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Difficulty:
95%
(hard)
Question Stats:
39% (02:48) correct
61%
(02:56)
wrong
based on 579
sessions
History
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When a certain drug was administered to a group of patients, some patients showed improvement and some patients experienced side effects. If at least 10 patients experienced side effects and 60 percent of the patients who showed improvements also experienced side effects, did more patients in the group show improvement than experience side effects?
(1) 90 percent of the patients in the group showed improvement.
(2) 90 percent of the patients in the group who experienced side effects also showed improvement.
(1) 90 percent of the patients in the group showed improvement.
(2) 90 percent of the patients in the group who experienced side effects also showed improvement.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. Both statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. Both statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
02 Nov 2023, 00:12
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edwin.que
We can plot the information given in the question over a 2*2 matrix as shown below -
Attachment:
Screenshot 2023-11-02 122628.png [ 33.85 KiB | Viewed 18234 times ]
- Number of people who show improvement = \(i \)
- Number of people who show side-effects = \(s\)
- Number of patients = \(p\)
Question: \(i > s\) = ?
Let's start with Statement 2
Statement 2
(2) 90 percent of the patients in the group who experienced side effects also showed improvement.
Hence, we can infer that 0.9s = 0.6i
\(\frac{s}{i} =\frac{6}{9}\)
As the ratio is less than 1, we can conclude that \(i > s\). Hence, this statement alone is sufficient to answer the question. We can eliminate A, C, and E.
Attachment:
Screenshot 2023-11-02 123310.png [ 25.89 KiB | Viewed 17824 times ]
Statement 1
(1) 90 percent of the patients in the group showed improvement.
From the information given in this statement, we can infer that \(i = 0.9p\)
The number of people who do not show improvement = \(0.1p\)
Hence, the number of people who show side-effects and also show improvement = \(0.6i = 0.6 * 0.9*p = 0.54p\)
Let's assume that all the people who do not show improvement also exhibit side effects, the maximum number of people who show side effects = \(0.54p + 0.1p = 0.64p\)
Even at the maximum possibility, \(0.64p < 0.9p\).
Hence, we can conclude that \(i > s\) i.e. more patients in the group show improvement than experience side effects. This statement is also sufficient.
Attachment:
Screenshot 2023-11-02 123637.png [ 39.24 KiB | Viewed 17652 times ]
Option D
27 Jun 2024, 01:09
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edwin.que
Use Venn diagram for a quick solution.
(1) 90 percent of the patients in the group showed improvement.
Since 60% of I is in the Both region and I is 90% of Total, the Both region has 60% of 90% of T = 54% of T.
54% of T are in the both region and 36% of T are in ONLY I; this means that at most 10% of T can be in ONLY SE. Hence, yes, more patients in the group did show improvement than experience side effects.
Attachment:
Screenshot 2024-06-27 at 1.32.25 PM.png [ 60.88 KiB | Viewed 12518 times ]
(2) 90 percent of the patients in the group who experienced side effects also showed improvement.
60% of I lie in Both and 90% of SE lie in Both.
Hence, 60/100 * I = 90/100 * SE
I/SE = 9/6
Hence, yes, more patients in the group did show improvement than experience side effects.
Attachment:
Screenshot 2024-06-27 at 1.24.09 PM.png [ 60.11 KiB | Viewed 12335 times ]
Answer (D)
Check another similar official Sets problem here:
https://youtu.be/1RZdJTKCDYs
