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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: 63
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
4
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Difficulty:

45% (medium)

Question Stats:

64% (01:46) correct 36% (01:01) wrong based on 224 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. Senior RC Moderator Status: It always seems impossible until it's done!! Joined: 29 Aug 2012 Posts: 1173 Location: India 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: 127 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: 10
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.
Re: Jose purchased several large and small dressers at a flea market to ad   [#permalink] 24 May 2018, 13:18
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