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There is a certain number of apples, guavas and oranges in a basket.

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There is a certain number of apples, guavas and oranges in a basket.  [#permalink]

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New post 25 Aug 2018, 12:05
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Number of each variety is more than one. Ratio of number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges. If total number of fruits is 61, then find the number of guavas.

A) 16
B) 20
C) 25
D) 28
E) Cannot be determined
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There is a certain number of apples, guavas and oranges in a basket.  [#permalink]

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New post 25 Aug 2018, 14:16
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sultanatehere wrote:
Number of each variety is more than one. Ratio of number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges. If total number of fruits is 61, then find the number of guavas.

A) 16
B) 20
C) 25
D) 28
E) Cannot be determined


Question seems incomplete. "No of each variety of what?" Object of the sentence is missing. I assume it to be fruits by reading the next sentence.

Given,
a) \(n_{a}+n_{g}+n_{0}=61\)
b) \(\frac{n_{a}}{n_{g}}=\frac{n_{g}}{n_{o}}\)
Or,\(n_{g}^2=n_{a}*n_{o}\) implies that \(n_{a}*n_{o}\) is a perfect square .

Let's check options that satisfies (a) and (b).
A. \(n_{g}=16\), \(n_{g}^2=16^2\). Prime factorizing \(16^2=2^8=2^5*2^3=n_{a}*n_{o}\)
So, \(n_{a}=2^5=32\) and \(n_{o}=2^3=8\), but total no of fruits=16+32+8=56 DISCARD
B. \(n_{g}=20\), \(n_{g}^2=20^2\). Prime factorizing \(20^2=2^4*5^2=16*25=n_{a}*n_{o}\)
So, \(n_{a}=16\) and \(n_{o}=25\), total no of fruits=20+25+16=61. Given condition met.

Ans. (B)
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There is a certain number of apples, guavas and oranges in a basket.  [#permalink]

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New post 26 Aug 2018, 09:55
1
2
sultanatehere wrote:
Number of each variety is more than one. Ratio of number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges. If total number of fruits is 61, then find the number of guavas.

A) 16
B) 20
C) 25
D) 28
E) Cannot be determined


Let the number of apples, guavas, and oranges be A, G, and O respectively

\(A : G = G : O\) -> \(G^2 = AO\) | \(A + G + O = 61\) (from the question stem)

From the given answer options, where the number of G is given - we can try to arrive
at the number for the other fruits, such that the necessary condition is satisfied.

If \(G = 16, A + O = 45\) -> \((16)^2 = AO = A(45 - A)\) -> \(A^2 - 45A + 256 = 0\)-> Don't get integer values
If \(G = 20, A + O = 41\) -> \((20)^2 = AO = A(41 - A)\) -> \(A^2 - 41A + 400 = 0\) -> \(A = 25\) or \(16\)

Therefore, there are 20(Option B) guavas - with 16 apples and 25 oranges because A : G = G : O.
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There is a certain number of apples, guavas and oranges in a basket. &nbs [#permalink] 26 Aug 2018, 09:55
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