Quantitative Reasoning

I took the prep exam and got 700. However, I'm not sure how to do some of the questions and there are no

explanations, so I'm turning to the collective. This is also a good way for me to study by writing down the

troubling questions. I found that as I wrote down the questiosn below, I learnt how to do some of them.

1.
5^(21) x 4^(11) = 2x10^(n) what is n?

We know 5 x 4 is 20 or 2 x 10^(1).

I guessed the correct answer to be [spoiler]n = 21[/spoiler], but i'm not sure why. Anyone know?

2. - DS
are x and y both positive?
(1) 2x - 2y = 1
(2) x/y > 1

The answer is [spoiler]C (both needed)[/spoiler] but I think it should be E.
(1) : x - y = 1/2
(2): x & y both have to have the same sign. I'm not sure how to work it out to get C


3. - DS
if x and y are positive integers, what is the value of xy?
(1) the GCF (greatest common factor) of x and y is 10
(2) the LCM (least common multiple) of x and y is 180

the answer is C but I don't know how. I suck at the GCf/LCM questions.

4. -DS
In the xy-plane, what is the y-intercept of line l?
(1) the slope of line l is 3 times its y-intercept
(2) the x-intercept of line l is -1/3

y = mx + b, where m is slope and b is y-intercept
..so
(1): y = 3bx + b - doesn't help
(2): 0 = m(-1/3) + b, -b/m = -1/3 or b/m = 1/3 We know the ratio but not exact values

(1) & (2) cancels out the b, so I guess it tells us the same thing? Confused?

5. - DS
The sum of positive integers x and y is 77. What is value of xy?
(1) x = y + 1
(2) x and y have the same tens digit.

The answer is D but I incorrectly chose A. Not sure how they get D.
(1) thats easy to see why its sufficient.
y + 1 + y = 77 => 2y = 76, you know y and x.
(2) this just tells us that :
10s + t + 10s + r = 77 => 20s + t + r = 77
you don't know t or r, so can you find out the product of x and y?

6. - DS
Martha bought a chair and a table at an auction and sold both items at her store. Her gross profit from the

purchase and sale of the chair was what percent greater than her gross profit from the purchase and sale of the

table?
(1) Martha paid 10% more for the chair than for the table
(2) Martha sold the chair for 20% more than she sold the table.

profit for chair (p_c) = selling price of chair (s_c) - purchase price of chair (b_c)
profit for table (p_t) = selling price of table (s_t) - purchase price of table (b_t)

(1) b_c = 1.1(b_t)
(2) s_c = 1.2(s_t)

p_c = 1.2(s_t) - 1.1(b_t)
p_t = s_t - b_t

[spoiler]Ok I see why this can't be solved. I thought it was C, but now I know why its E. Thanks to writing it out.[/spoiler]

7. - DS
Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many animals are cows?
(1) the farm has more than twice as many cows as it has pigs
(2) the farm has more than 12 pigs

60 animals -> 2/3 (60), 40 animals that can be either pigs or cows
(1) c > 2p
40 = 2p + p => 40 = 3p
(2) p > 12

[spoiler]I thought the answer should be E since (1) and (2) are both inconclusive, however I am wrong. While writing this, I

just realized that if p > 12, than p could be 13, in which case c > 26. 13 + 27 = 40

so the answer is C. [/spoiler] I just wish I realized that while writing the test!!!

8. - DS
Are at least 10% of the people in the Country X who are 65yrs old or older employed?
(1) in country X, 11.3% of population is 65 years old or older
(2) in country X, of the population 65 years or older, 20% of the men and 10% of the women are employed.

[spoiler]Answer is B but I didn't get it originally (chose E). [/spoiler]

I think I do now... Let there be 100 people how are 65 or older and try different combinations of men and women...


As I wrote these down, I figured out how to get most of them. However, I still don't know how to do #1, #3, and #5.

Thanks

[/spoiler]