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Difficulty:
95%
(hard)
Question Stats:
45% (02:45) correct
55%
(02:53)
wrong
based on 842
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.
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gmatophobia
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Joined: 22 Dec 2016
Last visit: 09 Sep 2026
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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 24643 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 23962 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 23663 times ]
Option D
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
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 18276 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 17737 times ]
Answer (D)
Check another similar official Sets problem here:
https://youtu.be/1RZdJTKCDYs
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General Discussion
edwin.que
Patients who experienced side effects = x
Patients who experienced showed improvements = y
Q. Is y>x
(1) 90 percent of the patients in the group showed improvement.
Let us find the maximum possible number of those who could have had side effects.
We know that 60% of these 90% showed side effects. To maximize, let is take the remaining 100-90 or 10% patients who did not show improvement showed side effects too. Thus, total = 10% + 60% of 90% = 10% + 54% or 64%.
64%<90% or y<x.
Sufficient
(2) 90 percent of the patients in the group who experienced side effects also showed improvement.
So, this is the common group in terms of y, that is 90% of y belong to overlap.
But we also know that 60 percent of the patients who showed improvements also experienced side effects,so, 60% of x belong to overlap. Also, the overlap space cannot be different.
This gives 90% of y = 60% of x or 0.9y = 0.6x or 1.5y=x
Hence x>y
Sufficient
D
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From the first statement , we can say that even at maximum value of the number of people who showed side effects i.e 64 ( which is also 10+ , satisfying the condition given ) , the people who showed improvement i.e 90 is greater than it.
Hence statment 1 is sufficeinet to tell "Showing Side effects " < "Showing Improvement "
Statemnt 2 ,
3/5 * x = 9/10*y
where x = no of people showing improvement
y= showing side effects
x/y = 3/2
Hence again , "showing improvement " > "showing side effect ".
GMATinsight KarishmaB
Hence statment 1 is sufficeinet to tell "Showing Side effects " < "Showing Improvement "
Statemnt 2 ,
3/5 * x = 9/10*y
where x = no of people showing improvement
y= showing side effects
x/y = 3/2
Hence again , "showing improvement " > "showing side effect ".
GMATinsight KarishmaB
Attachments
27thJune_SecondStatement.png [ 21.42 KiB | Viewed 17429 times ]
27th_June.png [ 23.27 KiB | Viewed 17393 times ]
one inference if missed could make this problem much more challenging than it is, is the fact that 0 people didn't experience improvement or side effects.
For statement 1) how can we conclude from 0.9s = 0.6i which is bigger? if we don't know the absolute values ?
thanks,
thanks,
gmatophobia
INprimesItrust
We can conclude because 0.9s = 0.6i gives s/i = 0.6/0.9 = 2/3.
Since both i and s are positive, this directly implies i > s (and also |i| > |s|) - the ratio already captures that without needing the exact values.
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I got this question on an official mock, and my reasoning was that since we are not told anything about the group of people who neither improved nor showed side effects, how can we disregard that variable?
I had statement 1 as insufficient, by this logic.
Could anyone please help explain?
I had statement 1 as insufficient, by this logic.
Could anyone please help explain?
You do not disregard but take the worst case scenario for improvement>side effects...
90% had improvement, so 60% of 90 % or 54% had sidr effects.
Now let us take remaining 100-90%(those who did not show improvement) to be having side effects. (We are trying to find max possible % of side effects).
Thus 54%+10% or 64%, which is still less than 90%..
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90% had improvement, so 60% of 90 % or 54% had sidr effects.
Now let us take remaining 100-90%(those who did not show improvement) to be having side effects. (We are trying to find max possible % of side effects).
Thus 54%+10% or 64%, which is still less than 90%..
shivampaul
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A is sufficient in the following manner by venn diagram -
GMAT-Club-Forum-75o4k5em.png [ 147.72 KiB | Viewed 140 times ]
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Attachment:
GMAT-Club-Forum-75o4k5em.png [ 147.72 KiB | Viewed 140 times ]
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Anushree
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