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

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Senior Manager
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If 500 is the multiple of 100 that is closest to x and 400 [#permalink]

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26 Oct 2005, 22:03
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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
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Re: DS - Prep2 - Multiple [#permalink]

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26 Oct 2005, 22:33
rigger 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

A very gripping one
from the stem statement, we can conclude that x>=450 ( because if x, for example, = 449---> the multiple of 100 that is closest to x is 400), similarly we can conclude that y>=350
---> x+y>=800

Is OA E? ...if correct, I'll explain further.
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27 Oct 2005, 01:44
From the question, we can notice ;

451 <= x <= 550
351 <= y <= 450
---------------
802 <= x+y <= 1000

( statement 1) x < 500

451 <= x < 500
351 <= y <= 450
---------------------
802 <= x+y < 950

( statement 2) y < 400

451 <= x <= 550
351 <= y < 400
---------------------
802 <= x+y < 950

So my guess is D.
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27 Oct 2005, 02:44
yeah, i forgot the upper limit ...was too sleepy .. anyway, well done job, buddy
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27 Oct 2005, 03:30
agree with D. Same reasoning...
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27 Oct 2005, 03:42
gamjatang wrote:
From the question, we can notice ;

451 <= x <= 550
351 <= y <= 450
---------------
802 <= x+y <= 1000

( statement 1) x < 500

451 <= x < 500
351 <= y <= 450
---------------------
802 <= x+y < 950

( statement 2) y < 400

451 <= x <= 550
351 <= y < 400
---------------------
802 <= x+y < 950

So my guess is D.

btw, just a small comment:
I think x is not nescessarily >=451 ....it can be>= 450.00000000000000000........1 coz the stem statement doesn't say that x is an integer . Similar to y.. A little change doesn't do harm to the whole reasoning process anyway
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27 Oct 2005, 05:29
laxieqv wrote:
gamjatang wrote:
From the question, we can notice ;

451 <= x <= 550
351 <= y <= 450
---------------
802 <= x+y <= 1000

( statement 1) x < 500

451 <= x < 500
351 <= y <= 450
---------------------
802 <= x+y < 950

( statement 2) y < 400

451 <= x <= 550
351 <= y < 400
---------------------
802 <= x+y < 950

So my guess is D.

btw, just a small comment:
I think x is not nescessarily >=451 ....it can be>= 450.00000000000000000........1 coz the stem statement doesn't say that x is an integer . Similar to y.. A little change doesn't do harm to the whole reasoning process anyway

True, true.
Deep insight!

If we want to get 51, it's very important not to take for granted that those numbers are integers.
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27 Oct 2005, 05:48
I think it is E.

x â‚¬ (450,550)
y â‚¬ (350,450)

(1) x â‚¬ (450,500)
y â‚¬ (350,450)
x+y â‚¬ (800,950) Closest multiple of 100: 800 or 900

(2) x â‚¬ (450,550)
y â‚¬ (350,400)
x+y â‚¬ (800,950) Closest multiple of 100: 800 or 900

(1)+(2) Same thing.
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27 Oct 2005, 07:49
gamjatang wrote:
From the question, we can notice ;

451 <= x <= 550
351 <= y <= 450
---------------
802 <= x+y <= 1000

( statement 1) x < 500

451 <= x < 500
351 <= y <= 450
---------------------
802 <= x+y < 950

( statement 2) y < 400

451 <= x <= 550
351 <= y < 400
---------------------
802 <= x+y < 950

So my guess is D.

gamjatang nailed it. I think D has got to be the answer.
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27 Oct 2005, 10:09
Quote:
gamjatang nailed it. I think D has got to be the answer.

Doesnt "802 <= x+y < 950" mean that either 800 or 900 could be the closest multiple to x+y? Ie each one on their own is insufficient.
Manager
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27 Oct 2005, 10:18
Here is my attempt:

450 =< x < 550
350 =< y < 450

--
800 =< y+x < 1000

St 1: x < 500

450 =< x < 500
350 =< y < 450

800 =< y+x < 950 -insuff - closest multiple is either 900 or 800

St 2: y < 400

450 =< x < 550
350 =< y < 400

800 =< y+x < 950 insuff - closest multiple is either 900 or 800

St. 1 + 2 together

450 =< x < 500
350 =< y < 400
800 =< y+x < 900 insuff - closest multiple is either 900 or 800

so I would say E.
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27 Oct 2005, 11:19
I agree w/ the explanation above... E
27 Oct 2005, 11:19
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# If 500 is the multiple of 100 that is closest to x and 400

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