GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 12 Dec 2018, 01:46

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
• ### GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 09 Feb 2011
Posts: 9
Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

### Show Tags

Updated on: 04 Aug 2017, 23:16
9
91
00:00

Difficulty:

85% (hard)

Question Stats:

55% (01:30) correct 45% (01:55) wrong based on 2825 sessions

### HideShow timer Statistics

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, 01:26. Last edited by Bunuel on 04 Aug 2017, 23:16, edited 3 times in total. Edited the question and added the OA. ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 51115 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 11 Feb 2011, 02:50 20 24 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: 80 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 16 Feb 2012, 07:47 7 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
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

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

### Show Tags

10 Mar 2011, 04:42
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 !!!
_________________

Set out each day believing in your dreams.
Know without a doubt that you were made for amazing things.

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 742
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

### Show Tags

10 Mar 2011, 06:22
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 Joined: 02 Sep 2009 Posts: 51115 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 13 Jun 2013, 01:15 2 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: 684 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 15 Jun 2013, 13:13 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
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Manager
Joined: 26 Jan 2015
Posts: 79
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

### Show Tags

28 Nov 2015, 03:50
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'?
_________________

Kudos is the best way to say Thank you! Please give me a kudos if you like my post

Math Expert
Joined: 02 Sep 2009
Posts: 51115
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

### Show Tags

28 Nov 2015, 06:59
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.
_________________
Intern
Joined: 02 Oct 2014
Posts: 8
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

### Show Tags

23 Dec 2015, 06:42
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?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8662
Location: Pune, India
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

### Show Tags

16 Mar 2016, 06:35
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]+5[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. _________________ [b]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: 26 Oct 2016 Posts: 6 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 08 Jan 2017, 17:51 I thought about this conceptually. Since A costs$3 per kg and B costs $5 per kg, I used that in conjunction with statement 2 to prove sufficiency. In statement 2, 10kg of K is less than$40. Dividing both sides by 10, 1 kg of K is less than $4. Knowing the costs of X and Y, that to me would mean that there would have to be more of A than B to be less than$4 (equal amounts would have it equal $4). It's not perfect as we could be dealing with integers and you can't assume one of A or B isn't 0....but it's how I went about it. Intern Joined: 29 Mar 2017 Posts: 2 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 05 Apr 2017, 09:35 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 Moderator Joined: 21 Jun 2014 Posts: 1092 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 05 Apr 2017, 10:34 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. _________________ --------------------------------------------------------------- Target - 720-740 Project PS Butler - https://gmatclub.com/forum/project-ps-butler-practice-everyday-280904.html http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html Intern Joined: 30 Mar 2017 Posts: 15 Location: India GMAT 1: 700 Q50 V34 GPA: 4 WE: Investment Banking (Investment Banking) Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 04 Aug 2017, 23:13 We can work this out using weighted average method as well. Statement A: y>4 - clearly insufficient. Statement B: Cost of 10kg of Material K is less than$40.

Cost of A is $3/kg and of B is$5/kg. Average cost of 10 kgs of combined material is <$4 ($40/10kgs). Using weighted average method:

3------------------------5
l------------4
Weighted average is less than 4, which means ratio of quantity of A:B i.e. x:y is skewed towards A. Thus, x>y.
Senior Manager
Joined: 29 Jun 2017
Posts: 467
GPA: 4
WE: Engineering (Transportation)
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

### Show Tags

17 Aug 2017, 02:23
1) A 3$. B 5$.

x+y =10
x. 5 4 3
y. 5 6 7

x=y and x<y. Insufficient A,D gone

2) A 3 $and B 5$
suppose all material is A then cost will be 30 $when x=10 suppose all material is B then cost will be 50$ when y = 10
and when x=y=5 equal the cost is 40 $now since it is given that cost < 40$ means proportion of A is more than B

x>y clearly B is sufficient

_________________

Give Kudos for correct answer and/or if you like the solution.

Manager
Joined: 13 Mar 2013
Posts: 164
Location: United States
GPA: 3.5
WE: Engineering (Telecommunications)
Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram  [#permalink]

### Show Tags

17 Aug 2017, 08:44
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 _________________ Regards , Intern Joined: 19 Mar 2015 Posts: 41 Location: India Concentration: Marketing, International Business Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 19 Aug 2017, 00:03 Very nice Question ... I got it wrong because I didn't calculated statement 2 fully. I have come down to below points: 3x+7Y<40, 4x+6Y<40 and so on but I didn't solve without knowing that all will give the solution x>5. and as x+y is 10, x must be 6 and here we get the answer. Kudos to the question. Senior Manager Joined: 19 Oct 2012 Posts: 323 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 29 Aug 2017, 11:13 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.