When patients with clinical depression come to Royal Cornhill Mental..

Question

When patients with clinical depression come to Royal Cornhill Mental Health Institute, they are first treated with psychotherapy and antidepressants. Only 40 percent respond to their first treatment. More than 20 percent of depressed people did not respond to any treatment.

If the information given above is true, which of the following statements must be true?

A. At least 60% of the patients who do not respond to the first treatment respond to some other treatment.
B. At least 30% of the patients who do not respond to the first treatment do not respond to the subsequent treatments as well.
C. Of the 40% patients who respond to their first treatment, at least 50% also respond to some other treatment.
D. Of the people who respond to some treatment, the proportion that responds to the first medication is the lowest.
E. Of the 20% patients who responded to no treatment at all, at least 10% would have responded to some treatment had it not included the use of antidepressants.

DavidTutorexamPAL · Accepted Answer

The answer is B.   
This is quite tricky - a CR question which is actually more like a quant question. solving requires carefully reviewing each answer:

If the information given above is true, which of the following statements must be true?

A. At least 60% of the patients who do not respond to the first treatment respond to some other treatment.  we have no data on this  
B. At least 30% of the patients who do not respond to the first treatment do not respond to the subsequent treatments as well.  30% of 60% is .3*.6=0.18=18% - while the stem tells us this group (did not respond to anything) is more than 20% - this  must  be true! 
C. Of the 40% patients who respond to their first treatment, at least 50% also respond to some other treatment. - The issue is that we don't know how many don't respond at all: if it's only 20%, then 80% respond to something, meaning at  least  20% are included in the 40% group who responded to the first treatment - that's 20%/40% - at least 50%! however, if say 60% don't respond at all, this means that 0 of the 40% do - no way of knowing!  
D. Of the people who respond to some treatment, the proportion that responds to the first medication is the lowest.  exactly the opposite - 40% responded to the first, and the absolute max that the group which responded at all is 80% - meaning they are AT LEAST 50% of this group - definitely the largest part!  
E. Of the 20% patients who responded to no treatment at all, at least 10% would have responded to some treatment had it not included the use of antidepressants.  This is completely hypothetical - we have absolutely no information on how these patients would have responded if things were different

Archit3110 · Answer

if total patients = 100
first treated who responded = 40 and out of 60 if we say that >20 % did not respond 
so it has to be at least 12 patients

A. At least 60% of the patients who do not respond to the first treatment respond to some other treatment => not true
B. At least 30% of the patients who do not respond to the first treatment do not respond to the subsequent treatments as well ; 30%*60 ; 18 so in our finding at least 12 patients do not respond to any treatment so 18 is a possibility 
C. Of the 40% patients who respond to their first treatment, at least 50% also respond to some other treatment. ; 50 % respond to other means at least 30 respond so for balance 30 we do not know whether they respond or not so this 50% can be 99% of 60 as well 
D. Of the people who respond to some treatment, the proportion that responds to the first medication is the lowest. ; not relevant 
E. Of the 20% patients who responded to no treatment at all, at least 10% would have responded to some treatment had it not included the use of antidepressants ; count of 20% patient who do not respond to any treatment is not given in argument irrelevant

out of the given options IMO B stands out

deepverma · Answer

B . 30% of 60% ppl is 18% who didn't respond to ny treatment. Already given this no is more than 20%

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rajamech · Answer

The answer is B as 30% of 60% is 18% - while the stem tells us that this group did not respond to anything is more than 20% - this must always be true!

Aderonke01 · Answer

Hello Bunuel, How can 18% be more than 20%.ie. x is more than 20%. Option B tells us that x is > 18%. that is less than 20%. m lost please

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ProfChaos · Answer

I used Venn Diagram, considering 100 patients. 40 respond to first treatment (psychotherapy+antidepressants) This includes people who responded to first treatment+any other treatment as well (A intersection B) >20 did not respond to any treatment <40 responded to any other treatment alone. D,E are easily eliminated D : First medication response is 40 and 'only other medication response' will be <40 because >20 did not respond to any treatment, thus, proportion of response to first medication is highest E : Irrelevant Eliminating A and C is tricky A : Do not respond to first treatment=60, atleast 60% of 60= >36 responded to some other treatment which can be true because <40 responded to any other treatment alone C : >20 responded to some other treatment + first treatment ==> IT IS NOT A 'MUST BE TRUE' type statement CORRECT OPTION : B B : atleast 30% of 60= >18 do not respond to subsequent treatment as well which MUST BE TRUE because we have been told >20 did not respond to any treatments

Ishaan18 · Answer

All the answers are very complicated. And few are wrong as well. Lets make this simple !

This is numerical sort of questions where you need to draw inference
Total=100
Respond to first treatment=40
Don't Respond to first treatment=60

A. At least 60% of the patients who do not respond to the first treatment respond to some other treatment.
The above statement means greater than 36 people respond to someother treatment. But in the question more than 20 people don't respond to any treatment. More than 20 can mean a value of 40%. Then The patients who don't respond to the first treatment responding to some other treatment will beome 20% (60%-40%). Hence not a must be true statement
B. At least 30% of the patients who do not respond to the first treatment do not respond to the subsequent treatments as well.
In 60 --
Greater than 20 is depressed people. So we can infer that greater than 30% of 60 (=18) do not respond to subsequent treatments. If we think as a set >20 is greater than >18 or 18 is the subset of 20. Hence the below option is correct !
C. Of the 40% patients who respond to their first treatment, at least 50% also respond to some other treatment. - No information about people who respond to first treatment
D. Of the people who respond to some treatment, the proportion that responds to the first medication is the lowest. - Its proportion will be the highest. Since, after that the proportion of people who respond to mediciation will only decrease. 
From 60%, >20% don't respond. 40% left. Then from 40% the people who will respond will be less than <40%
E. Of the 20% patients who responded to no treatment at all, at least 10% would have responded to some treatment had it not included the use of antidepressants.-Out of scope

ak2121 · Answer

Isnt the construction of the argument very awkward?
It is not inferable that more than 20 percent refers to the remaining 60 percent, but with the construction more like looks that it refers to the 20 percent of all the patients
Can this type of construction be seen in the actual gmat?

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Invincible_147 · Answer

Totally Agreed. Its clearly written that 20% of depressed people. But the answer is correct if we take 20% of those who didnt respond to the first treatment.

Sudeep16011995 · Answer

Please someone explain me this. Unable to comprehend the provided solution

DmitryFarberMPrep · Answer

There's no ambiguity or mistake int he language. "More than 20%" is out of all depressed people. In fact, this doesn't work otherwise, since B needs to be provable, not just possible.

Start with 100 people.

1st treatment: Out of 100 people, 40 people respond well (in other words, their depression improves); 60 do not 
Additional treatments: The remaining 60 people are given additional treatments. Presumably, some respond to the 2nd or 3rd treatment, etc. But some do not. How many? More than 20% of the total, so > 20 people. That means the # of people who did respond to additional treatments is < 40.

Total who responded: 40 in the first round, and 0-39 in the second round, so somewhere between 40 and 79.
Total who never responded: All the rest, from 21-60 people.

B is asking about the % of people who did NOT respond to additional treatment. That group consists of 60 people. Of those > 20 didn't respond to any treatment, so that's > 20/60, or > 1/3. That exceeds 30%, so B is provably true.

If we (incorrectly) interpreted the 20% to just be of those who did not respond, then we would be able to cut B without any math at all. We'd have > 20% of the group, but B says at least 30% of that same group. Knowing we had > 20% would not prove we had at least 30%, so B would not be inferable. But again, that's not what the prompt says. The subject of the final sentence is "more than 20% of depressed people." The part after is the predicate, starting with the verb phrase "did not respond." So > 20% of the total were people who didn't respond to treatment.

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When patients with clinical depression come to Royal Cornhill Mental..

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