A certain electronic component is sold in boxes of 54 for $1

Question

A certain electronic component is sold in boxes of 54 for $16.20 and in boxes of 27 for $13.20. A customer who needed only 54 components for a project had to buy 2 boxes of 27 because boxes of 54 were unavailable . Approximately how much more did the customer pay for each component due to the unavailability of the larger boxes?

(A) $0.33
(B) $0.19
(C) $0.11
(D) $0.06
(E) $0.03

Show Answer

Official Answer

B

(A) $0.33
(B) $0.19
(C) $0.11
(D) $0.06
(E) $0.03

dbiersdo · Accepted Answer

Is there a reason people are choosing to do long division two times in this problem? Here's how I worked this one out,

Cost for 54 components from one box = $16.20
Cost for 54 components from two boxes = $13.20 * 2 = $26.40
Difference is $26.40 - $16.20 = $10.20

We want to know how much more we paid per piece so just take $10.20/54 = .19 cents. Wouldn't this be quicker in most cases?

Bunuel · Answer

SOLUTION

A certain electronic component is sold in boxes of 54 for $16.20 and in boxes of 27 for $13.20. A customer who needed only 54 components for a project had to buy 2 boxes of 27 because boxes of 54 were unavailable . Approximately how much more did the customer pay for each component due to the unavailability of the larger boxes?

(A) $0.33
(B) $0.19
(C) $0.11
(D) $0.06
(E) $0.03

Show Answer

Official Answer

B

(A) $0.33
(B) $0.19
(C) $0.11
(D) $0.06
(E) $0.03

Boxes of 54: the price per one component = 16.20/54;
Boxes of 27: the price per one component = 13.20/27;

The difference = 13.20/27 - 16.20/54 = (26.4 - 16.2)/54 = ~0.19.

Answer: B.

HarveyS · Answer

B?

26.40/54- 16.20/54 = ~ .19

w1ck3d64 · Answer

i got B as well..same reasoning as  Mountain14  but i used sets of 27 instead of 54

PareshGmat · Answer

Per piece price from boxes of 54 = 16.2/54
Per piece price from boxes of 27 = 13.2/27

Excess money paid = 13.2/27 - 16.2/54

= 13.2/27 - 8.1/27

= 5.1/27 = 0.19 (nearly) = Answer = B

CCMBA · Answer

I just wanted to find the difference in unit price of each scheme. 54 for $16.2 is the same as 27 for $8.1. That's a difference of 5.3 for 27 items, which is just under 20 cents. The answer is B. Laziness ftw! Actually the difference is 5.1. Perhaps too lazy. Still the closest answer though.

BrainLab · Answer

for me was the part of dividing the most time connsuming... So, may be this will help you also:
10,20/54 = (Divide by 6) = 1,7/9 = 0,19.... It's much easier to delete 1,7 by 9 than 10,20 / 54

anilisanil · Answer

He paid 26.4 instead of 16.2 for 54 items.

So 10.2$ more for 54 or 10.2/54 per item

Or 20.4/108 so closest is .19.

DJ1986 · Answer

So far, every time I do one of these arithmetic questions I've found that the answer choices are far enough apart that rounding always works.

15/30 = .5
16/56= 2/7 = .29 = .30

.5-.3 = .2

I took me 30 secs to read the question. 30 seconds to do the math.

ajdse22 · Answer

Difference in cost per component = (26.40-16.20)/54 = 10.2/54. 
Now since we notice that the answer choices are well separated, we can go for estimation. 10.2/54 is somewhat smaller than 1/5. The only answer choice that does that is B. So B.

JarvisR · Answer

I have a query here. Request members to share their inputs.
As answer choices are quite far from each other, is it right to approx 10.20/54 ~ 10/54 = .18 (close to option B) ?

Bunuel · Answer

________________
Yes, you can do this.

mamun2871 · Answer

Here, 13.2*2=26.40-16.2=10.2/54=.19
 So, Correct Answer is B.

BorisDa · Answer

I just rewrote as follows: 26/50 - 16/50 = .2 or ~.19

Before I was doing it the long way and was getting frustrated. The way above took me like 10 seconds.

Harry8014 · Answer

Can't we directly solve this -:

since he need to now buy 2 boxes of 27 : total spent = 13.20 * 2 = 26.40

Originally, 54 box cost = 16.20

So, he's loosing on 26.40 - 16.20 = 10.20

per component, we need to divide by 54 : so ans = 10.20/ 54 = 0.19

is this approach correct?

Sabby · Answer

Box of 54 units= 16,20$
Box of 27 units = 13,20$=> 2 boxes of 27 units= 13,20*2=26,40$

26,40$-16,20$= 10,20$ paid in extra for the total 54 units
For each unit, extra paid is 10,20$/54 units ==> approx 10$/50 units= 0,20$

Therefore, it has to be a bit less than 0,20$ and the closest answer to 0,20$ is 0,19$

BrentGMATPrepNow · Answer

Strategy: Before performing any calculations, be sure to check whether the answer choices permit any approximation. In this case, there's a pretty good spread between the numbers, so we can use a little approximation Given: 54 components cost $16.20 Price per component = $16.20/54 More strategy: Dividing a larger number into a smaller number is time consuming. We can make our calculations much easier by converting collars to cents We get: price per component = 1620¢/54 ≈ 1600/50 ≈ 160/5 = 32¢ per component Aside: Here's a brief video on how to divide any number by 5 in your head: https://www.gmatprepnow.com/module/gene ... video/1112 Given: 27 components cost $13.20 Price per component = $13.20/27 = 1320¢/27 ≈ 1300/25 TIP: To divide by 25, first divide by 5, and then divide the result by 5 We: 1300/25 = 260/5 = 52¢ per component So, the difference = 52¢ - 32¢ = 20¢ The closest possible answer choice is B Answer: B

ArnauG · Answer

To find out how much more the customer paid for each component due to the unavailability of the larger boxes, we need to compare the price per component in both cases.

In a box of 54 components, the price is $16.20. Therefore, the price per component is $16.20 / 54 = $0.30.

In a box of 27 components, the price is $13.20. Therefore, the price per component is $13.20 / 27 ≈ $0.4889.

Since the customer had to buy 2 boxes of 27 components, they paid a total of 2 * $13.20 = $26.40.

The customer needed a total of 54 components for the project, so they paid $26.40 for 54 components.

To find out how much more the customer paid for each component, we subtract the price per component in the larger box from the price per component in the smaller box:

$0.4889 - $0.30 = $0.1889

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A certain electronic component is sold in boxes of 54 for $1

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