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Math Expert V
Joined: 02 Sep 2009
Posts: 65012
A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 68% (01:58) correct 32% (02:03) wrong based on 71 sessions

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A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8. What is the minimum number of fruits in his shop?

A. 90
B. 105
C. 120
D. 240
E. 360

Are You Up For the Challenge: 700 Level Questions

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8753
Re: A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The  [#permalink]

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Bunuel wrote:
A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8. What is the minimum number of fruits in his shop?

A. 90
B. 105
C. 120
D. 240
E. 360

Are You Up For the Challenge: 700 Level Questions

oranges, apples and guavas in the ratio 2:5:8... or 2x, 5x, 8x

The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8, so basically we are looking at LCM and the multiples of LCM..
LCM(6,8)=24

Since we are looking at MINIMUM fruits, so we take the LCM itself......5x-2x=24.....x=8

Total fruits = (2x+5x+8x)=15*8=120

C
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GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 6427
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The  [#permalink]

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Bunuel wrote:
A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8. What is the minimum number of fruits in his shop?

A. 90
B. 105
C. 120
D. 240
E. 360

Are You Up For the Challenge: 700 Level Questions

no of apples = 5x/15
no of oranges = 2x/15
and given that The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8
5x/15-2x/15 = multiple of 6 and 8
3x/15 ; x/5
now use plugin and check value of x which is which is factor of both 6 and 8 in this case x= 120 ; we get 120/5 ; 24
sufficient
OPTION C ;120
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3410
A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The  [#permalink]

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Solution

Given
• Oranges : Apples : Guavas = 2:5:8.
• The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8.

To find
• Minimum number of fruits in the shop.

Approach and Working out
Though the question appears that it involves a combination of many concepts. But, we at e-gmat provide a methodical approach of using ‘Process Skills’ to master GMAT Quant.

This question uses couple of process skills i.e. ‘Inference’ and ‘Translate’.

Let’s see how we use ‘inference’ to solve this question.

Let oranges, apples and guavas = 2x, 5x and 8x respectively where x = positive integer.
• We need to find 2x+5x+8x = 15x.
• Two inferences can come out of this equation.
1. For minimum 15x, x should be minimum (Inference -1)
2. Answer should be a multiple of 15. (Inference –2).
 This makes us focus on only the multiples of 15 in the options.
 Since all are multiples of 15, we can quickly proceed on other part of the question.

Next comes the application of another process skill called ‘Translate’.

Using process skill of translate, we can translate the statement, ‘The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8’ into the following mathematical equation,
• Apples = Oranges + k*LCM(6,8), where k = positive integer.
• Solving the above equation: 5x = 2x + k*(24)
o 3x = k*24.
o Thus x=8k

Thus 15x= 120k.

Using the first inference, we can find minimum value of 15x using minimum value of k which is 1.

Thus 120*1 = 120 is the solution.

You see how using only a couple of process skills helped us solve a question? Essentially, we proceeded as follows:
• Applied the process skills of ‘inference’ and ‘translate’.
• Used the conceptual knowledge of LCM.
• That’s all we needed to solve the question.

Good thing is there are only 6 process skills to understand and they can be applied to GMAT questions helping us find the right answer.

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CEO  V
Joined: 03 Jun 2019
Posts: 3183
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The  [#permalink]

### Show Tags

Bunuel wrote:
A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8. What is the minimum number of fruits in his shop?

A. 90
B. 105
C. 120
D. 240
E. 360

Are You Up For the Challenge: 700 Level Questions

Given:
1. A fruit seller has oranges, apples and guavas in the ratio 2:5:8.
2. The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8.

Asked: What is the minimum number of fruits in his shop?

1. A fruit seller has oranges, apples and guavas in the ratio 2:5:8.
Let fruit seller has 2k oranges, 5k apples and 8k guavas where k is a positive integer.

2. The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 8.
LCM(6,8) = 24
5k - 2k = 3k = 24
k = 8

Minimum number of fruits in the shop = 2k + 5k + 8k = 15k = 15*8 = 120

IMO C
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The   [#permalink] 30 May 2020, 22:04

# A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The  