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22 Jan 2026, 22:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
42% (02:31) correct
58%
(01:56)
wrong
based on 81
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If 40 percent of the people who bought a particular smartphone bought a smartwatch, what percent of the smartphone buyers bought headphones?
(1) 50 percent of people who bought the smartphone and the smartwatch also bought headphones.
(2) 80 percent of people who bought the smartphone and the headphones also bought the smartwatch.
(1) 50 percent of people who bought the smartphone and the smartwatch also bought headphones.
(2) 80 percent of people who bought the smartphone and the headphones also bought the smartwatch.
23 Jan 2026, 05:28
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ExpertsGlobal5
let’s consider a three set venn diagram:
Where Circle containing Physics denotes the circle for Smart phone, Circle containing Chemistry denotes the circle for Smart watch, and Circle containing Math denotes Handphones.
given that : 40 percent of the people who bought a particular smartphone bought a smartwatch
If the number of people who bought smartphone is 100x, then 40%(100x) = 40x = (d+g)
We need to find: what percent of the smartphone buyers bought headphones? If we are able to find the value of (e+g) , the we can find the percent.
Statement 1:
50 percent of people who bought the smartphone and the smartwatch also bought headphones.
g = 50%(d+g) = 50%*(40x) = 20x
g = 20x, then d = 20x.
a+e = 80x
Hence, Insufficient
Statement 2:
80 percent of people who bought the smartphone and the headphones also bought the smartwatch.
80%(e+g) = g
4e +4g = 5g
g:e = 4:1
Hence, Insufficient
Combining both statements 1 and 2, we get
g:e = 4:1
If g=20x , then e = 5x
Thus , (e+g) = 25x
(e+g) / Total Smartphone = 25x/100x = 25%
Option C
Attachment:
GMAT-Club-Forum-uau87quw.png [ 5.91 KiB | Viewed 654 times ]
25 Jan 2026, 11:30
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ExpertsGlobal5
Correct answer: C
Evaluation by MS:
Quality – 4
Difficulty – 3
Topic – Word Problem
To be included in CBTs? – No
= = = = = = = = = = = = = = = = = = = = = =
Explanation:
Let P be the event that a person buys a smartphone.
Let W be the event that a person buys a smartwatch.
Let H be the event that a person buys headphones.
40 percent of the people who bought a particular smartphone bought a smartwatch, which can be expressed as: P Ո W = 0.4P (Equation I)
We have to find what percent of the smartphone buyers bought headphones, which can be expressed as: What percent of P is (P Ո H)?
We need to find whether the value of “100 x (P Ո H)/P” can be determined.
Statement (1)
50% x (P Ո W) = (P Ո W Ո H)
From Equation I:
50% x 0.4P = (P Ո W Ո H)
0.5 x 0.4P = (P Ո W Ո H) (Equation II)
Since it is not possible to express (P Ո H) in terms of P from the given information, it is NOT possible to determine with certainty the percentage of smartphone buyers that bought headphones. Hence, Statement (1) is insufficient.
Statement (2)
80% x (P Ո H) = (P Ո W Ո H)
0.8 x (P Ո H) = (P Ո W Ո H) (Equation III)
Since it is not possible to express (P Ո H) in terms of P from the given information, it is NOT possible to determine with certainty the percentage of smartphone buyers that bought headphones. Hence, Statement (2) is insufficient.
As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements.
Statement (1) and Statement (2) combined
From Equation II and Equation III,
0.5 x 0.4P = 0.8 x (P Ո H)
(P Ո H)/P = (0.5 x 0.4)/0.8
It is possible to determine the exact percentage of smartphone buyers that bought headphones. Hence, Statement (1) and Statement (2) combined are sufficient.
C is the correct answer choice.
