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# At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a

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Intern
Joined: 15 Dec 2015
Posts: 34
At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a  [#permalink]

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22 Dec 2015, 21:36
00:00

Difficulty:

65% (hard)

Question Stats:

69% (02:58) correct 31% (03:20) wrong based on 111 sessions

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At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a 20-pack for \$3.05, and a 250-pack for \$22.95. What is the greatest number of hot dogs you can buy at this store with \$200?

(A) 1,108

(B) 2,100

(C) 2,108

(D) 2,124

(E) 2,256

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Intern
Joined: 15 Dec 2015
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Re: At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a  [#permalink]

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22 Dec 2015, 21:40
If you know the answer to this question , plz explain how you got it by showing full working out ...

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Re: At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a  [#permalink]

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23 Dec 2015, 02:20
Price of 8-pack = \$1.55
Price of 20-pack = \$3.05
Price of 250-pack =\$22.95
Initially we need to check which of these packs will provide us with the highest value for money (Minimum unit price of a hot dog )
LCM of 8 , 20 and 250 is 1000
Total cost of 1000 hot dogs
-when all hot dogs are bought in 8-pack = 1.55* (1000/8) = 1.55 *125 = 193.75 \$
-when all hot dogs are bought in 20-pack = 3.05 * (1000/20) = 3.05 * 50 = 152.5 \$
-when all hot dogs are bought in 250-pack = 22.95 * 4 = 91.8 \$
At this step we know that in order to buy greatest number of hot dogs we need to maximize the number of 250 pack , then 20 pack and then 8 pack .( with the amount remaining after each successive steps)

To maximize number of hot dogs with 200\$
Total number of hot dogs bought in 250-pack = 22.95*8 =183.6\$
Amount remaining = 200 - 183.6 = 16.4\$
With this we can buy 5 of 20-pack = 3.05*5 15.25 \$
Amount remaining = 16.4 - 15.25 = 1.15\$
This amount is too less to buy any 8- pack .

Greatest number of hot dogs one can buy with 200 \$ = 250*8 + 20*5 = 2100

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Re: At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a  [#permalink]

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23 Dec 2015, 08:01
Thank You!!

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Re: At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a  [#permalink]

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23 Dec 2015, 17:09
Is there a 2 min solution for this problem? The above calculations seem time-intensive.
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Joined: 20 Feb 2015
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Re: At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a  [#permalink]

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24 Dec 2015, 05:02
price per hot dog in 1st case = \$0.19
Price per hot dog in 2nd case = \$0.152
Price per hot dog in 3rd case = \$0.091

the lowest being the 3rd
max number of hot dogs he can buy as per 3rd case =200/22.95 =8.714 = 8 -- > total hot dogs =8*250=2000
The answer should be > 2000
not much of a help
the money left = 200-183.6= \$16.4
he can now use the price in case 2
16.4/3.05 =5.3 = ~5 = 5*20 = \$100
money left=\$1.1 which is < the minimum required \$1.55
Thus total hot dogs = 2100

Too much calculation though !!
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Re: At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a  [#permalink]

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24 Dec 2015, 05:26
1
Anonamy wrote:
Is there a 2 min solution for this problem? The above calculations seem time-intensive.

Hi Anonamy,
Initially we need to check which of these packs will provide us with the highest value for money (Minimum unit price of a hot dog )

LCM of 8 , 20 and 250 is 1000
Total cost of 1000 hot dogs
-when all hot dogs are bought in 8-pack = 1.55* (1000/8) = 1.55 *125 = 193.75 \$
-when all hot dogs are bought in 20-pack = 3.05 * (1000/20) = 3.05 * 50 = 152.5 \$
-when all hot dogs are bought in 250-pack = 22.95 * 4 = 91.8 \$

Though i have shown the calculations here , you need not do the above on the test . One can use estimation here .
Price of 8-pack = \$1.55
Price of 20-pack = \$3.05
20 is 2.5 times 8 , so we can estimate here that 1.55*2.5 ~ 3.75+ (+ signifies slightly more) . More than cost of 8 - pack.

Now , comparing 20 -pack vs 250 - pack
250 is 12.5 times 20 . Even if we estimate it as 12 .
We can estimate price as 12* 3.05 ~ 36+ (+ signifies slightly more) .

At this step we know that in order to buy greatest number of hot dogs we need to maximize the number of 250 pack , then 20 pack and then 8 pack .( with the amount remaining after each successive steps)

To maximize number of hot dogs with 200\$
Total number of hot dogs bought in 250-pack = 22.95*8 =183.6\$
Amount remaining = 200 - 183.6 = 16.4\$
With this we can buy 5 of 20-pack = 3.05*5 15.25 \$
Amount remaining = 16.4 - 15.25 = 1.15\$
This amount is too less to buy any 8- pack .

Since two answers are really close - 2100 and 2108 , i would not recommend estimation here .

Greatest number of hot dogs one can buy with 200 \$ = 250*8 + 20*5 = 2100

_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
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Manager
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Posts: 54
Schools: Rotman '17 (A)
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Re: At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a  [#permalink]

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24 Dec 2015, 07:44
Thank you SkyWalker18, the estimation you did there is more promising.

When I approached the question, my first step was to figure out the price per hotdog in a package of 8, then a package of 20, and then of 250. By this time I was 90 seconds in. Then I divided 200 by \$23 (slight estimation). Could go explaining my steps but my point is, by the time I can finish this question (accurately) I'm at 3 minutes or more. nmery easy, I understand what it's asking and what's required very well. But the steps are just too lengthy and if I got this question on test day (in 2 weeks) I know I would find myself with only 30 seconds left on the next question... That's disconcerting.
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Re: At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a  [#permalink]

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23 Jul 2017, 17:36
this kind of math will most probably not appear on GMAT.
Re: At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a   [#permalink] 23 Jul 2017, 17:36
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