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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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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.
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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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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
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