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g.shankaran: Master | Next Rank: 500 Posts; Posts: 101; Joined: Tue Oct 27, 2009 8:19 amFollowed by: 2 members; Thanked: 4 times

by g.shankaran » Sat Apr 09, 2011 9:28 pm

For a certain examination, a score of 58 was 2 Standard deviation (SD) below the mean, and the score of 98 was 3 SD above the mean. what was the mean score for the exam?

1. 74
2. 76
3. 78
4. 80
5. 82.

Ans is 1.

can you please explain the solution

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Source: Beat The GMAT — Problem Solving | Sat Apr 09, 2011 9:28 pm

Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Sat Apr 09, 2011 10:02 pm

g.shankaran wrote:For a certain examination, a score of 58 was 2 Standard deviation (SD) below the mean, and the score of 98 was 3 SD above the mean. what was the mean score for the exam?

1. 74
2. 76
3. 78
4. 80
5. 82.

Ans is 1.

can you please explain the solution

Let the SD be x. In that case:

the mean is equal to 58+2x
OR
98-3x.
In other words:
58+2x = 98-3x.
Find x:
5x = 98-58 = 40
x=8

So the mean is 58+2*8 (or 98-3*8) = 74.

Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

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g.shankaran: Master | Next Rank: 500 Posts; Posts: 101; Joined: Tue Oct 27, 2009 8:19 amFollowed by: 2 members; Thanked: 4 times

by g.shankaran » Sat Apr 09, 2011 10:31 pm

1. When a certain tree was first planted, it was 4 feet tall and the height of the tree increased by a constant amount each year for hte next 6 yr. At the end of the 6th yr the tree was 1/5 taller than it was at the end of the 4th yr. By how many feet did the height of the tree increase each year?

a. 3/10
b. 2/5
c. 1/2
d. 2/3
e. 6/5

Can you please help

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Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Sat Apr 09, 2011 10:41 pm

g.shankaran wrote:1. When a certain tree was first planted, it was 4 feet tall and the height of the tree increased by a constant amount each year for hte next 6 yr. At the end of the 6th yr the tree was 1/5 taller than it was at the end of the 4th yr. By how many feet did the height of the tree increase each year?

a. 3/10
b. 2/5
c. 1/2
d. 2/3
e. 6/5

Can you please help

algebraic: let the amount the tree grows each year be x.
So:
Tree's height at the end of the 4th year is 4+4x.
Tree's height at the end of the 6th year is 4+6x.

According to the question
4+6x = 4+4x + 1/5*(4+4x) (OR 6/5*(4+4x)
and solve for x.

4+6x = 4+4x + 4/5 + 4x/5 /*5
20+30x = 20+20x + 4+4x
20+30x = 24 + 24x
6x = 4
x=2/3

Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

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