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The youngest of 4 children has siblings who are 3, 5, and 8 years olde

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Joined: 02 Sep 2009
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The youngest of 4 children has siblings who are 3, 5, and 8 years olde  [#permalink]

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13 Dec 2015, 05:07
00:00

Difficulty:

5% (low)

Question Stats:

90% (00:55) correct 10% (01:17) wrong based on 102 sessions

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The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling?

A. 17
B. 18
C. 19
D. 21
E. 22

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Re: The youngest of 4 children has siblings who are 3, 5, and 8 years olde  [#permalink]

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13 Dec 2015, 05:27
Bunuel wrote:
The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is.

Let age of the youngest child be " y "

Age of the all the children in the family is y , (y + 3) ,(y + 5) and (y + 8)

Total age of all the children in the family is y + (y + 3) + (y + 5) + (y + 8) => 4y + 16

Bunuel wrote:
If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling?

Total age of the 4 sibling is 21 x 4 = 84 years ..

We already have the total age of alll the children is 4y + 16

So, 4y + 16 = 84

Or, 4y = 68

Or, y = 17

So, Age of the youngest child is 17 years.

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Re: The youngest of 4 children has siblings who are 3, 5, and 8 years olde  [#permalink]

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13 Dec 2015, 11:16
let the youngest be Y
sum of ages of all the children = 4y+16=4*(avg)
4y+16=84
y=17
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Re: The youngest of 4 children has siblings who are 3, 5, and 8 years olde  [#permalink]

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14 Dec 2015, 16:57
Hi All,

This question can be solved by TESTing THE ANSWERS.

We're told that the YOUNGEST of 4 children has siblings who are 3, 5, and 8 years OLDER than she is and that the average age of the 4 siblings is 21. We're asked for the age of the youngest sibling.

Since the average age is 21 and we're trying to figure out the age of the YOUNGEST sibling, we should look for an answer that is several years LESS than 21...

Let's TEST Answer B: 18 years

IF...
Youngest = 18
Siblings = 21, 23 and 26
Sum = 88
Average = 88/4 = 22
This is TOO HIGH (the average is supposed to be 21).

Since the average is too high, all 4 of the children are TOO OLD. There's only one answer left that would lower the average...

GMAT assassins aren't born, they're made,
Rich
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Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Current Student Joined: 02 Jun 2015 Posts: 82 Location: Brazil Concentration: Entrepreneurship, General Management GPA: 3.3 Re: The youngest of 4 children has siblings who are 3, 5, and 8 years olde [#permalink] Show Tags 15 Dec 2015, 11:45 Testing the answer in my opinion takes a long time. We know that each one is 3,5,8 years OLDER X + (3+X) + (5+X) + (8+X) = 21*4 4X + 16 = 84 4X = 68 X = 17 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13058 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The youngest of 4 children has siblings who are 3, 5, and 8 years olde [#permalink] Show Tags 15 Dec 2015, 15:55 Hi douglasvg, If you're not using Tactics (such as TEST THE ANSWERS) very often, then it might take you a little longer to use that approach right now (since you're not used to thinking in that way). However, in the long run - and on harder questions - those same Tactics can be extremely valuable. 1) How have you been scoring on your practice CATs (including the Quant and Verbal Scaled Scores)? 2) How is your pacing in the Quant section? Do you have to rush just to finish? GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

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Re: The youngest of 4 children has siblings who are 3, 5, and 8 years olde  [#permalink]

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15 Dec 2015, 16:06
EMPOWERgmatRichC wrote:
Hi douglasvg,

If you're not using Tactics (such as TEST THE ANSWERS) very often, then it might take you a little longer to use that approach right now (since you're not used to thinking in that way). However, in the long run - and on harder questions - those same Tactics can be extremely valuable.

1) How have you been scoring on your practice CATs (including the Quant and Verbal Scaled Scores)?
2) How is your pacing in the Quant section? Do you have to rush just to finish?

GMAT assassins aren't born, they're made,
Rich

On GMATPREP software Im scoring between 45-50 in quant
For hard question I indeed use it, then its a fast way to solve it.

Thank you Empower
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Joined: 11 Sep 2015
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The youngest of 4 children has siblings who are 3, 5, and 8 years olde  [#permalink]

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09 Jan 2018, 09:12
Top Contributor
Bunuel wrote:
The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling?

A. 17
B. 18
C. 19
D. 21
E. 22

Let y = the age of the youngest child

So, y + 3 = age of sibling who is 3 years older than the youngest child
y + 5 = age of sibling who is 5 years older than the youngest child
y + 8 = age of sibling who is 8 years older than the youngest child

The average (arithmetic mean) age of the 4 siblings is 21
This means: [y + (y+3) + (y+5) + (y+8)]/4 = 21
Multiply both sides by 4 to get: y + (y+3) + (y+5) + (y+8) = 84
Simplify: 4y + 16 = 84
Solve: y = 17

Cheers,
Brent
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Re: The youngest of 4 children has siblings who are 3, 5, and 8 years olde  [#permalink]

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10 Jan 2018, 00:31
1
X + (3+X) + (5+X) + (8+X) = 21*4
4 X + 16 = 84
4 X = 68
X = 17
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Re: The youngest of 4 children has siblings who are 3, 5, and 8 years olde  [#permalink]

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30 Jul 2018, 10:33
Bunuel wrote:
The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling?

A. 17
B. 18
C. 19
D. 21
E. 22

We can let x = the age of the youngest child; thus, the ages of the three older children are x + 3, x + 5 and x + 8, respectively. We can create the equation:

(x + x + 3 + x + 5 + x + 8)/4 = 21

4x + 16 = 84

4x = 68

x = 17

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Re: The youngest of 4 children has siblings who are 3, 5, and 8 years olde  [#permalink]

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21 Nov 2018, 08:45
If the average age of the 4 siblings is 21, we can determine the sum of ages by reversing division by 4.

$$\frac{x}{4}= 21$$
$$x = 4*21$$
$$x = 84$$

From there, we can set up an equation to find the age of the youngest child based on their age relative to their siblings.

If the youngest child = x:

$$x + (x+3) + (x+5) + (x+8) = 84$$
$$4x + 16 = 84$$
$$4x = 68$$
$$x = 17$$

Therefore, the youngest child is 17 (option A).
Re: The youngest of 4 children has siblings who are 3, 5, and 8 years olde &nbs [#permalink] 21 Nov 2018, 08:45
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