The discount offer "Buy 2 and get 3" is equivalent

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Wed Oct 24, 2018 1:47 am

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The discount offer "Buy 2 and get 3" is equivalent to what percentage discount?

A) 10%
B) 20%
C) 33.33%
D) 40%
E) 50%

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Source: Beat The GMAT — Problem Solving | Wed Oct 24, 2018 1:47 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Wed Oct 24, 2018 12:37 pm

GMATinsight wrote:The discount offer "Buy 2 and get 3" is equivalent to what percentage discount?

A) 10%
B) 20%
C) 33.33%
D) 40%
E) 50%

Source: www.GMATinsight.com

$$?\,\, = \,\,\Delta \% \,\,\,\,\,\,\,\left( {\Delta \% < 0} \right)$$
Three items with price of (say) $10 each would cost $30 (all 3 of them) but they are offered by $20 (all 3 of them). Hence:
$$?\,\,\,\, = \,\,\,\,\Delta \% \,\,\left( {30 \to 20} \right)\,\,\,\, = \,\,\,\,{{20 - 30} \over {30}}\,\,\,\, = \,\,\,\, - {1 \over 3}\,\,\,\, = \,\,\,\, - 33{1 \over 3}\% $$
The correct answer is (C).

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Portuguese-speakers :: https://www.gmath.com.br

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kaylajiang: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Wed Oct 24, 2018 4:07 pm

answer

by kaylajiang » Wed Oct 24, 2018 4:46 pm

Here is my solution:

The original price for each item is a, then the original total price for 3 items should be 3a. However, since we only need to pay for 2 items (2a), so the discount is 3a-2a/3a=1/3=33.33%

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8188; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Oct 25, 2018 5:02 pm

GMATinsight wrote:The discount offer "Buy 2 and get 3" is equivalent to what percentage discount?

A) 10%
B) 20%
C) 33.33%
D) 40%
E) 50%

Let's say the cost of 1 item is 2 dollars. So, without the discount, 3 items would cost 6 dollars. But with the discount, the 3 items would cost 4 dollars. Thus, the percent discount is:

(4 - 6)/6 x 100 = -2/6 x 100 = -1/3 x 100 = 33.33% discount.

Alternate Solution:

Let the price of one item be x. We only pay 2x but get 3 items in return; thus we end up paying 2x/3 per item. Thus, the discount on one item is x - 2x/3 = x/3; which represents a discount of (x/3)/x = 1/3 = 33.33%.

Answer: C

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