QR from kaplan white books

[joonkimdds]

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1. If x and y are integers such that x>y, which of the following cannot be a positive interger?
I. y(y-x)
II. y(x-y)
III. (x-y)/(y-x)
==> I picked x = 2, y = 1 to solve this problem.
1(1-2) = -1 so this cannot be +
1(2-1) = 1 so this can be +
(2-1)/(1-2) = 1/-1 = -1 so this cannot be +
However, there was no answer choice saying I and III are answers.



2. Over the course of a year, a certain factory increased its output by 90%. At the same time, it decreased its total working hrs by 20%. By what % did the factory increase its output per hr?
==> If I say it had 100% originally then increasing output by 90% changed it into 190%. If I say total working hour was 100 hrs, but it decreased by 20% then it means total working hour now is only 80 hrs.
100 hr = 190%
80 hr = ? %
152% is what I got for 80hr.

80hr = 80% was original
now it's 80hr = 152%
(152-80)/ 80 = 72/80 = 36/40 = 18/20 = 9/10 = 0.9 = 90% increase per hr than original.
But 90% is not the answer choice.
A. 70%
B. 110%
C. 112.5%
D. 137.5%
E. 237.5 %



please help me~ 🙂😍

 

[Streetwolf]

1. If x and y are integers such that x>y, which of the following cannot be a positive interger?
I. y(y-x)
II. y(x-y)
III. (x-y)/(y-x)
==> I picked x = 2, y = 1 to solve this problem.
1(1-2) = -1 so this cannot be +
1(2-1) = 1 so this can be +
(2-1)/(1-2) = 1/-1 = -1 so this cannot be +
However, there was no answer choice saying I and III are answers.
You can't just choose random numbers for something like this because you might miss something. You need to generalize it! If x > y then what do you know? Is x > 0? Is y > 0? The answer to both of these is "we don't know." All we know FOR SURE, aside from x > y, is that (x-y) > 0 (WHY?). From that we also know that (y-x) < 0 (WHY?).

I. y(y-x)... well the (y-x) part is negative for sure, but without knowing the sign on 'y' we can't say anything with certainty.
Example where it is positive: x = 3 and y = -1.
Example where it is negative: x = 3 and y = 2.

II. y(x-y)... again we know that (x-y) is positive for sure, but we don't know what's going on with y. This could be anything.
Example where it is positive: x = 3 and y = 2.
Example where it is negative: x = 3 and y = -1.

III. (x-y)/(y-x)... we can see that the top is always positive and the bottom always negative. That means the entire expression is always negative. In fact, we can solve it and it straight up equals -1. So III is ALWAYS negative or in other words NEVER positive.

Answer = III only.


2. Over the course of a year, a certain factory increased its output by 90%. At the same time, it decreased its total working hrs by 20%. By what % did the factory increase its output per hr?
==> If I say it had 100% originally then increasing output by 90% changed it into 190%. If I say total working hour was 100 hrs, but it decreased by 20% then it means total working hour now is only 80 hrs.
100 hr = 190%
80 hr = ? %
152% is what I got for 80hr.

80hr = 80% was original
now it's 80hr = 152%
(152-80)/ 80 = 72/80 = 36/40 = 18/20 = 9/10 = 0.9 = 90% increase per hr than original.
But 90% is not the answer choice.
A. 70%
B. 110%
C. 112.5%
D. 137.5%
E. 237.5 %

This is output per hour. You need to figure out the new output and the new hours and divide. You got the right idea by plugging in numbers. Let's say they do 100 output in 100 hours. Then the new and improved factory does 190 output (90% increase) in 80 hours (20% decrease). The new output per hour is 190/80 = 19/8. The old one was 100/100 = 1. So the increase is 19/8 - 1 which is 19/8 - 8/8 which is 11/8 or 1 and 3/8. This is 137.5%.

Answer is D.

please help me~ 🙂😍

Bold text.

 

[Shinpe]

Agreed

Unless number one says x and y are POSITIVE integers, then the answer is III only. If it says positive integers, then yes I and III.