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# Jose purchased several large and small dressers at a flea market to ad

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Manager
Joined: 17 Apr 2013
Posts: 56
Location: United States
Concentration: Other, Finance
Schools: SDSU '16
GMAT 1: 660 Q47 V34
GPA: 2.76
WE: Analyst (Real Estate)
Jose purchased several large and small dressers at a flea market to ad  [#permalink]

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15 Sep 2014, 01:25
1
6
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:43) correct 33% (01:27) wrong based on 307 sessions

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Jose purchased several large and small dressers at a flea market to add to his antique furniture
collection. The large dressers cost $31 apiece, while the small dressers cost$25 apiece. If Jose did not
purchase any other items at the flea market, how many small dressers did he buy?

1) Jose purchased as many small dressers as large dressers.

2) In total, Jose spent $280 at the flea market. _________________ Please +1 KUDO if my post helps. Thank you. ##### Most Helpful Expert Reply Math Expert Joined: 02 Aug 2009 Posts: 7742 Jose purchased several large and small dressers at a flea market to ad [#permalink] ### Show Tags 05 Sep 2018, 19:39 3 1 alphak3nny001 wrote: Jose purchased both large dressers and small dressers to add to his antique furniture collection. The large dressers cost$31 each, while the small dressers cost $25 each. If Jose did not purchase any other items, how many small dressers did he buy? (1) Jose purchased as many small dressers as large dressers. (2) In total, Jose spent$280 at the flea market

Merging topics..

Otherwise solution...

Info from main stem
Cost = $$31l+25s$$

(1) Jose purchased as many small dressers as large dressers.
l and s could be any value
Insufficient

(2) In total, Jose spent $280 at the flea market $$31l+25s=280$$.... Since we have 25 and 280 in two terms, l must be a multiple of 5.. So if $$l=5......31*5+25s=280......25s=280-155=125......s=\frac{125}{25}=5$$ Case possible l=s=5 Say l is next multiple 10 then $$31*10+25s=280$$...not possible Only possibility $$l=s=5$$ Sufficient B _________________ ##### General Discussion Current Student Status: Chasing my MBB Dream! Joined: 29 Aug 2012 Posts: 1112 Location: United States (DC) WE: General Management (Aerospace and Defense) Re: Jose purchased several large and small dressers at a flea market to ad [#permalink] ### Show Tags 15 Sep 2014, 11:53 1 clipea12 : Statement 1 : It doesn't say any information about how many small dressers did jose bought. Apart from saying, Number of small= number of large. So insufficient. Statement 2: It says total amount is 280 dollars. let, L=large & S=small. 31L + 25S= 280. It may look insufficient in the beginning. But if you look closely, and plugging values you can find. If S=10 and L=1. We get 281. So the total number of large and small dressers should be less 11. So if you continue doing that, we get only one value gives us 280, that is 5. 31*5 + 25*5= 155+ 125=280. Other method is that when you add the unit digit of multiple of 31 and multiple of 25 should give us 0 and it should be 280 as well. When you multiply 25 with any number the unit digit will either be 0 or 5. Never other numbers so we can eliminate- 1 to 9(apart from 5). And if unit digit is 0. then unit digit for multiple of 31 also be 0. But we get only in 310. So unit digit of 25 cannot be 0. you can go about like this and find that only when we multiple 5 to both 31 and 25. We get a sum of 280. Statement 2 is sufficient. How to check, whether 5 will be only number?. Well, we can now look at statement-1(NOTE: Just to verify, not while solving). In GMAT, the both statements never contradicts each other. St.1 says Number of large dresser=Number of small dresser. So 5 is the number of small dresser. _________________ Manager Status: I am not a product of my circumstances. I am a product of my decisions Joined: 20 Jan 2013 Posts: 109 Location: India Concentration: Operations, General Management GPA: 3.92 WE: Operations (Energy and Utilities) Re: Jose purchased several large and small dressers at a flea market to ad [#permalink] ### Show Tags 15 Sep 2014, 23:04 1 clipea12 wrote: Jose purchased several large and small dressers at a flea market to add to his antique furniture collection. The large dressers cost$31 apiece, while the small dressers cost $25 apiece. If Jose did not purchase any other items at the flea market, how many small dressers did he buy? 1) Jose purchased as many small dressers as large dressers. 2) In total, Jose spent$280 at the flea market.

Let number of small dressers be "S"
Number of large dressers be "L"

Here the idea is to understand that the dressers have to take a positive integer value.

Statement 1)

the statement only tells us that S = L and nothing else.

Say L=S= 6, then 25*S + 31*L = 25*6 + 31*6 = 336
If L=S= 5, then 25*S + 31*L = 25*5 + 31*5 = 280

So, nothing can be concluded from this statement. Hence, Statement 1 is "Insufficient"

Statement 2)

This statement tells us that 25*S + 31*L = 280

Now we know that the number of dressers is an integer value and that total cost of both dressers is 280

So there is only one value that satisfies this condition when S=5 & L=5

Hence Statement 2 is " Sufficient "

Intern
Joined: 18 Aug 2017
Posts: 30
GMAT 1: 670 Q49 V33
Re: Jose purchased several large and small dressers at a flea market to ad  [#permalink]

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25 Aug 2017, 20:10
Let number of small dresser is x, number of large dresser is y
We need to find x

Statement 1: x=y. INSUFF, x and y could be any number

Statement 2: We know the price of each unit so we can set up the equation as

25x + 31y = 280.
or x = $$\frac{(280-31y)}{25}$$

In order for x to be an interger, 280-31y must be divisible by 25.
All multiple of 25 has 5 or 0 as its last digit, to make (280 - 31y) has 5 or 0 as the last digit 31y must have 0 or 5 as the last digit. Therefore y can be 0, 5, 10, 15, etc..
y can't be 0, and if y = 10 then 31y > 280. Therefore only y= 5 is possible.
y =5 then x = 5.

SUFF

Intern
Joined: 09 Apr 2018
Posts: 20
Re: Jose purchased several large and small dressers at a flea market to ad  [#permalink]

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24 May 2018, 13:18
Once you think that 31L + 25S = 280, since 25S is a multiple of 25, therefore whatever the expense on Large ones, it has to have a 5 or 0 at the units place.
For Units digit of 31L to be 5, Only one possible solution, L=5 below 280. L cant be Zero, if L is 10, 31L = 310 which is not possible.
Total expense on L = 31*5=155
Remaining Amount = (280-155)=125, 25S=125 => S = 5
B Sufficient.
Intern
Joined: 03 Apr 2018
Posts: 41
GMAT 1: 750 Q50 V41
Jose purchased both large dressers and small dressers  [#permalink]

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05 Sep 2018, 19:26
1
Jose purchased both large dressers and small dressers to add to his antique furniture collection. The large dressers
cost $31 each, while the small dressers cost$25 each. If Jose did not purchase any other items, how many small

(1) Jose purchased as many small dressers as large dressers.

(2) In total, Jose spent $280 at the flea market Manager Joined: 16 Sep 2011 Posts: 91 Jose purchased several large and small dressers at a flea market to ad [#permalink] ### Show Tags 05 Sep 2018, 19:44 1 alphak3nny001 wrote: Jose purchased both large dressers and small dressers to add to his antique furniture collection. The large dressers cost$31 each, while the small dressers cost $25 each. If Jose did not purchase any other items, how many small dressers did he buy? (1) Jose purchased as many small dressers as large dressers. (2) In total, Jose spent$280 at the flea market

Option A: Jose purchased as many small as large, so small can be 1 dress, 2 dress and so on....we cannot zero in at a particular number

Option B: Jose spent $280 and did not purchase any other items Lets says number of large dress= x and number of small dress=y so, 31x + 25y =280 now if you look at it the highest number of small dress that can be purchased is 11 as 11*25=$275 but in this fashion Jose will not be able to spend $280, similar highest large dress can be bought as 9*31=$279 , still $1 will be left Hence there needs to be a split between the two, now$25 will have either 5 or 0 at the end in its multiple, while $31 has all the numbers from 1 to 9 at the end in its multiple. How can we have those multiples of 25 an 31 which when added gives 0 at the end as we need$280 in total.....
Only 2 ways possible, either 5 from $25 multiple and 5 from$31 multiple.... or 0 from $25 multiple and 0 from$31 multiple....but $31 multiple cant come with 0 at the end as maximum large dress can be only 9 not 10. Multiple of$31 possible in this scenario is only 5*$31=$155 so for small left amount will be $280-$155= \$125.....

So small dress number will be 5....

Hence B is sufficient

Jose purchased several large and small dressers at a flea market to ad   [#permalink] 05 Sep 2018, 19:44
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