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Bunuel
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A jewel necklace contains only emeralds, rubies, and diamonds. If the 16 Aug 2017, 01:56
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79% (01:37) correct 21% (01:58) wrong based on 401 sessions

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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
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B
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A jewel necklace contains only emeralds, rubies, and diamonds. If the 16 Aug 2017, 02:00
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B.
Rest all are multiple of 41 and ratio of e:d:r marble is 6:21:14. Add 6+21+14=41.


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A jewel necklace contains only emeralds, rubies, and diamonds. If the 16 Aug 2017, 02:06
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B -81 is the answer

Coz after simplifying
Emeralds : diamond : rubies

6 : 21: 14

So total 41 so every option that is divisible by 41 can be the no of jewels

So the only no not divisible by 41 is 81

So 81 is the answer B


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A jewel necklace contains only emeralds, rubies, and diamonds. If the Updated on: 16 Aug 2017, 13:17
Originally posted by generis on 16 Aug 2017, 13:06.
Last edited by generis on 16 Aug 2017, 13:17, edited 1 time in total.
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DOUBLE POST, SEE BELOW
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A jewel necklace contains only emeralds, rubies, and diamonds. If the 16 Aug 2017, 13:13
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genxer123
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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
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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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A jewel necklace contains only emeralds, rubies, and diamonds. If the 16 Aug 2017, 20:17
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Let the emeralds in the necklace be represented by E,
the rubies in the necklace be represented by R and diamonds in the necklace by D.
Therefore,
E:D = 2x:7x
D:R = 3x:2x

Since we need to find a common ratio, we need to multiply the emerald, diamond ratio by a factor of 3 and the diamond, ruby ratio by a factor of 7.
E:D also equals 6x : 21x and D:R equals 21x : 14x
Hence, the common ratio is 6x : 21x : 14x.

Therefore, the total number of jewels in the necklace is a mutliple of 41(6x + 21x +14x = 41x)
Of the answer options(Only B, 81) is not a multiple of 41 and is our answer.
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A jewel necklace contains only emeralds, rubies, and diamonds. If the 03 Feb 2026, 07:26
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Deconstructing the Question

Given:
E : D = 2 : 7
D : R = 3 : 2

Match the common term (diamonds).

Step-by-step

LCM of 7 and 3 is 21.

Multiply first ratio by 3:
\(E:"D"= 6:21\)

Multiply second ratio by 7:
\(D:R = 21:14\)

So:
\(E:"D":R = 6:21:14\)

Total parts:
\(6+21+14=41\)

Total jewels must be a multiple of \(41\).

Check options:
\(41, 82, 123, 205\) are multiples
\(81\) is not

Answer: B (81)
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