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605-655 (Medium)|   Mixture Problems|         
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During a certain GMAT marathon, the average blood pressure of female 18 Apr 2022, 22:45
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45% (medium)

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65% (01:23) correct 35% (01:50) wrong based on 528 sessions

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During a certain GMAT marathon, the average blood pressure of female GMAT students increased by 12.5% and the average blood pressure of male GMAT students increased by 23%. What fraction of the GMAT students were female?

(1) 92% of male students suffered from increased blood pressure during the marathon.
(2) The average blood pressure for all students increased by 19% during the marathon.
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B
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PyjamaScientist
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During a certain GMAT marathon, the average blood pressure of female Updated on: 20 Apr 2022, 06:13
Originally posted by PyjamaScientist on 18 Apr 2022, 22:56.
Last edited by PyjamaScientist on 20 Apr 2022, 06:13, edited 1 time in total.
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Hope this helps. The last solution was too brief perhaps.
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BongBideshini
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During a certain GMAT marathon, the average blood pressure of female 25 Jun 2026, 11:37
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KarishmaB
Can we use a weighted average here without knowing whether the initial average blood pressure of females and males is equal?
I got the answer as E
GMATNinja
During a certain GMAT marathon, the average blood pressure of female GMAT students increased by 12.5% and the average blood pressure of male GMAT students increased by 23%. What fraction of the GMAT students were female?

(1) 92% of male students suffered from increased blood pressure during the marathon.
(2) The average blood pressure for all students increased by 19% during the marathon.
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KarishmaB
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During a certain GMAT marathon, the average blood pressure of female 05 Jul 2026, 05:40
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GMATNinja
During a certain GMAT marathon, the average blood pressure of female GMAT students increased by 12.5% and the average blood pressure of male GMAT students increased by 23%. What fraction of the GMAT students were female?

(1) 92% of male students suffered from increased blood pressure during the marathon.
(2) The average blood pressure for all students increased by 19% during the marathon.
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The question is testing your understanding of weighted averages but you do not need to calculate anything.

Female students - Average increased by 12.5%
Male students - Average increased by 23%

What fraction were female students? We can get it if we know the overall average increase. This is equivalent to our standard weighted averages questions on say profit%. For one group of items, profit was 12.5%, for another it was 23%. If overall profit is say 19%, then what fraction of the cost was the first group? We can find it by using our weighted average formula discussed here: https://anaprep.com/arithmetic-weighted-averages/

So look at the statements:

(1) 92% of male students suffered from increased blood pressure during the marathon.

Irrelevant to our question. We know that overall for males the BP increased by 23%. For some it could have not increased and for some it could have increased by 50% or more to give the overall of 23%. This statement tells us that for 8% of males, BP did not increase and for 92% it increased by at least some amount. It's ok how the average of 23% was obtained - we don't care. We know that as a whole for the male group, the BP increased by 23% so effectively, for us, for each male it increased by 23%.

(2) The average blood pressure for all students increased by 19% during the marathon.

This gives us the overall average. We don't need to do the actual calculation, but if we were to do it, this is what we would do:

So now we know wf/wm = (23 - 19)/(19 - 12.5) = 4/6.5

So overall 4/10.5 were females. This statement alone is sufficient.

Answer (B)
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During a certain GMAT marathon, the average blood pressure of female 05 Jul 2026, 22:35
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Let F = number of female students and M = number of male students Let Bf = initial average BP of females and Bm = initial average BP of males

Statement (2): Overall average BP increased by 19%

Total BP increase = (female group's increase) + (male group's increase):
\(\\
0.19 *(F * B_f + M * B_m) = 0.125 * (F * B_f) + 0.23 * (M * B_m)\\
0.065 * (F * B_f) = 0.04 * (M * B_m)\\
\)

So:
\(\frac{(F * B_f) }{ (M*B_m)} = \frac{0.04 }{ 0.065 }= \frac{8}{13}\)
Since Bf and Bm are unknown and don't cancel, F/M cannot be isolated.

I'm not able to understand where I missed. :|


KarishmaB


The question is testing your understanding of weighted averages but you do not need to calculate anything.

Female students - Average increased by 12.5%
Male students - Average increased by 23%

What fraction were female students? We can get it if we know the overall average increase. This is equivalent to our standard weighted averages questions on say profit%. For one group of items, profit was 12.5%, for another it was 23%. If overall profit is say 19%, then what fraction of the cost was the first group? We can find it by using our weighted average formula discussed here: https://anaprep.com/arithmetic-weighted-averages/

So look at the statements:

(1) 92% of male students suffered from increased blood pressure during the marathon.

Irrelevant to our question. We know that overall for males the BP increased by 23%. For some it could have not increased and for some it could have increased by 50% or more to give the overall of 23%. This statement tells us that for 8% of males, BP did not increase and for 92% it increased by at least some amount. It's ok how the average of 23% was obtained - we don't care. We know that as a whole for the male group, the BP increased by 23% so effectively, for us, for each male it increased by 23%.

(2) The average blood pressure for all students increased by 19% during the marathon.

This gives us the overall average. We don't need to do the actual calculation, but if we were to do it, this is what we would do:

So now we know wf/wm = (23 - 19)/(19 - 12.5) = 4/6.5

So overall 4/10.5 were females. This statement alone is sufficient.

Answer (B)
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During a certain GMAT marathon, the average blood pressure of female 05 Jul 2026, 22:48
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BongBideshini
Let F = number of female students and M = number of male students Let Bf = initial average BP of females and Bm = initial average BP of males

Statement (2): Overall average BP increased by 19%

Total BP increase = (female group's increase) + (male group's increase):
\(\\
0.19 *(F * B_f + M * B_m) = 0.125 * (F * B_f) + 0.23 * (M * B_m)\\
0.065 * (F * B_f) = 0.04 * (M * B_m)\\
\)

So:
\(\frac{(F * B_f) }{ (M*B_m)} = \frac{0.04 }{ 0.065 }= \frac{8}{13}\)
Since Bf and Bm are unknown and don't cancel, F/M cannot be isolated.

I'm not able to understand where I missed. :|



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The population - male and female together - has a certain average BP. Hence the question assumes that initially everyone had the average BP. Increase happened over the same initial BP for males and females differently. That is why initial BP has been ignored.
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During a certain GMAT marathon, the average blood pressure of female 05 Jul 2026, 22:59
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Thanks for the reply. But it was difficult for me to interpret from the question that we need to assume that initially everyone had the average BP.
KarishmaB


The population - male and female together - has a certain average BP. Hence the question assumes that initially everyone had the average BP. Increase happened over the same initial BP for males and females differently. That is why initial BP has been ignored.
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