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# If 500 is the multiple of 100 that is closest to X and 400

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Math Expert
Joined: 02 Sep 2009
Posts: 55618
Re: If 500 is the multiple of 100 that is closest to X and 400  [#permalink]

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16 Nov 2014, 07:34
vpranavanshu91 wrote:
I am thoroughly confused, here it says that "500 is a multiple of 100" a "100 that is closest to X"

X can be definitely between 350-450, but why cannot it be between, 50-150 , since closest 100 would be 100, which is a factor of 500. ??

VeritasPrepKarishma Bunuel

gmatbull wrote:
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

Above is a GMATPREP2 question. One solution says:
"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)..."

If x < 500 and 500 is the multiple of 100 closest to it, i think the condition
450 <= x < 550 would suffice - after all, 450 to the nearest 100 = 500?
Same issue applicable to 350 < y < 450 should be 350 <= y < 450

Kindly respond please. (N.B: I've tried a search on the topic but the response returned 2081 results!!)

Have you read this: if-500-is-the-multiple-of-100-that-is-closest-to-x-and-99421.html#p766455 or this: if-500-is-the-multiple-of-100-that-is-closest-to-x-and-99421.html#p843371 or this: if-500-is-the-multiple-of-100-that-is-closest-to-x-and-99421.html#p844635 or this: if-500-is-the-multiple-of-100-that-is-closest-to-x-and-99421.html#p1028956 ?
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Re: If 500 is the multiple of 100 that is closest to X and 400  [#permalink]

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16 Nov 2014, 20:39
1
vpranavanshu91 wrote:
I am thoroughly confused, here it says that "500 is a multiple of 100" a "100 that is closest to X"

X can be definitely between 350-450, but why cannot it be between, 50-150 , since closest 100 would be 100, which is a factor of 500. ??

I think you are messing up the grammar. Read it again:

500 is THE multiple of 100 that is closest to X ...

What is "closest to X"?
"THE multiple of 100" - a specific multiple of 100.
So which specific multiple of 100? 500

Hence X must lie in the range 450 < X < 550.
500 is that multiple of 100 which is closest to X. This does not mean that 100 is closest to X.

So
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Karishma
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Re: If 500 is the multiple of 100 that is closest to X and 400  [#permalink]

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16 Nov 2014, 22:27
I finally understood the grammar of the question, got too involved with SCs recently. !

Thank you Both !!

VeritasPrepKarishma wrote:
vpranavanshu91 wrote:
I am thoroughly confused, here it says that "500 is a multiple of 100" a "100 that is closest to X"

X can be definitely between 350-450, but why cannot it be between, 50-150 , since closest 100 would be 100, which is a factor of 500. ??

I think you are messing up the grammar. Read it again:

500 is THE multiple of 100 that is closest to X ...

What is "closest to X"?
"THE multiple of 100" - a specific multiple of 100.
So which specific multiple of 100? 500

Hence X must lie in the range 450 < X < 550.
500 is that multiple of 100 which is closest to X. This does not mean that 100 is closest to X.

So
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Re: If 500 is the multiple of 100 that is closest to X and 400  [#permalink]

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16 Mar 2016, 07:18
How can we know the ranges as in terms of 49 the multiples amy change many times
hence E
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Re: If 500 is the multiple of 100 that is closest to X and 400  [#permalink]

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10 Sep 2018, 13:28
Did this question very literally.
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

Say X is 499 --> and Y is 399--> X+Y = 898.
if Y is 400 then 499 +400 = 899
but if Y is 300 (multiple of 100, is closest to 300) --> 499+ 300 = 799.
Not suff

(2) Y < 400
Y = 399 and X is 400. x + y = 799. if Y =399 + 499 =898 if we take different cases we get different values which are multiples of 100

1) 2) getting more than 1 multiple of 100. So E.

Kudos if you like my post
Re: If 500 is the multiple of 100 that is closest to X and 400   [#permalink] 10 Sep 2018, 13:28

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