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Is the price of an apple greater than that of an orange?

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Is the price of an apple greater than that of an orange?  [#permalink]

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New post 13 Jul 2017, 23:52
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Is the price of an apple greater than that of an orange?

(1) The price of 10 apples and 15 oranges is $8.
(2) The price of 5 apples is $1.30 greater than the price of 6 oranges.

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Re: Is the price of an apple greater than that of an orange?  [#permalink]

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New post 14 Jul 2017, 00:32
Bunuel wrote:
Is the price of an apple greater than that of an orange?

(1) The price of 10 apples and 15 oranges is $8.
(2) The price of 5 apples is $1.30 greater than the price of 6 oranges.


Given: Apples and Oranges
DS: price of apple say A > price of orange O ?

Statement 1 : 10 A + 15 O = 8
So in this case we can't determine price of apple is greater than oranges or not.
NOT SUFFICIENT

Statement 2 : 5A = 1.3 + 6O
Price 5A > 6O
So apple is costlier than orange
SUFFICIENT

Answer B

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Re: Is the price of an apple greater than that of an orange?  [#permalink]

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New post 14 Jul 2017, 00:34
Bunuel wrote:
Is the price of an apple greater than that of an orange?

(1) The price of 10 apples and 15 oranges is $8.
(2) The price of 5 apples is $1.30 greater than the price of 6 oranges.


It should be B.

1- 10A + 15O = 8

Gives us nothing about price of either. Insufficient.

2- 5A = 6O + 1.3

A = 1.2O + 1.3/1.5

Statement 2 is sufficient.
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Re: Is the price of an apple greater than that of an orange?  [#permalink]

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New post 14 Jul 2017, 00:57
Bunuel wrote:
Is the price of an apple greater than that of an orange?

(1) The price of 10 apples and 15 oranges is $8.
(2) The price of 5 apples is $1.30 greater than the price of 6 oranges.


Apples - A
Oranges - B

1) 10A + 15B = 8
A = 0.2
B = 0.4
10A = 2
15B = 6

If A = 0.5
B = 0.2
10A = 5
15B = 3

Insufficient.

2) 5A = 6B + 1.30
Sufficient.

B is the answer.
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Re: Is the price of an apple greater than that of an orange?  [#permalink]

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New post 14 Jul 2017, 03:43
Question stem: (a = apple price, o = orange price)
Is a > o
Statement 1:
10 a + 15 o = 8
this does not give any information as a > o or a < o

Statement 2:
5 a = 1.3 + 6 o

If 5 a > 6 o
a > 1.2 o

Even after increasing 'o' by a factor of 1.2, it is still less than a, hence o is originally less than a
Sufficient.
Answer is B

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Re: Is the price of an apple greater than that of an orange?  [#permalink]

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New post 30 Nov 2017, 10:39
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Top Contributor
Bunuel wrote:
Is the price of an apple greater than that of an orange?

(1) The price of 10 apples and 15 oranges is $8.
(2) The price of 5 apples is $1.30 greater than the price of 6 oranges.


Let A = the price (in dollars) of ONE apple
Let O = the price (in dollars) of ONE orange
Target question: Is O < A?

Statement 1: The price of 10 apples and 15 oranges is $8
We can write: 10A + 15O = 8
This doesn't tell us the RELATIONSHIP between the two prices.
Here's what I mean...
There are several values of A and O that satisfy statement 1. Here are two:
Case a: A = $0.50 and O = $0.20. So, 10A + 15O = 8 becomes = 10(0.5) + 15(0.2) = 8 (which checks out). In this case, O < A
Case b: A = $0.20 and O = $0.40. So, 10A + 15O = 8 becomes = 10(0.2) + 15(0.4) = 8 (which checks out). In this case, O > A
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The price of 5 apples is $1.30 greater than the price of 6 oranges.
This tells us that the cost of 5 apples is GREATER THAN the cost of 6 oranges
We can write: 6O < 5A
IMPORTANT: We also know that the cost of 5 oranges is LESS THAN the cost of 6 oranges. So, we can write: 5O < 60
When we combine the two red inequalities, we get: 5O < 6O < 5A
From this, we can conclude that 5O < 5A
Divide both sides by 5 to get: O < A (PERFECT!)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Re: Is the price of an apple greater than that of an orange?  [#permalink]

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New post 15 Dec 2017, 13:04
x - price of apple.
y - price of orange.

Statement 1: The price of 10 apples and 15 oranges is $8
\(10 x + 15 y = 8\) => \(15y = -10x + 8\)
=> \(y = -2 * x /3 + 8 / 15\)
If we observe, the slope of this line is -2/3 (negative), y intercept (at x = 0) = 8/15, x intercept (at y = 0) = 4/5
so if we start at x = 0, y = 8/15 and move towards x = 4/5, y = 0 , as we move x increases and y decreases
=> so we can't conclude which is greater. i.e price of apple or orange => Insufficient

Statement 2: \(5x = 1.3 + 6b\) => \(x = 1.3/5 + 1.2 y\) => x clearly creater than y => Sufficient (Answer B)
Re: Is the price of an apple greater than that of an orange? &nbs [#permalink] 15 Dec 2017, 13:04
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