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Ray is 2 inches taller than Lin, and Ray is 3 inches taller than Sam.

Quantity A

Quantity B

The average (arithmetic mean) height of Ray, Lin, and Sam

The median height of Ray, Lin, and Sam

A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
08 Nov 2018, 08:39

1

This post received KUDOS

Expert's post

Carcass wrote:

Ray is 2 inches taller than Lin, and Ray is 3 inches taller than Sam.

Quantity A

Quantity B

The average (arithmetic mean) height of Ray, Lin, and Sam

The median height of Ray, Lin, and Sam

A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

Let's write all heights in terms of Ray's height.

Let R = Ray's height (in inches) So, R - 2 = Lin's height And R - 3 = Sam's height

Average height = [R + (R-2) + (R-3)]/3 = [3R - 5]/3 = 3R/3 - 5/3 = R - 5/3

To find the median height, arrange heights in ASCENDING ORDER: R-3, R-2, R So, the median height = R-2

So, we get: QUANTITY A: R - 5/3 QUANTITY B: R - 2

Subtract R from both quantities to get: QUANTITY A: -5/3 QUANTITY B: -2

Since -5/3 is greater than -2, the correct answer is A

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Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
09 Nov 2018, 14:30

The answer is Quant A:

Ray= 2+Lin's age Ray= 3+Sam's age If Lin is aged 6 then Ray is 8 which means Sam (8-3) is 5 Quant A=5+6+8=(20/3)= 6+ Quant B=6 is the median So Quant A is greater

Please share if there is an easier way to solve this.

Re: Ray is 2 inches taller than Lin, and Ray is 3 inches taller [#permalink]
09 Nov 2018, 19:20

Expert's post

Carcass wrote:

Ray is 2 inches taller than Lin, and Ray is 3 inches taller than Sam.

Quantity A

Quantity B

The average (arithmetic mean) height of Ray, Lin, and Sam

The median height of Ray, Lin, and Sam

A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

2 inches and 3 inches more means the lower two heights are consecutive integers.But the third height is not consecutive but slightly more.. Had the third height too been consecutive, both median and mean would be EQUAL. Because the third number is not consecutive but slightly more, the mean will be greater .

You can check with values.. x,x+1,X+3... Median is x+1 Mean is x+\(\frac{4}{3}\) So A is more.
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