Material A costs $3 per kilogram, and material B costs$5 : GMAT Data Sufficiency (DS)
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# Material A costs $3 per kilogram, and material B costs$5

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Director
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Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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13 Aug 2009, 14:55
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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. [Reveal] Spoiler: OA _________________ http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902 Last edited by Bunuel on 13 Oct 2014, 06:40, edited 4 times in total. Edited the question and added the OA Manager Joined: 25 Jul 2009 Posts: 116 Schools: NYU, NUS, ISB, DUKE, ROSS, DARDEN Followers: 5 Kudos [?]: 224 [0], given: 17 Re: Material A costs$3 per kilogram, and material B costs $5 [#permalink] ### Show Tags 13 Aug 2009, 15:10 tejal777 wrote: 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.

umm...(D) is it??

Yeah...its D.

St1:
if y>4, then x =< 5
=> x =< y
=> SUFFICIENT

St2:
If 10 kg of material k cost $40, then x = y = 5 But if it costs less than$40 then y < 5 => x > 5
=> SUFFICIENT

ANS: D
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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13 Aug 2009, 20:49
What if x = 4.9 kgs and y = 4.1 kgs? How do you know that material k consists materials A and B only in whole kgs?

B is not a big deal.

samrus98 wrote:
tejal777 wrote:
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. umm...(D) is it?? Yeah...its D. St1: if y>4, then x =< 5 => x =< y => SUFFICIENT St2: If 10 kg of material k cost$40, then x = y = 5
But if it costs less than $40 then y < 5 => x > 5 => SUFFICIENT ANS: D _________________ Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html GT Manager Joined: 25 Jul 2009 Posts: 116 Schools: NYU, NUS, ISB, DUKE, ROSS, DARDEN Followers: 5 Kudos [?]: 224 [1] , given: 17 Re: Material A costs$3 per kilogram, and material B costs $5 [#permalink] ### Show Tags 14 Aug 2009, 03:14 1 This post received KUDOS yezz wrote: samrus98 wrote: tejal777 wrote: 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.

umm...(D) is it??

Yeah...its D.

St1:
if y>4, then x =< 5
=> x =< y
=> SUFFICIENT

St2:
If 10 kg of material k cost $40, then x = y = 5 But if it costs less than$40 then y < 5 => x > 5
=> SUFFICIENT

ANS: D

Can you plz explain why we are excluding non intiger values for x,y? thanks

Its a mistake.

X & Y can take non-integer values as well and that makes St1 insufficient.
Revised ANS: B
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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17 Sep 2009, 10:13
B. couple of examples:
x=4, y=6, sum>40. not satisfies
x=5, y=5, sum =40. not satisfies
x=6, y=4, sum<40. satisfies
non-integers should be taken into account as well. However, they all satisfy this.
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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23 Sep 2009, 14:53
x=3, y=6 <40
x=8, y=3 <40

B is not sufficient.

Am I missing something?
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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24 Sep 2009, 08:51
tejal777 wrote:
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. umm...(D) is it?? Hi, From the stem we have: X (MAT A) + Y (MAT B) =10 (i) and 3X+5Y=TOTAL COST. (II) FOR (1): Y>4. Y=4,1 and X=5,9 OR Y=6 and X=4 (INSUFFI) FOR (2): 3X+5Y<40 ; 40*(I) => 40X+40Y=40 ; We have that 3x+5y< 40X+40Y => -37x<35y; Again (X+Y=10)=> X=6,Y=4 or X=4,Y=6 We dont know really. (INSUFFI) FOR (1) and (2) => The same, we dont any more information! FOR THIS, IMO (E) Director Joined: 25 Oct 2008 Posts: 608 Location: Kolkata,India Followers: 12 Kudos [?]: 766 [0], given: 100 Re: Material A costs$3 per kilogram, and material B costs $5 [#permalink] ### Show Tags 19 Oct 2009, 23:57 Came back to the question again:( 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.

OE says:
Since x + y = 10, the relation x > y is equivalent to
x > 10 – x, or x > 5.
(1) The given information is consistent with
x = 5.5 and y = 4.5, and the given
information is also consistent with x = y = 5.
Therefore, it is possible for x > y to be true
and it is possible for x > y to be false; NOT
sufficient.

How can we take the case of x = y = 5 when we know x>5??
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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20 Oct 2009, 01:48
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X + Y = 10

3X + 5Y < 40

Now 3X + 5Y = 3( X + Y ) + 2Y = 30 + 2Y < 40
=> 2Y < 10
=> Y < 5

that means x must be > 5 .

Now to check whether if X > Y can be solved if we can find the range of Y then we can check whether X >y or not as both will sum up to 10.

Since equation 1 and 2 both give the range of Y...thus both are individually sufficient.

Ans is D , OA pls
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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20 Oct 2009, 02:05
Oh yea Ans is B

as if y >4

y = 10-x > 4 ==> 6 > x thus its not sufficient....
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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20 Oct 2009, 07:19
for me it's A

1)
y > 4 => y >= 5

y = 5 x = 5 => x = y
y = 6 x = 4 => x < y

in both case x is not > y

2) 3x + 5(10 - x) <= 40

=> x >= 5

x = 5 y = 5
x = 6 y = 4

=> x >=y so it is not sufficient

ans is then A

what is OA?

EDIT

Dam it' !!! less than 40 means < 40... B is then suffiscient too
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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20 Oct 2009, 07:28
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pierrealexandre77 wrote:
for me it's A

1)
y > 4 => y >= 5

y = 5 x = 5 => x = y
y = 6 x = 4 => x < y

in both case x is not > y

2) 3x + 5(10 - x) <= 40

=> x >= 5

x = 5 y = 5
x = 6 y = 4

=> x >=y so it is not sufficient

ans is then A

what is OA?

EDIT

Dam it' !!! less than 40 means < 40... B is then suffiscient too

Its not given X n Y are integers , thus first condition is not sufficient
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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21 Oct 2009, 06:14
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I think i got a simplier explanation:

x + y = 10
1) y>4 : Y can be anything 4.2, 4.7, 6, 7. In this case, we can't determine if X is greater than 5.

2) Total cost of K is less than 40:

3x + 5y < 40
x + y = 10 ----> x = 10 - y

3(10 - y) + 5y < 40
30 - 3y + 5y < 40
2y < 10
y < 5

Since y is less than 5, we know that it can be 4.9 so X is greater than Y. B
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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23 Oct 2009, 04:11
mendelay wrote:
x=3, y=6 <40
x=8, y=3 <40

B is not sufficient.

Am I missing something?

Hi mendelay...

ur mising the condition X+ Y = 10.

so ur assumptions of x =3 and y =6 wont work out .so does 8 and 3.
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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06 Dec 2009, 09:18
Material A cost 3$/kg and B cost 5$/kg.
If 10 kg of material K consist of x kg of A and y kg of B, is x>y?

1- y>4

2- the cost of 10kg of K is less than $40. _________________ Senior Manager Joined: 30 Aug 2009 Posts: 286 Location: India Concentration: General Management Followers: 3 Kudos [?]: 156 [0], given: 5 Re: Material A costs$3 per kilogram, and material B costs $5 [#permalink] ### Show Tags 06 Dec 2009, 09:41 Hussain15 wrote: Material A cost 3$/kg and B cost 5$/kg. If 10 kg of material K consist of x kg of A and y kg of B, is x>y? 1- y>4 2- the cost of 10kg of K is less than$40.

B

1. insuff as y can be any value from 4.1kg to 9.9kg
2. cost of K per kg is less than $4 which means A will be more. hence suff Retired Moderator Status: The last round Joined: 18 Jun 2009 Posts: 1310 Concentration: Strategy, General Management GMAT 1: 680 Q48 V34 Followers: 77 Kudos [?]: 979 [0], given: 157 Re: Material A costs$3 per kilogram, and material B costs $5 [#permalink] ### Show Tags 06 Dec 2009, 09:45 kp1811 wrote: 2.cost of K per kg is less than$4 which means A will be more. hence suff

I didn't get this one. Can you kindly explain in detail?
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Re: Material A costs $3 per kilogram, and material B costs$5 [#permalink]

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06 Dec 2009, 09:58
Hussain15 wrote:
kp1811 wrote:
2.cost of K per kg is less than $4 which means A will be more. hence suff I didn't get this one. Can you kindly explain in detail? lets consider the below cases if x and y are equal i.e. 5kg then avg price of K will be = x* price of A + y* price of B = (5* 3 + 5*5)/10 =$4/kg.

now let x be 4kg then y is 6kg so avg price will be = (4* 3 + 6*5)/10 = $4.2/kg if x is 6kg then y is 4kg then avg price will be ( 6*3+ 4*5)/10 =$3.8/kg
so we can see that only if x>y then cost of K will be less than $4 note: avg price of K is same as cost of K Manager Joined: 06 Apr 2010 Posts: 143 Followers: 3 Kudos [?]: 637 [1] , given: 15 Material A costs$3 per kilogram, and material B costs $5 per kilogram [#permalink] ### Show Tags 12 Sep 2010, 06:24 1 This post received KUDOS 5 This post was BOOKMARKED 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.
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Re: Material A costs $3 per kilogram, and material B costs$5 per kilogram [#permalink]

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12 Sep 2010, 07:02
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We lnow first that x + y = 10.

(1) if y > 4 so we can have y = 4.5 kg and x = 5.5 kg (so y<x) or the oppositive : y = 5.5 kg and x = 4.5 kg (so x<y).
INSUFFICIENT

(2) we knows that 3x + 5y < 40 (1) . But we also know that x + y = 10 <=> 3x+3y = 30 (2).
By doing (2) - 1 we obtain 2y < 10 <=> y < 5kg. So, as x + y = 10, x > 5kg.

Thus, x > y. SUFFICIENT.

Last edited by alexn49 on 12 Sep 2010, 08:36, edited 1 time in total.
Re: Material A costs $3 per kilogram, and material B costs$5 per kilogram   [#permalink] 12 Sep 2010, 07:02

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