In a health club, 60% of the members take protein supplements and

Question

In a health club, 60% of the members take protein supplements and report getting good results. 80% of the members who not take the supplements report not getting good results. If 70% of the members of the club take protein supplements, what percentage of the members report getting good results?

A. 48
B. 60
C. 66
D. 70
E. 76

A. 48
B. 60
C. 66
D. 70
E. 76

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Dereno · Answer

Let the total number of persons be 100.

Let’s create a 4*4 matrix.

70% of the members take protein supplements, which means 30% do not take.

60%*(70) report good results.

80%*(30) report not getting good results.

so, with these we can fill the remaining gaps.

Good Results  
 ~ Good Results  
  Total  
 
  Protein supplement  
  42 
  28 
  70 
 
  ~ Protein Supplement  
  6 
  24 
  30 
 
   Total  
   48  
  52  
  100

48

Option A

Edskore · Answer

Great solution by Dereno with the matrix approach! Let me add a slightly faster way to think about this using direct weighted calculation — useful when you're short on time.
The quick approach:
The question gives us two groups and their "good results" rates. We just need to find the weighted total.

70% take supplements → 60% of these get good results → 0.70 × 0.60 = 0.42 (42% of all members)
30% don't take supplements → 80% of these get NOT good results, so 20% DO get good results → 0.30 × 0.20 = 0.06 (6% of all members)

Total getting good results = 42% + 6% = 48%
Answer: A
The common mistake here is misreading the conditional percentages. The problem says "60% of those who take supplements report good results" and "80% of those who DON'T take supplements report NOT getting good results." Students often confuse which percentage applies to which subgroup, or accidentally apply 80% as the good-results rate instead of the bad-results rate.
Takeaway: For overlapping-group problems with conditional percentages, the "multiply-and-add" shortcut (group size × rate for each group, then sum) is often faster than building a full matrix — especially under GMAT time pressure.

vasu1104 · Answer

taking supplement 
 not taking supplement 
 total 
 
  Good results 
 60 
 6 
 66 
 
  Not good results 
 10 
 24 
 34 
 
  total 
 70 
 30 
 100

the people getting good results= 66
so its 66% of the members getting good results.

i am not sure with the first sentence. does it mean 60% of the people taking supplement or does it mean 60% of the all members.
i am going with the latter inference here.

harirah121 · Answer

The problem says 60% of the members take protein supplement and report good results, not 60% of those who take supplements report good results. Its 60% for supplement/good results, and 10% for supplement/not good, then 30% for no supplements so .8*.3 = .24 or 24% no supplement/bad results, and 6% no supplement/good results, therefore good results is 60+6 = 66%

ExpertsGlobal5 · Answer

Video explanation:    https://www.youtube.com/watch?v=sqSqY7t36LM

Adit_ · Answer

This approach is more or less completely wrong!
So basically 60% already get good results. Answer anything below 60 is already entirely ruled out.
Secondly we need to find ppl who do not take supplements and still get good results.
This will be added to 60 to get final answer

Now we know 70% take supplements therefore 30% dont take supplements.

80% of this 30 dont seem to get good results which is 24%

Remaining 6% is No protein and Good results which is what we need!!

Therefore 60 + 6 = 66%

Overall summary:

60% ==> Take pro and good res
40% ==> Not take pro or No good results

From this 40%

6% No pro BUT good results
24% No protein AND No good res
10% Take Pro BUT No good res

So to confirm our answer we use:
No of good results = 100% - (No.of No good results)
==> 100%-(10+24)% = 66%

Hence our answer is correct.

The MISTAKE:

70% take protein supplements OF THE TOTAL. There is no mention of 60% of THESE 70% of ppl getting good results. Such problems need to be tackled separately using complementaries and handling individual cases separately with careful reading.

Hope it helps!

In a health club, 60% of the members take protein supplements and

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	Good Results	~ Good Results	Total
Protein supplement	42	28	70
~ Protein Supplement	6	24	30
Total	48	52	100

	taking supplement	not taking supplement	total
Good results	60	6	66
Not good results	10	24	34
total	70	30	100

GMAT Problem Solving (PS) Questions

In a health club, 60% of the members take protein supplements and

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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My Rewards