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Doubts - (GMAT Prep - Quant Ques)

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by sudhanshu99 » Fri Sep 30, 2011 9:51 pm
Guys,
I found difficulty in solving the following GMAT Prep PS & SC ques. Pl help with explanations. Thanks in advance.

1. (-1)k+1(½k). T is the sum of the first 10 k, is t
a.> 2
b.between 1 and 2
c.between 1/2 and 1
d.between 1/4 and 1/2
e.< 1/4
Ans-D

2.Does line k intersect quadrant II?
a.Slope of k is -1/6
b.Y intercept of k is -6
Ans-A

3.If x ≠ 0, then √x2/x =
a.-1
b.0
c.1
d.x
e.|x|/x
Ans-E

4. Lines n and p lie in xy plane. Is slope of line n less than slope of line p? C
a.Lines n and p intersect at (5, 1)
b.Y-intercept of line n is greater than y intercept of line p
Ans-C

5. A basket has 5 apples, one is spoiled. If Henry picked 2 apples simultaneously and at random, what is probability that the 2 selected apples will include the spoiled one.
a.1�5
b.2�10
c.2�5
d.1�2
e.3�5
Ans-C
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by Anurag@Gurome » Fri Sep 30, 2011 10:06 pm
Q2. While solving coordinate geometry problems, try to visualize the scenario. In this case for statement 1, try visualizing different straight lines with negative slope. And then you'll see their is no way you can draw a straight line with negative slope without intersecting the quadrant II.

This is because the slope is measured with respect to the angle made by the straight line with the positive x-axis. And if the angle is less than 90 degrees, slope is positive and if it is greater than 90 degrees, slope is negative.

Refer to figure below,
Image

Hence, statement 1 is sufficient to answer the question in YES.

But for statement 2, slope may be negative or positive and accordingly the line may or may not intersect quadrant II.

The correct answer is A.
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by Anurag@Gurome » Fri Sep 30, 2011 10:08 pm
Q4. Given: Say equation of the line n is y = nx + a and equation of line p is y = px + b, where n and p are slopes of the lines and a and b are the y-intercepts of the lines respectively.
We need to determine whether n is greater than p or not.

Statement 1: Lines n and p intersect at (5, 1)
Therefore,

1 = 5n + a
1= 5p + b

Thus, (5n + a) = (5p + b) => (n - p) = (b - a)/5

As we don't know the relation between a and b, we can't determine whether n is greater than p or not; Not sufficient.

Statement 2: Y-intercept of line n is greater than y intercept of line p
Therefore, a > b
This is clearly not enough to determine whether n is greater than p or not; Not sufficient.

1 & 2 Together: Combining the above relations,
Thus, (n - p) = (b - a)/5 < 0, as a > b => (b - a) < 0

=> n < p; Sufficient.

The correct answer is C.
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by Anurag@Gurome » Fri Sep 30, 2011 10:13 pm
Q5. Probability of not choosing the rotten apple in 1st pick = 4/5
Probability of not choosing the rotten apple in 2nd pick = 3/4
Hence, required Probability = 1 - (4/5 * 3/4) = 1 - 3/5 = 2/5

The correct answer is C.
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by Anurag@Gurome » Fri Sep 30, 2011 10:21 pm
Q1. a^n + a^(n-1)+ ... + a+1=(a^(n+1)-1)/(a-1)

T = 1/2 - 1/2^2 + 1/2^3 -...+ 1/2^10
T = 1/2 * [1 + (-1/2) + (-1/2)^2 + ... + (-1/2)^9]
T = 1/2 * (1 - (-1/2)^10)/(1 - (-1/2))
T = (2^10 - 1)/(3 * 2^10)
(2^10 - 1) is appr 2^10, so T = 1/3, which lies between 1/2 and 1/4

The correct answer is D.
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by Anurag@Gurome » Fri Sep 30, 2011 10:25 pm
Q3. Here the square root symbol means "the positive square root of". So, √(x²) will always be positive, which will be the absolute value of x or we can say that √(x²)/x = |x|/x

The correct answer is E.
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