GmatPrep 2 DS questions - help required.

[pramod_d]

Hi,
Following are few questions i did wrong in Gmat Prep 2 exam. but could not understand the answer. Please help me.

1. In xy coordinate plane, line l and line k intersect at the point (4,3). Is the product of their slopes negetive?

a. the product of the x-intercepts of lines l and k is positive.
b. the product of the y-intercepts of lines l and k is negetive.

my ans: e
correct answer: c

I guessed this question. didnt know how to attempt it.

Ps

2. if x < 0, then sqrt(-x * |x|) is?

1 -x
2 -1
3 1
4 x
5 sqrt (x)

my answer: d
correct answer: a

my approach.

if x is negetive,

sqrt ( -(-x) |-x| ) = sqrt ( x. x ) = x.

I am confused with modulus definition.

if x < 0, | x | = -x : Is this statement correct?
If so, the answer would be option a. Please let me know.


3. A certain group of car dealerships agreed to donate x dollars to a red cross chapter for each car sold during a 30 day period. what was the total amount that was expected to be donated?

a. A total of 500 cars were expected to be sold.
b. 60 more cars were sold than expected, so that the total amount actually donated was $28 k.

my answer: b
correct answer: c

The question asked is, what is the total amount expected to be donated.

a. number of cars alone will not help because we need the value of x. => not sufficient.
b. irrespective of the no of cars, the total amount is presented (28k). So, this should be sufficient.

if we combine both a and b, we might get total no of cars and the value of x. However, the question asked is the amount which option b gives. Why the answer is not b? Please explain.

4. if y >= 0, what is the value of x?


a. | x-3| >= y
b. | x-3| <= -y

my answer: e
correct answer: b

This question has multiplied my confusion on modulus and inequalities. Please let me know how do i approach this problem.

Pramod.

[Anurag@Gurome]

2. if x < 0, then sqrt(-x * |x|) is?

1 -x
2 -1
3 1
4 x
5 sqrt (x)

The first question is much discussed in this forum. I'm solving the rest.

If x < 0, |x| = -x
And √(x²) = |x|, to remove the confusion regarding negative roots. This is where you had done the mistake.

Now √[(-x)*(|x|)] = √[(-x)*(-x)] = √(x²) = |x| = -x

The correct answer is A.

[Anurag@Gurome]

3. A certain group of car dealerships agreed to donate x dollars to a red cross chapter for each car sold during a 30 day period. what was the total amount that was expected to be donated?

a. A total of 500 cars were expected to be sold.
b. 60 more cars were sold than expected, so that the total amount actually donated was $28 k.

Note that the question is asking the expected amount to be donated, not the actual amount that was donated. And that was your mistake.

Statement 1: A total of 500 cars were expected to be sold.
Therefore, expected amount to be donated = $ 500x.
But as we don't know the value of x, we can't determine the amount.

Not Sufficient

Statement 2: 60 more cars were sold than expected, so that the total amount actually donated was $28 k
Say, number of cars expected to be sold = C
Therefore, (C + 60)x = 28,000
=> Expected amount to be donated = Cx = (28,000 - 60x)
But as we don't know the value of x, we can't determine the amount.

Not Sufficient

Statement 1: C = 500
Thus, 500x = (28000 - 60x)
It is a linear equation in x, hence we can solve for x. And the expected amount to be donated (= $ 500x) can be easily determined.

Sufficient

The correct answer is C.

[pramod_d]

Thanks Anurag. I got some clarity on modulus. Thanks alot.

[Anurag@Gurome]

4. if y >= 0, what is the value of x?

a. | x-3| >= y
b. | x-3| <= -y

Statement 1: |x - 3| ≥ y
As y is a non-negative quantity, there may be infinite number of x such that |x - 3| ≥ any non-negative quantity, y.

Not Sufficient

Statement 1: |x - 3| ≤ -y
As y is a non-negative quantity, -y must be a non-positive quantity, i.e. -y ≤ 0. Meaning either -y is a negative quantity or it is equal to zero.

According to the statement, |x - 3| is either less than or equal to -y, a non-positive quantity.
Now |x - 3| is always a non-negative quantity, hence it is impossible that |x - 3| is less than zero. Hence |x - 3| must be equal to zero.
Therefore, |x - 3| = 0
=> x = 3

Sufficient

The correct answer is B.

[shovan85]

1. In xy coordinate plane, line l and line k intersect at the point (4,3). Is the product of their slopes negetive?

a. the product of the x-intercepts of lines l and k is positive.
b. the product of the y-intercepts of lines l and k is negetive.

a. the product of the x-intercepts of lines l and k is positive.

So either the intercepts are positive x(l) and x(k) > 0
Or the intercepts are negative x(l) and x(k) < 0

Nothing can be told about the slope. Not Sufficient.

b. the product of the y-intercepts of lines l and k is negative.

So either y(l) > 0 and y(k) < 0 Or y(l) < 0 and y(k) > 0

Nothing can be told about the slope. Not Sufficient.

Combine both,
We will have 4 cases
1. x(l) > 0, y(l) > 0 and x(k) > 0, y(k) < 0
2. x(l) < 0, y(l) > 0 and x(k) < 0, y(k) < 0
3. x(l) > 0, y(l) < 0 and x(k) > 0, y(k) > 0
4. x(l) < 0, y(l) < 0 and x(k) < 0, y(k) > 0

See the Figure 1 below, Case 2 and 4 are not possible. So discard them.

Case 1 and 3 both line L and K have opposite sign in terms of slope. To get the concept pf slope see fig 2. In Fig 2,

1. Red: Angle subtended by this line with X axis is less than 90. Slope is +ve. (Remember trigonometry? TAN(angle) is the slope)
2. Blue: Angle subtended by this line with X axis is equal to 90. Slope is infinite(cannot be determined).
3. Green: Angle subtended by this line with X axis is greater than 90. Slope is -ve.

So Sufficient.