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# What is the average of x and y?

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Manager
Joined: 26 Nov 2014
Posts: 101
What is the average of x and y? [#permalink]

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04 Nov 2015, 06:27
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Difficulty:

5% (low)

Question Stats:

77% (00:19) correct 23% (00:18) wrong based on 179 sessions

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What is the average of x and y?

1. x + y = 20
2. 2x + 4y = 54
[Reveal] Spoiler: OA

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Consider Kudos for my post, if it is helpful.
TIA

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Joined: 12 Sep 2015
Posts: 2298
Re: What is the average of x and y? [#permalink]

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04 Nov 2015, 08:23
1
KUDOS
Expert's post
shyind wrote:
What is the average of x and y?

1. x + y = 20
2. 2x + 4y = 54

Target question: What is the average of x and y?
Average of x and y = (x + y)/2
So, to find the average, we need only find the value of x+y

Statement 1: x + y = 20
Perfect!
So, average = (x + y)/2
= 20/2
= 10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2x + 4y = 54
Divide both sides by 2 to get: x + 2y = 27
This doesn't help, because we need the value of x + y.
To understand why this statement is not sufficient, let's test some values. There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 13, in which case the average of x and y = (1+13)/2 = 7
Case b: x = 9 and y = 9, in which case the average of x and y = (9+9)/2 = 9[/color]
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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Brent Hanneson – Founder of gmatprepnow.com

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Joined: 12 Sep 2015
Posts: 2298
Re: What is the average of x and y? [#permalink]

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04 Nov 2015, 09:06
shyind wrote:
What is the average of x and y?

1. x + y = 20
2. 2x + 4y = 54

Target question: What is the average of x and y?
Average of x and y = (x + y)/2
So, to find the average, we need only find the value of x+y

Statement 1: x + y = 20
Perfect!
So, average = (x + y)/2
= 20/2
= 10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2x + 4y = 54
Divide both sides by 2 to get: x + 2y = 27
This doesn't help, because we need the value of x + y.
To understand why this statement is not sufficient, let's test some values. There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 13, in which case the average of x and y = (1+13)/2 = 7
Case b: x = 9 and y = 9, in which case the average of x and y = (9+9)/2 = 9
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

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Joined: 19 Mar 2014
Posts: 977
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: What is the average of x and y? [#permalink]

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08 Jul 2017, 14:50
shyind wrote:
What is the average of x and y?

1. x + y = 20
2. 2x + 4y = 54

$$Average = \frac{Sum}{Count}$$

So in order to find the average of x and y we will need the sum of $$x + y$$

$$(1) x + y = 20$$
As this equation directly gives us the value of x + y which is what we are looking for, we will be able to find average.

$$Average = \frac{x + y}{2}$$

$$Average = \frac{20}{2}$$

$$Average = 10$$

Hence, (1) ===== is SUFFICIENT

$$(2) 2x + 4y = 54$$

From this equation we will not be able to determine the value of x + y and hence this equation is not sufficient.

Hence, (2) ===== is NOT SUFFICIENT

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Re: What is the average of x and y?   [#permalink] 08 Jul 2017, 14:50
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