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Register now and save up to $200 Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code ## DS OG 13th 105 problem This topic has 2 expert replies and 2 member replies sohailmbaprep Senior | Next Rank: 100 Posts Joined 23 Feb 2012 Posted: 59 messages #### DS OG 13th 105 problem Sat Sep 15, 2012 12:06 am Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) Material A costs$3 /kg ,and MAterial B costs $5/kg .If 10Kg of material K consists of X kilograms of Material A and y Kg of Material B,is x>y ? 1) y>4 2) the cost of the 10kg of material K is less than$40.

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### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Sat Sep 15, 2012 12:26 am
Quote:
Material A costs $3 per kilogram, and material B costs$5 per kilogram. If 10 kilograms
of material K consists of x kilograms of material A and y kilograms of material B, is x >
y?
(1) y > 4
(2) The cost of the 10 kilograms of material K is less than $40. Since statement 1 is in terms of y, we should rephrase the question stem in terms of y. x = the number of kilograms of A. y = the number of kilograms of B. Since a total of 10 kilograms are purchased: x + y = 10. x = 10-y. Substituting x=10-y into the question stem (Is x>y?), we get: 10-y > y? 10 > 2y? 5 > y? Question rephrased: Is y < 5? Statement 1: y>4. Since it's possible that y=4.5 or that y=6, no way to determine whether y<5. INSUFFICIENT. Statement 2: The cost of the 10 kilograms of material K is less than$40.
Since the cost of each of the x kilograms is $3 and the cost of each of the y kilograms is$5, we get:
3x + 5y < 40.

Substituting x=10-y into 3x+5y<40, we get:
3(10-y) + 5y < 40
30 - 3y + 5y < 40
2y < 10
y < 5.
SUFFICIENT.

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GMATGuruNY GMAT Instructor
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Sat Sep 15, 2012 2:54 am
Quote:
Material A costs $3 per kilogram, and material B costs$5 per kilogram. If 10 kilograms
of material K consists of x kilograms of material A and y kilograms of material B, is x > y?
(1) y > 4
(2) The cost of the 10 kilograms of material K is less than $40. One more approach. Since 10 kilograms are purchased, x+y = 10. Statement 1: y>4 It's possible that y=5 and that x=5, in which case x=y. It's possible that y=4.5 and that x=5.5, in which case x>y. INSUFFICIENT. Statement 2: The cost of the 10 kilograms of material K is less than$40.
If 10 kilograms are purchased at a total cost of $40, the average cost per kilogram = 40/10 =$4.
Since the total cost here is actually LESS than $40, the average cost per kilogram is less than$4 -- LESS THAN HALFWAY between x ($3) and y ($5).
For the average cost to be LESS THAN HALFWAY between x and y, more of x must be purchased, implying that x>y.
SUFFICIENT.

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sarawutc Newbie | Next Rank: 10 Posts
Joined
31 Mar 2013
Posted:
5 messages
Wed Jul 24, 2013 11:55 am
Hi Experts,
I have one question as for this question.
The two statements are contradictory right ?
I thought we wouldn't confront this situation in GMAT though.

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Wed Jul 24, 2013 7:41 pm
Hi sarawutc,

The two Facts/statements in DS questions will NOT be contradictory, but one of them may contain "options" that the other does not.

In this question:

Fact 1 tells us that y > 4
Fact 2 tells us that y < 5

While your first reaction might be to call these two Facts contradictory, they're not....

IF you were dealing with a DS question that required you to Combine Facts, then there will be at least one possible answer (it's just that sometimes there's more than 1 answer and you're responsible to find those possibilities).

In this case, y could = 4.01, 4.5, 4.999999, etc.

GMAT assassins aren't born, they're made,
Rich

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