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a, b, c, and d are consecutive integers such that a < b < c [#permalink]
30 Aug 2018, 16:27

Expert's post

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Question Stats:

69% (00:32) correct
30% (00:48) wrong based on 53 sessions

a, b, c, and d are consecutive integers such that \(a < b < c < d\).

Quantity A

Quantity B

The average (arithmetic mean) of a, b, c, and d

The average (arithmetic mean)of b and c

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

Re: a, b, c, and d are consecutive integers such that a < b < c [#permalink]
01 Sep 2018, 10:10

1

This post received KUDOS

sandy wrote:

a, b, c, and d are consecutive integers such that \(a < b < c < d\).

Quantity A

Quantity B

The average (arithmetic mean) of a, b, c, and d

The average (arithmetic mean)of b and c

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

Let the series be 4<3<2<1 as consecutive integers.

Re: a, b, c, and d are consecutive integers such that a < b < c [#permalink]
20 Aug 2019, 10:33

1

This post received KUDOS

Expert's post

sandy wrote:

a, b, c, and d are consecutive integers such that \(a < b < c < d\).

Quantity A

Quantity B

The average (arithmetic mean) of a, b, c, and d

The average (arithmetic mean)of b and c

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

Here's an algebraic approach:

If a, b, c, and d are consecutive integers such that \(a < b < c < d\), then we can conclude the following: \(a = a\) (no duh ) \(b = a + 1\) \(c = a + 2\) \(d = a + 3\)

We can now replace b, c and d with their equivalent values to get:

Quantity A: Average \(= \frac{a+(a+1)+(a+2)+(a+3)}{4}= \frac{4a+6}{4}=\frac{4a}{4}+\frac{6}{4}=a+1.5\)

Quantity B: Average \(=\frac{(a+1)+(a+2)}{2}=\frac{2a+3}{2}=\frac{2a}{2}+\frac{3}{2}=a+1.5\)

Answer: C

Cheers, Brent

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Re: a, b, c, and d are consecutive integers such that a < b < c
[#permalink]
20 Aug 2019, 10:33