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

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Director
Joined: 21 Dec 2009
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If 500 is the multiple of 100 that is closest to X and 400 [#permalink]

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19 Aug 2010, 02:57
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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!!)
[Reveal] Spoiler: OA

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Re: If 500 is the multiple of 100 [#permalink]

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19 Aug 2010, 07:15
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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!!)

"x rounded to the nearest hundred is 500" means $$450\leq{x}<550$$ (inequality you've written) BUT it IS NOT the same as "500 is the multiple of 100 that is closest to x", which should be $$450<x<550$$ as 450 is equidistant from 400 and 500 and we cannot say that 450 rounded to nearest multiple of 100 is 500, it's 500 OR 400. That's why endpoints must be excluded.

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 ?

"500 is the multiple of 100 closest to X" --> $$450<x<550$$;
"400 is the multiple of 100 closest to Y" --> $$350<y<450$$.

(1) x<500 --> $$450<x<500$$ --> add this inequality to inequality with y --> $$800<x+y<950$$. If x+y=810 then closest multiple of 100 is 800 BUT if x+y=860 then closest multiple of 100 is 900. Not sufficient.

(2) y<400 --> $$350<y<400$$ --> add this inequality to inequality with x --> $$800<x+y<950$$. The same here: if x+y=810 then closest multiple of 100 is 800 BUT if x+y=860 then closest multiple of 100 is 900. Not sufficient.

(1)+(2) Sum $$450<x<500$$ and $$350<x<400$$ --> $$800<x+y<900$$ --> and again if x+y=810 then closest multiple of 100 is 800 BUT if x+y=860 then closest multiple of 100 is 900. Not sufficient.

Hope it's clear.
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Re: If 500 is the multiple of 100 [#permalink]

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19 Aug 2010, 21:01
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I think you need to focus on what the question is asking, the questions i asking x+ y. I did it the same way as Brunel and added the two inequalities. You can either round to 800, 900, or 1000 depending on the statement you're looking at.
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Re: If 500 is the multiple of 100 [#permalink]

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02 Jan 2011, 09:18
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MICKEYXITIN wrote:
:( i even could not grasp the point on what the question is about.
If 500 is the multiple of 100 that is closest to X --> i dont know whether 500 is closest to X or 100 is. The same with E maybe i must learn by heart the word translation from these explanations above.

If 500 is the multiple of 100 that is closest to X
If it is difficult to understand, think of it this way:

500 is A.

A - the multiple of 100 that is closest to X

What is 500? It is the multiple of 100 that is closest to X. There are lots of multiples of 100 like 100, 200, 300, 400, 500, 600 etc but 500 is the one which is closest to X. So X could be 472 or 518 etc....
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 12 Oct 2011 Posts: 4 If 500 is the multiple of 100 that is closest to x and 400 [#permalink] ### Show Tags 06 Nov 2011, 18:16 1 This post received KUDOS If 500 is the multiple of 100 that is closest to x and 400 is the multiple of 100 that is closest to y. Which multiple of 100 is closest to x+y? 1) x < 500 2) y < 400 Need clear explanation of the question pls??? Intern Joined: 22 May 2013 Posts: 49 Concentration: General Management, Technology GPA: 3.9 WE: Information Technology (Computer Software) Re: If 500 is the multiple of 100 that is closest to X and 400 [#permalink] ### Show Tags 26 Jun 2013, 08:49 1 This post received KUDOS 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!!) 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 Question : 450<X<550 and 350<Y<450 ?<X+Y<? (1) X < 500 Now, 450<X<500 and 350<Y<450 Higher range => 490+440 = 930 (No closest: 900) Lower range => 460+360 = 820 (No closest: 800) Not sufficient (2) Y < 400 Now, 450<X<550 and 350<Y<400 Higher range =>540+390 = 930 (No closest: 900) Lower range =>460+360 = 820 (No closest: 800 ) Not sufficient (1) + (2) combined. Now, 450<X<500 and 350<Y<400 Higher range =>490+390 = 880 (No closest: 900) Lower range =>460+360 = 820 (No closest: 800 ) Not sufficient Ans: E _________________ PS: Like my approach? Please Help me with some Kudos. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7446 Location: Pune, India Re: If 500 is the multiple of 100 that is closest to X and 400 [#permalink] ### Show Tags 16 Nov 2014, 20:39 1 This post received KUDOS Expert's post 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. ?? Please Help !! 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: If 500 is the multiple of 100 [#permalink]

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20 Aug 2010, 07:47
kudos again; it's very clear now.

Very appreciative of your time and skill devoted in such detailed explanations.
Dunno whether to wish you success -if my wish would add any value- in your
GMAT exam. Out of curiosity, i asked whether you've actually taken the GMAT
but you seem to remain silent over the question.

Great personality out there, "Bunuel."
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Re: If 500 is the multiple of 100 [#permalink]

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29 Dec 2010, 21:16
Expert's post
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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!!)

Besides, be aware that when you talk about rounding, there are different rules you can use in case of a tie i.e. 450 needs to be rounded off to a multiple of 100. Since it is equidistant from 400 and 500, it can be rounded up (i.e. to 500) or rounded down (i.e. to 400). It can be rounded towards 0 on the number line (i.e. 400) or away from 0 (i.e. to 500) etc. Generally, in schools, rounding up is taught but it is biased towards giving a higher value. Nevertheless, GMAT uses rounding up by default. (e.g. in Question 64, OG12)

Here anyway, as Bunuel mentioned, the question is not about rounding but about distance.
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Re: If 500 is the multiple of 100 [#permalink]

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01 Jan 2011, 08:32
i even could not grasp the point on what the question is about.
If 500 is the multiple of 100 that is closest to X --> i dont know whether 500 is closest to X or 100 is. The same with E maybe i must learn by heart the word translation from these explanations above.
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Re: If 500 is the multiple of 100 [#permalink]

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04 Jan 2011, 21:01
gmatbull wrote:
kudos again; it's very clear now.

Very appreciative of your time and skill devoted in such detailed explanations.
Dunno whether to wish you success -if my wish would add any value- in your
GMAT exam. Out of curiosity, i asked whether you've actually taken the GMAT
but you seem to remain silent over the question.

Great personality out there, "Bunuel."

Bunuel was the only guy to ever get Q52 on the GMAT :D
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Re: If 500 is the multiple of 100 [#permalink]

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05 Jan 2011, 21:37
VeritasPrepKarishma wrote:
MICKEYXITIN wrote:
:( i even could not grasp the point on what the question is about.
If 500 is the multiple of 100 that is closest to X --> i dont know whether 500 is closest to X or 100 is. The same with E maybe i must learn by heart the word translation from these explanations above.

If 500 is the multiple of 100 that is closest to X
If it is difficult to understand, think of it this way:

500 is A.

A - the multiple of 100 that is closest to X

What is 500? It is the multiple of 100 that is closest to X. There are lots of multiples of 100 like 100, 200, 300, 400, 500, 600 etc but 500 is the one which is closest to X. So X could be 472 or 518 etc....

thanx for your help Karishma. Your explantion is very clear, now i can understand the meaning without try to cram it to my head
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Re: Tough GMAT prep DS [#permalink]

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21 Feb 2011, 06:01
Considering x,y as integers for convenience. find (x+y) to know the closest multiple of 100

from stem;
451<x<549
351<y<449

802<x+y<998

This range covers three multiples; 800,900,1000. We need to nail it down to 1.

1) x < 500.
451<x<500
351<y<449
802<x+y<949
Still; 2 multiples of 100 may be close; 800,900. Not sufficient.

2) y < 400
351<y<400
451<x<549
802<x+y<949
Still; 2 multiples of 100 may be close; 800,900. Not sufficient.

Combing both;
451<x<500
351<y<400

802<x+y<900
Still; 2 multiples
800 and 900. Not sufficient.

Ans: "E"
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06 Nov 2011, 21:02
The answer is E and not C.

acc. to given conditions
450<x<550
350<y<450

x & y are not necessarily integers.
1. Insufficient
2. Insufficient

1+2
x+y can be close to 800 or 900
Insufficient.
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06 Nov 2011, 21:47
rvind wrote:
If 500 is the multiple of 100 that is closest to x and 400 is the multiple of 100 that is closest to y. Which multiple of 100 is closest to x+y?

1) x < 500
2) y < 400

Need clear explanation of the question pls???

1) x < 500 --> lets consider x = 451 or 499 (taking closest and farthest value possible for x)
2) y < 400 --> lets consider y = 351 or 399 (taking closest and farthest value possible for y)

x+y = 802 or 898, which means it can be 800 or 900.

Cheers!
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Re: If 500 is the multiple of 100 that is closest to x and 400 [#permalink]

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25 Nov 2011, 04:52

450<x<550
350<y<450

Statememt 1. 450<x<500 .
So 800<x+y<950 . Insufficient as both 800 and 900 can be the answer.

Statement 2. 350<y<400
So 800<x+y<950 . Insufficient as both 800 and 900 can be the answer.

Combining both answers , 800<x+y<900 . Still insufficient as 800 (e.g x+y=815) and 900(e.g. x+y=850) are both potential answers.

So (E) is the correct answer choice.
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Re: If 500 is the multiple of 100 that is closest to x and 400 [#permalink]

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17 Dec 2011, 22:55
Can someone please explain the question stem? I am pretty confused by the question itself. How to interpret the question? What is asked here? What is x and what is y? Are they integers? If they are, how does that affect the solution and if they are not, again the same question?
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Re: If 500 is the multiple of 100 that is closest to x and 400 [#permalink]

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17 Dec 2011, 23:27
Hi Siddharth,
X and Y has to be integers as they are multiples of 100.

For the explanation see Capricon's answer
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Re: If 500 is the multiple of 100 that is closest to x and 400 [#permalink]

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13 Jan 2012, 18:19
Merging similar topics.

siddharthmuzumdar wrote:
Can someone please explain the question stem? I am pretty confused by the question itself. How to interpret the question? What is asked here? What is x and what is y? Are they integers? If they are, how does that affect the solution and if they are not, again the same question?

Please refer to my solution above. Hope it helps to understand the question. Side note: x and y are some numbers, not necessarily integers, for example from (1) we have that 450<x<500, so x can be any number from this range: 470, 480.5, 499,9999...

Check similar question for practice: the-numbers-x-and-y-are-not-integers-107346.html?hilit=multiple%20that%20closest
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Re: If 500 is the multiple of 100 that is closest to X and 400 [#permalink]

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26 Jun 2013, 01:41
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If 500 is the multiple of 100 that is closest to X and 400   [#permalink] 26 Jun 2013, 01:41

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