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02 Dec 2020, 01:15
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Difficulty:
95%
(hard)
Question Stats:
22% (02:33) correct
78%
(03:19)
wrong
based on 144
sessions
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There are five different coins of five different colors: red, blue, green, yellow, and white.
The value of 1 red coin = the value of n blue coins;
The value of 1 blue coin = the value of n green coins;
The value of 1 green coin = the value of n yellow coins;
The value of 1 yellow coin = the value of n white coins.
If the value of 12 blue coins and 168 white coins equals to the value of 1 red coin, 33 green coins, and 38 yellow coins. What is the sum of all possible values of n if n is a positive integer?
A. 7
B. 10
C. 11
D. 12
E. 14
Are You Up For the Challenge: 700 Level Questions
The value of 1 red coin = the value of n blue coins;
The value of 1 blue coin = the value of n green coins;
The value of 1 green coin = the value of n yellow coins;
The value of 1 yellow coin = the value of n white coins.
If the value of 12 blue coins and 168 white coins equals to the value of 1 red coin, 33 green coins, and 38 yellow coins. What is the sum of all possible values of n if n is a positive integer?
A. 7
B. 10
C. 11
D. 12
E. 14
Are You Up For the Challenge: 700 Level Questions
02 Dec 2020, 01:50
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1 red = n^4 White coins
1 blue = n^3 White coins
1 Green = n^2 White coins
1 Yellow = n White coins
As per the question
12*n^3 + 168 = n^4 + 33*n^2 + 38n
So we have n^4 +33*n^2 + 38n - 12*n^3 -168 = 0
(n+2)(n^3 -14n^2 + 61n -84) = 0
(n+2)(n-3)(n-4)(n-7) = 0
Roots are -2,7,4 and 3
Thus, sum of positive roots are 14
1 blue = n^3 White coins
1 Green = n^2 White coins
1 Yellow = n White coins
As per the question
12*n^3 + 168 = n^4 + 33*n^2 + 38n
So we have n^4 +33*n^2 + 38n - 12*n^3 -168 = 0
(n+2)(n^3 -14n^2 + 61n -84) = 0
(n+2)(n-3)(n-4)(n-7) = 0
Roots are -2,7,4 and 3
Thus, sum of positive roots are 14
General Discussion
pearljiandani
Joined: 21 Oct 2019
Last visit: 03 Jul 2024
Posts: 23
Own Kudos:
Given Kudos: 22
Location: India
Schools: Kellogg '25 (M$) Ross '25 (A$)
GMAT 1: 720 Q49 V39
GPA: 3.64
03 Dec 2020, 23:38
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SharadIIFT
Hi,
Can you please explain the detailed steps after the highlighted bit? I'm not sure how to get to the 4 roots from there.
