Need explanations

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Need explanations

by ksioss » Tue Nov 30, 2010 12:57 pm
I've been writing down the questions that I missed from several practice tests I've taken. They do not have explanations, so knowing the right answer does nothing for me if I don't know how to arrive at that answer! There is nine in total, so any help would be greatly appreciated :)

Data sufficiency Questions
Are x and y both positive?
1 - 2x-2y + 1
2 - x/y > 1

In Isosceles Triangle RST what is the measure of <R
1 - Measure of <T is 100
2 - Measure of <S is 40

Ratio of number of women to men attending an event is 5 to 2. What was the number of men that attended?
1- Ratio of children to men is 5 to 11
2 - The number of women is less than 30

(1/5)^m(1/4)^18 = 1/2(10)^35
m = ?
Choices: 17, 18, 34, 35, 36

If n is a positive integer and the product of all integers from 1 to n, inclusive is a multiple of 990, what is the least possible value of n?
Choices: 10,11,12,13,14


In the figure a square is inscribed in a circle. If the area of the square is 16 what is the area of the circular region?
2π, 4 π, 8 π, 12 π, 16 π

If 0 < x < 1, what is the median of the values x, x -1, x2, Square root (x), x3
For which iof the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
F(x) = x2
F(x) = x + 1
F(x) = square root (x)
F(x) = 2/x
F(x) = -3x

Susan drove an average of 30 miles per house for the first 30 miles of her trip and then an average of 60 miles per her for the remaining 30 miles of her tirp. If she made no stops, what was the average speed of her trip?
35, 40, 45, 50, 55
Source: — Quantitative Reasoning |

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by Geva@EconomistGMAT » Wed Dec 01, 2010 1:32 am
you really should split these into separate posts - otherwise this thread can get mighty confusing.
ksioss wrote:I've been writing down the questions that I missed from several practice tests I've taken. They do not have explanations, so knowing the right answer does nothing for me if I don't know how to arrive at that answer! There is nine in total, so any help would be greatly appreciated :)

Data sufficiency Questions
Are x and y both positive?
1 - 2x-2y + 1 typo here: need an equation or inequality.
2 - x/y > 1

In Isosceles Triangle RST what is the measure of <R
1 - Measure of <T is 100
2 - Measure of <S is 40
Answer is A: the question is whether R is equal to T or to S. However, if T is 100 degrees, then R cannot equal T, as then you would have two angles of 100 degrees each, which is more than 180. Thus, from (1), R must equal S, and both are half of 80.

For stat. (2), R could equal to S (yielding a 40, 40, 100 triangle), or to T (in which case R and T are together 140 angles, or R=&=70. Insufficient.


Ratio of number of women to men attending an event is 5 to 2. What was the number of men that attended?
1- Ratio of children to men is 5 to 11
2 - The number of women is less than 30


Men : women
5:2

children : men
5: 11

the problem with combining the ratios is that that the same REAL number of combine men is represented as a ratio of 5 in the first one, and 11 in the 2nd. Bring both ratios to the same comparison platform by expanding the first by 11 and the 2nd by 5, to make the number of men ratio units the same:

1st ratio
men : women
55:22

2nd ratio
children:men
25:55

Now that the men are 55 in both ratios, we can combine the ratios:
men : women: children
55 : 22 : 25

Alone, this does not tell you how many men are there - it's just a ratio, and the actual number of men could be 55, 110, 165, as long as we expand the women and children by the same multiplier. HOWEVER, stat. (2) comes in and limits the number of women to 30 - which means we cannot expand the ratio, as the women hold 22 ratio units already. Thu, the actual number of men must be also the same as the ratio: 55. Answer is C.



(1/5)^m(1/4)^18 = 1/2(10)^35
m = ?
Choices: 17, 18, 34, 35, 36

i remember posting about this, and it's been brought up many times before my post. Search for it on the forums .

If n is a positive integer and the product of all integers from 1 to n, inclusive is a multiple of 990, what is the least possible value of n?
Choices: 10,11,12,13,14

Break down 990 into prime factors: 990 = 10*99 = 2*5*9*11 = 2*5*3*3*11.
Thus, for n to be a multiple of 990, it must have be divisible by 11 (the greatest prime factor in 990), which means that 11 is the least possible value of n.


In the figure a square is inscribed in a circle. If the area of the square is 16 what is the area of the circular region?
2π, 4 π, 8 π, 12 π, 16 π

Side of the square is 4
diagonal of the square is 4*sqrt(2)
the diagonal is the diameter of the circle, so radius of the circle is half of 4*sqrt(2) = 2*sqrt(2)
Area of circle is π*r^2 =π*{2*sqrt(2)}^2 = π*4*2 = 8π.

If 0 < x < 1, what is the median of the values x, x -1, x2, Square root (x), x3

Plug in a number such as 1/4, order the results from smallest to greatest, find the number in the middle:
x, x -1, x2, Square root (x), x3
1/4, -3/4, 1/16, 1/2, 1/64

Ordered, these are -3,4, 1/64, 1/16, 1/4, 1/2, and the median is 1/16 =x^2.

For which iof the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
F(x) = x2
F(x) = x + 1
F(x) = square root (x)
F(x) = 2/x
F(x) = -3x

Again, I've posted and seen posts on this one before. Search for it.

Susan drove an average of 30 miles per house for the first 30 miles of her trip and then an average of 60 miles per her for the remaining 30 miles of her tirp. If she made no stops, what was the average speed of her trip?
35, 40, 45, 50, 55

average speed is total distance / total time.

Total distance is 30 +30 = 60 miles.
total time:
first phase: 30 miles at 30 mph: 30/30 = 1 hour
2nd phase: 30 miles at 60 mph: 20/60 = 1/2 an hour
Total time = 3/2 hours.

Average speed: 60 / 3/2 = 60 * 2/3 = 40 mph.
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