Bunuel wrote:
A jewel necklace contains only emeralds, rubies, and diamonds. If the ratio of emeralds to diamonds is 2:7 and the ratio of diamonds to rubies is 3:2, then which of the following could not be the number of jewels on the necklace?
(A) 41
(B) 81
(C) 82
(D) 123
(E) 205
Emeralds : Diamonds = 2:7 and
Diamonds : Rubies = 3:2
Before you can figure out how many total jewels might be on a necklace, you have to know the relationship among emeralds and diamonds and rubies.
But because the ratio number for diamonds doesn't match, you can't figure out that relationship until you make a common term.
The method is derivable, but maybe just writing it out will help.
There are two ratios that share a common element , diamonds. To find the combined relationship, find the equivalent of the least common multiple.
That is, figure out how to make diamonds equal in both ratios, and then you can combine ratios .
1. Write the ratios as you have them, putting the element they have in common in the middle
|__E__|__D__|__R__||__2__|__7__|-------||-------|__3__|__2__|2. You need the Ds (diamonds) to be equal. Take the LCM of 3 and 7 = 21.
3. Then multiply each row by the number that will get you to D = 21: multiply
both parts of the first row by 3, and
both parts of the second row by 7
|__E__|__D__|__R__|---------------->
|__E__|__D__|__R__||__2__|__7__|-------| ----
x 3------->
|__6__|__21__|--------||-------|__3__|__2__| ----
x 7------->
|--------|__21__|__14__| The right hand chart shows the combined ratio where E: D: R = 6x: 21x: 14x
Total parts of combined ratio: 6x + 21x + 14x = 41x
So the answer has to be a multiple of 41.
81 is not a multiple of 41.
Answer B
P.S. If you're on a phone, turn it to landscape. Then the charts will line up. (Wow is it hard to make charts . . . .)
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