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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, 01:57

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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!!)

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!!)

I see your point.

"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.

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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:( 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....
_________________

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

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26 Jun 2013, 07:49

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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!!)

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
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PS: Like my approach? Please Help me with some Kudos.

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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KUDOS me if you feel my contribution has helped you.

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.
_________________

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.
_________________

Consider giving me kudos if you find my explanations helpful so i can learn how to express ideas to people more understandable.

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
_________________

:( 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
_________________

Consider giving me kudos if you find my explanations helpful so i can learn how to express ideas to people more understandable.

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???

Answer should be E.

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. Hencem answer E.

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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17 Dec 2011, 21:55

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? I am very confused about this one because I am not clear with the question itself. Can someone please help me understand to interpret such questions? TIA.
_________________

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? I am very confused about this one because I am not clear with the question itself. Can someone please help me understand to interpret such questions? TIA.

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...

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