 549. Please check out Ron's excellent explanation above.

_________________
Jamie Nelson
ManhattanGMAT Instructor

As per the question stem 450<X<550 ; why is it necessary to exclude end points in this case? Numbers 450 and 550 ...what integers will they be rounded off to?

"rounding" is not the issue. the issue is just obeying the literal meaning of the words in the problem.

the words say
THE multiple of 100 that is closest to...
the word "THE", along with the singular "multiple", imply that there must be only one such multiple.

so, 450 is out, because there are two multiples that are closest to it (namely, 400 and 500). i.e., you can't say that 500 is THE multiple... in this case, because 400 is just as close.

550 is also out, because you have the same problem, this time with 500 and 600.