1. At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew, If the night crew has 4/5 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load?

A. 1/2
B. 2/5
C. 3/5
D. 4/5
E. 5/8

2. As x increases from 165 to 166, which of the following must increse?

I. 2x-5
II. 1-1/x
III. 1/(x^2-x)

A. I only
B. III only
C. I and II
D. I and III
E. II and III

OPEN DISCUSSION OF THE FIRST QUESTION IS HERE: at-a-loading-dock-each-worker-on-the-night-crew-loaded-128407.html

OPEN DISCUSSION OF THE SECOND QUESTION IS HERE: as-x-increases-from-165-to-166-which-of-the-following-must-144732.html

Q#2:
As x increases from 165 to 166, which of the following must increse?

I. 2x-5
II. 1-1/x
III. 1/(x^2-x)

A. I only
B. III only
C. I and II
D. I and III
E. II and III

I. 2x - 5 --> x increases from 165 to 166 --> 2x increases --> 2x-5 increases. Correct.

II. 1-\frac{1}{x} --> x increases from 165 to 166 --> \frac{1}{x} decreases --> 1-\frac{1}{x} increases. Correct.

At this point you can stop and even not consider III, since only answer choice to have both I and II is C.

Still if interested:
III. \frac{1}{x^2-x} --> x increases from 165 to 166 --> x^2 increases more than x --> x^2-x increases --> \frac{1}{x^2-x} decreases.

Answer: C.

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total boxes loaded = numbers of workers * boxes loaded per worker

For day shift,
let numbers of workers be x and boxes per worker be y

then for night,
number of workers = 4x/5
boxes per worker = 3y/4

total boxes loaded by day crew: xy
total boxes loaded by night crew: 4x/5 * 3y/4 = 3xy/5

So, ratio of boxes loaded by day crew to total boxes loaded = xy/(xy+3xy/5) = 1/(1+3/5) = 5/8

Cheers,
CJ
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Q1) Answer E

make a grid like this

------------------------------------------------------Night---------------day

No. of workers------------------------------------(4/5)y---------------y

No. of boxes loaded by each worker ----------(3/4)x-----------------x

Total No of boxes loaded ----------------------(4/5)(3/4)xy-------xy

Now we are asked ratio of TOTAL NO OF BOX LOADED DAY / (TOTAL NO OF BOX LOADED DAY + TOTAL NO OF BOX LOADED NIGHT)

XY/(XY+(3/5)XY) ----------> (XY/1) / (8XY/5) --------> 5/8 ----------> E


Q2) Answer C

I) in 2x-5 if x increase by 1 then equation will be 2(x+1)-5. If x is positive the equation will increase by 2 and if x is negative the equation will decrease by 2. We are given in ques that x increased from 165 to 166 that means x is positive so the equation will increase by 2. Eliminate B and E

II) 1-(1/x) now this equation will increase if 1/x decrease and 1/x will decrease if x increase. x is increased so this equation is also sure to increase. Eliminate A. Now Option D will also get eliminated because it does not contain II, so from here we do not need to proceed to check III. The correct choice is C. However for the study part we will check III

III) 1/(X^2-x) -------> 1/x(x-1) -------> we know as denominator increased the fraction decreases. in this case with the increase in x the denominator increases and the fraction decreases. so this equation will not increase with an increase in X.

Regards,

Abhijit
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OPEN DISCUSSION OF THE FIRST QUESTION IS HERE: at-a-loading-dock-each-worker-on-the-night-crew-loaded-128407.html

OPEN DISCUSSION OF THE SECOND QUESTION IS HERE: as-x-increases-from-165-to-166-which-of-the-following-must-144732.html
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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