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Intern  Joined: 09 Feb 2011
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Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 55% (02:08) correct 45% (02:36) wrong based on 2829 sessions

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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. Originally posted by alltimeacheiver on 11 Feb 2011, 02:26. Last edited by Bunuel on 05 Aug 2017, 00:16, edited 3 times in total. Edited the question and added the OA. ##### Most Helpful Expert Reply Math Expert V Joined: 02 Sep 2009 Posts: 59727 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 25 32 alltimeacheiver 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

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?

Given: x+y=10. Question: is x>y?

(1) y > 4. Clearly insufficient: if y=4.5<x=5.5 the answer will be YES but if y=6>x=4 the answer will be NO.

(2) The cost of the 10 kilograms of material K is less than $40 ---> 3x+5y<40, as y=10-x then: 3x+5(10-x)<40 --> 2x>10 --> x>5, so x>y. Sufficient. Answer: B. _________________ ##### Most Helpful Community Reply Manager  Status: Employed Joined: 17 Nov 2011 Posts: 78 Location: Pakistan Concentration: International Business, Marketing GMAT 1: 720 Q49 V40 GPA: 3.2 WE: Business Development (Internet and New Media) Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 8 2 The answer has to be B. Let's setup the weighted average equation for this question: $$x$$ kilograms at 3$ per Kilogram
$$y$$ kilograms at 5$per Kilogram Yields $$10$$ kilograms at z$ per Kilogram
We also know that $$x+y=10$$
So Equation would be : $$3(x)+5(y)=10(z)$$

Now let's look at the statements:

Statement 1: $$y>4$$

Remember: $$x+y=10$$
So: $$x$$ could range between 0 and 6. Insufficient

Statement 2: Cost is $$<40$$

So $$3(x)+5(y)<40$$
But $$x+y=10$$ so $$x=10-y$$
So $$3(10-y)+5(y)<40$$
So $$30-2y+5y<40$$
So $$2y<10$$
So $$y<5$$

If $$y<5$$ then $$x>5$$ so $$x>y$$ Sufficient

Hence B
##### General Discussion
Intern  Joined: 21 Feb 2011
Posts: 1
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

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5
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 $40. Solution: - 1) Insufficient Material A cost 3$/kg and B cost 5$/kg x+y=10 and y>4 is all we have from statement 1. Since the total price is not fixed, (x,y) can be anything satisfying x+y=10 ....even (5,5) can't be wrong in this case 2) Sufficient Material A cost 3$/kg and B cost 5$/kg x+y=10 and the cost of 10kg of K is less than$40.
Therefore, 3x+5y<40 => 3x+(10-x)5<40 => 10<2x => 5<x
So, x>5 and x+y=10 means x>y

Hope it helps !!!
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Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

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3
x = 10 - y
Rephrasing the question - Is x > y?
or Is 10 - y > y
Is y < 5 ?

1. Insufficient
2. Sufficient
3x + 5y < 40
3(10 - y) + 4y < 40
2y < 10
Hence y < 5

Hence B.
alltimeacheiver 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 Math Expert V Joined: 02 Sep 2009 Posts: 59727 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 2 3 Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE All DS Mixture Problems to practice: search.php?search_id=tag&tag_id=43 All PS Mixture Problems to practice: search.php?search_id=tag&tag_id=114 _________________ Director  Joined: 25 Apr 2012 Posts: 651 Location: India GPA: 3.21 WE: Business Development (Other) Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 2 alltimeacheiver 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.

Material K cost "C" can be found out by calculating

C= (3*x+5*y)/10

Now the cost C will be close to Material A cost if x is more than y and vice versa

from St 1 we have y>4
For eg y=5, x=5 Cost of Material K will be $4/kg (in between price of Material A and Material B) now if x=4,y=6 ,Cost of material K will be be$ 4.2/kg
if x=1,y=9 then Cost of material will be 4.8$per kg but if we take y=4 and x=6 we get cost of material K as$ 3.8 per kg less than $4 which would have been the price had both material A and B were added equally. Therefore if x>y we should have price of Material K <$ 4kg

Hence St1 alone not sufficient as we can have x=y or x<y

St 2, The cost of the 10 kilograms of Material K is less than $40.[/quote] Cost of Material per kg <$4 which meets our above requirement which means x>y

Therefore ans st B
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Manager  S
Joined: 26 Jan 2015
Posts: 92
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

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Bunuel wrote:
alltimeacheiver 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 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? Given: x+y=10. Question: is x>y? (1) y > 4. Clearly insufficient: if y=4.5<x=5.5 the answer will be YES but if y=6>x=4 the answer will be NO. (2) The cost of the 10 kilograms of material K is less than$40 ---> 3x+5y<40, as y=10-x then: 3x+5(10-x)<40 --> 2x>10 --> x>5, so x>y. Sufficient.

Hi...If in the question it is mentioned that x and y are integers, then will the answer be D? because it will lead to contradiction that 'x is not greater than y' or will still answer be b because (there is no clarity whether x may be equal to y or may be less than y'?
Math Expert V
Joined: 02 Sep 2009
Posts: 59727
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

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2
Alok322 wrote:
Bunuel wrote:
alltimeacheiver 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 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? Given: x+y=10. Question: is x>y? (1) y > 4. Clearly insufficient: if y=4.5<x=5.5 the answer will be YES but if y=6>x=4 the answer will be NO. (2) The cost of the 10 kilograms of material K is less than$40 ---> 3x+5y<40, as y=10-x then: 3x+5(10-x)<40 --> 2x>10 --> x>5, so x>y. Sufficient.

Hi...If in the question it is mentioned that x and y are integers, then will the answer be D? because it will lead to contradiction that 'x is not greater than y' or will still answer be b because (there is no clarity whether x may be equal to y or may be less than y'?

If we were told that x and y are integers then y > 4 (5, 6, 7, ...) together with x + y = 10, would be sufficient to say that x is NOT greater than y. But in this case the question would be flawed because the statements would contradict each other which never happens in proper GMAT DS questions.

Hope it's clear.
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Intern  Joined: 02 Oct 2014
Posts: 8
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

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1
Thank you Buennel!

Very important point since i came here with the same problem and i pulled my hair over this for a solid 20 minutes.

If you simplify (2) it results in y < 5. While (1) says that y > 4.

Contradicting? No. We might think its contradictory if we assume that the qty involved are integers (common mistake, since qty usually are).

Do note that the question does not say that x or y are integers. And it is for this reason, otherwise, the question would logically be incorrect.

My takeaway:
1) Always remember that GMAT statements are never contradictory
2) If at some point, it seems like they are contradicting, it could mean
a) i've done it incorrectly
b) they aren't contradicting in the first place! :p
3) In such WP questions, ask yourself, are the quantities divisible into decimals?
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Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

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1
alltimeacheiver 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. Responding to a pm: Quote: In solving the B part of this question (like in many situation i have faced) 3+5=15+25="40<40" This is my question: [Q-1] Can we ever take 40<40 ie x<x when x is same number. Similarly x>x and so on in GMAT? To be honest, I am not sure what your question means. 40 < 40 is not correct and neither is x < x since both are equal. And no, x > x doesn't work either. If they are the same number, one cannot be greater than the other. You might want to show me the steps of where you come across this problem. _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Intern  Joined: 29 Mar 2017 Posts: 2 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags I have a question, the question provide 10=x+y, it's about the weight but it doesn't mean 3x+5y<40 (money), cuz 40=10k, we don't know the unit price of k, so i don't think it's right. Is there anything wrong of me? I was confused a litte...hehe Retired Moderator V Joined: 22 Jun 2014 Posts: 1090 Location: India Concentration: General Management, Technology GMAT 1: 540 Q45 V20 GPA: 2.49 WE: Information Technology (Computer Software) Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 1 dxhzhu wrote: I have a question, the question provide 10=x+y, it's about the weight but it doesn't mean 3x+5y<40 (money), cuz 40=10k, we don't know the unit price of k, so i don't think it's right. Is there anything wrong of me? I was confused a litte...hehe x + y = 10 ---equation (1) from stmt-2 we can say 3x + 5y < 40 multiply equation (1) by 3 and you get 3x + 3y = 30 3x + 5y < 40 (to subtract the below equation, consider < as = sign) 3x + 3y = 30 2y < 10 (isnt it? because if you subtract 30 from somthing less than 40 then you get something less than 10) hence y < 5, it means x > y because x + y = 10 so B is correct. Hope your doubt is clear. _________________ Senior Manager  G Joined: 19 Oct 2012 Posts: 256 Location: India Concentration: General Management, Operations GMAT 1: 660 Q47 V35 GMAT 2: 710 Q50 V38 GPA: 3.81 WE: Information Technology (Computer Software) Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags alltimeacheiver 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.

The question can solved using weighted average concept easily without pen and paper calculation i.e can be solved within 30 seconds.

10kg of mixture uses x kg of Material A and y kg of Material B. If both X and Y are equal, the cost of the 10kg of material K will be right in the middle of $30 and$50 i.e. at $40. But using stmt B, 10kg of K costs less than$40 dollars i.e. the cost shift towards $30. Hence clearly the quantity of X is more and Y. Hence B is sufficient. I hope that helps. _________________ Citius, Altius, Fortius Intern  S Joined: 11 Sep 2017 Posts: 36 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 2 mixture price is less than 40/10 -- rs 4 per kg between 3 and 5 if less than 4 then it contains more x thats all simple Retired Moderator V Joined: 27 Oct 2017 Posts: 1326 Location: India Concentration: International Business, General Management GPA: 3.64 WE: Business Development (Energy and Utilities) Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags (1) y > 4 here difference cases possible: a) x= 5.5, y = 4.5 : x>y b) x=y=5 : x=y c) x= 4, y =6 : x<y so it is not sufficient. (2) The cost of the 10 kilograms of Material K is less than$40.
it means the cost per kg of mixture = 40/10 =4.
which is the average of cost of individual ingredients : (5+3)/2 = 4
hence if if both x = y , unit cost of mixture = 4
Since unit cost of mixture is less than 4, the ingredient of lesser cost is present in higher proportion.
Hence , x>y

Sufficient.

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

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Hi,

1 doubt... no where in the question it is mentioned that material K consists only of material A and B. What if it has some other type of material as well ? Is this a OG question?

Thanks
Dpz
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Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

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1
Hi
"If 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B"-It means that mixture has only 2 components A & B.
Consists of - to be made of or formed from something:Source:https://dictionary.cambridge.org/dictionary/english/consist-of-sth
It gives all the constituents.

Example:
If a Box contains 2 black and 3 white balls. We are not sure whether balls of other colors are present in the box.
But if a Box comprises/consists of 2 black and 3 white balls, it is certain that no other ball is in the box.

If you have seen any Official question testing your point of concern , please post here.

2) Yes it is an OG Question.

Dpzskr wrote:
Hi,

1 doubt... no where in the question it is mentioned that material K consists only of material A and B. What if it has some other type of material as well ? Is this a OG question?

Thanks
Dpz

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

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It's clear what the correct answer choice is and how to solve this problem. I think this question is odd though. Typically the 2 DS statements do not contrast each other; whereas, in this question, the two statements cannot both be right. Interesting.

And as Bunuel pointed out here below, this rule was actually not violated since the two statements can both be right as x and y do not have to be integers.
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$90/hour as of August 2019. I am not accepting any more students for the Fall 2019 application cycle, but if you are planning to apply in 2020, feel free to reach out! http://www.facebook.com/HanoiGMATtutor HanoiGMATTutor@gmail.com Originally posted by HanoiGMATtutor on 01 Sep 2019, 15:20. Last edited by HanoiGMATtutor on 03 Sep 2019, 16:36, edited 1 time in total. Math Expert V Joined: 02 Sep 2009 Posts: 59727 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags HanoiGMATtutor wrote: It's clear what the correct answer choice is and how to solve this problem. I think this question is odd. Typically the 2 DS statements do not contrast each other; whereas, in this question, the two statements cannot both be right. Interesting. Actually the statements do not contradict each other. Consider x = 5.5 and y = 4.5. The would contradict if we assume that a and y are integers but we are not told that they are. _________________ Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] 01 Sep 2019, 20:57 Go to page 1 2 Next [ 24 posts ] Display posts from previous: Sort by # Material A costs$3 per kilogram, and Material B costs \$5 per kilogram  