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There are some oranges and apples in a basket. After additional 4 and

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There are some oranges and apples in a basket. After additional 4 and  [#permalink]

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New post 07 Mar 2018, 05:08
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35% (02:15) correct 65% (75:01) wrong based on 20 sessions

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There are some oranges and apples in a basket. After additional 4 and 7 oranges and apples are added to the basket, the ratio of the number of oranges to apples was greater than ½. Find the initial number of oranges in the basket.

1. The total number of oranges and apples after the addition was 25.
2. The product of the initial number of apples and oranges is 33.

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There are some oranges and apples in a basket. After additional 4 and  [#permalink]

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New post 07 Mar 2018, 05:30
There are some oranges and apples in a basket. After additional 4 and 7 oranges and apples are added to the basket, the ratio of the number of oranges to apples was greater than ½. Find the initial number of oranges in the basket.

Given: \(\frac{O + 4}{A+7}>\frac{1}{2}\) --> 2O + 1 > A.

Question: \(\frac{O}{A} = ?\)


(1) The total number of oranges and apples after the addition was 25:

(O + 4) + (A + 7) = 25;
O + A = 14.
We could have many values of O and A (satisfying both O + A = 14 and 2O + 1 > A). For example, O = 13 and A = 1 OR O = 12 and A = 2.

Not sufficient.


(2) The product of the initial number of apples and oranges is 33:

O*A = 33. Since both O and A are integers, then there exist only two sets of O and A, which satisfy both O*A = 33 and 2O + 1 > A.
O = 33 and A = 1;
O = 11 and A = 3.

Not sufficient.


(1)+(2) From (2) only O = 11 and A = 3 satisfy O + A = 14 from (1). Sufficient.


Answer: C.
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Re: There are some oranges and apples in a basket. After additional 4 and  [#permalink]

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New post 07 Mar 2018, 06:21
Oranges = x & Apples = y
After Addition -
Oranges = x + 4 & Apples = y + 7

given ( x + 4 ) > 1/2 ( y + 7)
- 2x + 8 > y + 7
- 2x > y - 1 = all the numbers must satisfy this equation

Question : Find X?

[1] : x + 4 + y + 7 = 25 or x + y = 14

let's substitute y = 14 - x in equation 2x > y -1

2x > 14 - x - 1
3x> 13
x >= 5

x + y = 14
5 9
6 8
7 7 and so on : multiple values of x is possible hence [1] is alone not sufficient

[2] x * y = 33 [ since x & y has to be + ve integers as we can't have negative decimal oranges or apples ]

x = 1 ; y = 33 ==> 2 > 32 [ substituting numbers in the main equation 2x > y - 1] : no : this combination is not possible
x = 33 ; y = 1 ==> 66> 0 : Yes possible
x = 11 ; y = 3 ==> 22 > 2 : Yes possible
x = 3 ; y = 11 ==> 6> 10 : Not Possible

Again two different values of X are possible hence [2] alone is not sufficient

[1] + [2]

x + y = 14 & xy = 33
x = 11 ; y = 3 - this is our answer
x = 3 ; y = 11 - does not satisfy 2x > y - 1

Hence C

2x > y - 1

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Re: There are some oranges and apples in a basket. After additional 4 and &nbs [#permalink] 07 Mar 2018, 06:21
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