apples, mangoes and bananas

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coolhabhi: Master | Next Rank: 500 Posts; Posts: 141; Joined: Tue Oct 04, 2011 5:17 am; Thanked: 25 times

by coolhabhi » Sun Mar 25, 2012 4:37 am

Rama went to the market and bought some apples, mangoes and bananas. He bought 42 fruits in all. The number of bananas is less than half the number of apples; the number of mangoes is more than one-third the number of apples and the number of mangoes is less than three-fourths the number of bananas.

1. How many apples did Rama buy?
(A) 20 (B) 23 (C) 26 (D) 28

2. How many bananas did Rama buy?
(A) 8 (B) 9 (C) 10 (D) 11

[spoiler]OA: 1st question : B & 2nd question : D[/spoiler]

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Source: Beat The GMAT — Problem Solving | Sun Mar 25, 2012 4:37 am

seal4913: Master | Next Rank: 500 Posts; Posts: 106; Joined: Wed Mar 23, 2011 4:56 pm; Thanked: 8 times

by seal4913 » Sun Mar 25, 2012 6:42 am

So the first equation you get is a + b + m = 42.

Then with less than and greater than I tend to make them equal for the sake of making it easier.

So B = .5a; a = 1/3m; m = 3/4b

First I'm going to solve for bananas as when i know that I know apples is a little more than double that.

So b = .5a which equals a = 2b (as stated above);

So 2B + b + (3/4)B = 42 = (15/4)b = 42 = 15B = 168 which equals [spoiler]B = 11[/spoiler]

So you take that and plug it in for [spoiler]11 = .5A which is a 22 but remember bananas are less than half of so it's going to be greater than 22 and since fruits are whole it's 23.[/spoiler]

Hope that helps.

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maverick_andy: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Fri Aug 25, 2006 7:35 amFollowed by: 4 members; Thanked: 4 times

by maverick_andy » Sun Mar 25, 2012 9:14 am

coolhabhi wrote:Rama went to the market and bought some apples, mangoes and bananas. He bought 42 fruits in all. The number of bananas is less than half the number of apples; the number of mangoes is more than one-third the number of apples and the number of mangoes is less than three-fourths the number of bananas.

1. How many apples did Rama buy?
(A) 20 (B) 23 (C) 26 (D) 28

2. How many bananas did Rama buy?
(A) 8 (B) 9 (C) 10 (D) 11

Best way: Process Of Elimination and calculated with assumption that "Banana<=apple/2 (max)"

1. If we carefully observe, both (C) & (D) ruled out because 26/2=12 and 28/2=14
2. Now we left with 20 0r 23 apples, so to satisfy the condition "the number of mangoes is more than one-third the number of apples and the number of mangoes is less than three-fourths the number of bananas." ONLY B& D will qualify for the answer.

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