Let no.of emeralds be k.
No. of rubies = (8*k)/3
No.of diamonds = (5/6) * ((8*k)/3) = (20*k)/9
Hence the ratio is (20/9) : (8/3) : 1
i.e. 20 : 24 : 9
Hence the minimum number of jewels is 20+24+9 = 53.
The jewels in a crown consist of diamonds, rubies, and emeralds. If the ratio of diamonds to rubies is 5/6, and the ratio of rubies to emeralds is 8/3, what is the least number of jewels in the tiara?
I figured that this problem would be solved by finding the ratio between the three (20:48:9) for a total of 77, but the answer given is 53. I'm stumped!
Thanks... that explanation is over my head, but it did help me to realize my error. When calculating the total ratio, I used this method:
therefore, d/e = d/r*r/e = 5/6*8/3 = 40/18.
then, r in these new terms = r*r or 48
this gives me the total ratio of 40:48:18 or 20:24:9.
I made the mistake of reducing the ratio of d/e apart from reducing r, which gave me the ratio 20:48:9 which cannot be reduced.
It's a mistake I won't make again!
Great problem! I forgot you could reduce ratios to lowest terms. Was this a high-difficulty level question on PowerPrep™?
@ Coyote: Thanks! I've been working non-stop at the GRE for a little over 12 weeks now and am ready for the stress to end.
@ GRE Pupil: Haha, yes, but it's a little more like this!
Seriously, though... I am just starting to approach the AWA stuff (I am strong in writing) and finish up my vocab (1000+ flash cards from Barrons, all familiar, plus a few new vocab words when I come across them in PP).
Every day I work on math problems with specific attention on forcing myself to PROVE each problem on paper. I have flash cards with every quant problem that I've missed so that I can practice the setup of the problem. and I am doing scored math sections (e.g. Kaplan, Powerprep) every day. On Thursday I will do a few drills but no studying. On Friday I will go for a light run (get the circulation in my brain going) and do a few drills before the test.
Being a social science student, I am great at making inferences and grasping the relationship between ideas (broad thinking, good for verbal) but I need to work on focusing on details and deducing what they actually mean (detailed thinking, good for quant). In contrast, all the math majors have extensive practice proving mathematical principles and the broader inferences elude them (especially non-native english speakers!). The GRE wants us to do both.
The best of luck to all of us! We all are working as hard as we can to get the best education and opportunity in our lives!
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