MU-NLPC/Calc-aqua_rat huggingface dataset:
If 7^e is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of e?
Choose the correct choice from the following
A) 12	B) 13	C) 14	D) 15	E) 16

Solution: So the question just means that we have to find all the multiples e of 7 between 1 to 100   So there are 14 multiples of 7 ( 7 - 98)   But 49 and 98 contain two 7's as factors   so we have to add  14 + 2= 
 14 + 2 = 16
16   16
Answer: E
A bike covers a certain distance at the speed of 65km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
Answers:  A) 85 km/h  B) 85.34 km/h  C) 86.66 km/h  D) 90.25 km/h  E) 90.64 km/h

Solution: Ans.(C)   Sol. Total distance = 65 × 8 = 520 km   Now speed = 520/6 = 86.66 km/h
Answer: C
John Purchased 1325 large bottles at $1.89 per bottle and 750 small bottles at $1.38 per bottle. What was the approximate average price paid per bottle?  Choices.
A) $1.63
B) $1.71
C) $1.68
D) $1.72
E) $1.76

Solution: (1325*1.89+750*1.38)/(1325+750) =~1.71   Option ($1.71)
Answer: B
There were two candidates in an election. Winner candidate received 62% of votes and won the election by 348 votes. Find the number of votes casted to the winning candidate?
Choose one.
A) 456	B) 744	C) 899	D) 1200	E) 1400

Solution: W = 62% L = 38%   62% - 38% = 24%   24% -------- 348   62% -------- ?  62  - 38= 
 62  - 38 = 24
24%   24% -------- 348   62% -------- ?=> 899   ANSWER:899
Answer: C
The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?	Options
A) 16 2/6% B) 16 2/8% C) 16 2/3% D) 19 2/3% E) 16 2/5%

Solution: 10 16 2/3%P = 12 SP   12 --- 2 16 2/3%P loss   100 --- ? => 16 2/3%   Answer: 16 2/3%
Answer: C
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? Choose the correct choice:
A) 600
B) 2277
C) 297
D) 972
E) 121

Solution: Cost price = Rs.500   profit = 20% of 500 = Rs.100   Selling price = Cost price + Profit   = 500 + 100= 
500 + 100 = 600
600   600nswer: 600
Answer: A
Dimitri weighs 4x-3x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of y pounds. Which of the following represents Allen’s weight?	Choose the most appropriate option
A) y - x/2  B) 2x - y/2  C) (y - x)/2  D) y - 2x  E) 2x - y

Solution: These type of multi-variable story problems are usually perfect for TESTing VALUES.   Here, we're told that Dimitri weighs 4X-3X or X pounds more than Allen weighs and that they weight a combined TOTAL of Y pounds.   IF....   Dimitri = 30   Allen = 20   X = 10   Y = 50   We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.   Answer A:  50 - (10/2)= 
 50 - (10/2) = 45
45 NOT a match   Answer B: 20 - (50/2)= -5 NOT a match   Answer (y - x)/2: (50-10)/2 = 20 This IS a match   Answer D:   50 - 20= 
  50 - 20 = 30
30 NOT a match   Answer E: 20 - 50= -30 NOT a match   Final Answer:   (y - x)/2
Answer: C
The largest natural number which exactly divides the product of any four consecutive natural numbers is  Select the correct option.
A) 6	B) 12	C) 24	D) 120	E) 100

Solution: Solution   Required numbers	= 1×2×3×4   ‹=›24.   Answer 24
Answer: C
Today Jim is twice as old as Fred, and Sam is 4 years younger than Fred. Four years ago Jim was 8 times as old as Sam. How old is Jim now?
Choose the correct choice from the following options
A) 8	B) 12	C) 16	D) 20	E) 24

Solution: We're asked how old Jim is NOW. We're given three facts to work with:   1) Today, Jim is TWICE as old as Fred   2) Today, Sam is 4 years younger than Fred   3) Four years ago, Jim was 8 times as old as Sam.   let's TEST Answer D: 20   IF....Jim is currently 20 years old....   Fred is 10 years old   Sam is 6 years old   4 years ago, Jim was 16 and Sam was 2, so Jim WAS 8 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.   20
Answer: D
A train traveling at 72 kmph crosses a platform in 32 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?	Options
A) 280 meters
B) 360 meters
C) 420 meters
D) 600 meters
E) Cannot be determined

Solution: Speed of train = 72 * (5/18)= 
72 * (5/18) = 20
20 m/s   Lets consider the man as a stationery point on the platform.   Crossing the point gives us the length of the train.   Lt= 20 * 18= 
20 * 18 = 360
360 m.   Crossing the platform gives us the length of trainlength of platform.   L(t+p)= 20 * 32= 
20 * 32 = 640
640 m.   So, length of platform= 640 - 360= 
640 - 360 = 280
280 m   IMO, 280 metersnswer   280 meters
Answer: A
If TIER is written as 7193 and BRAIN is written as 23415, how is RENT coded ?
Pick one:
A) 3653  B) 3657  C) 2977  D) 3957  E) 2711

Solution: Explanation:   Given :   Letter : T I E R B A N   Code : 7 1 9 3 2 4 5   Thus, the code for RENT is 3957.   ANSWER:3957
Answer: D
There is a baseball tournament that is single elimination meaning that after one loss the team is out. There are 40 teams in this tournament. How many games are played? Pick.
A) 20	B) 10	C) 39	D) 40	E) 15

Solution: C   The number of games always adds up to one less than the number of teams in a single elimination tournament. You may calculate it any way. Therefore, 39 games were played.
Answer: C
In the recent, climate conference in New York, out of 500 men, 300 women, 500 children present inside the building premises, 10% of the men, 60% of the women and 70% of the children were Indians. Find the percentage of people who were not Indian?	Choose the correct choice from the following choices:	A) 59.54%	B) 66.25%	C) 55.39%	D) 63.21%	E) 64.22%

Solution: Solution: Number of Indians men present there = 500*10/100= 
500*10/100 = 50
50   Indian women= 300*60/100= 
300*60/100 = 180
180   Indian children= 500*70/100= 
500*70/100 = 350
350.   Total member present in climate conference= 500+300+500= 
500+300+500 = 1_300
1300   Total Indian= 50+180+350= 
50+180+350 = 580
580   Hence, % of Indian present there= 580*100/1300 = 44.61%   % of people who were not Indian = 100-44.61= 
100-44.61 = 55.39
55.39%.   Answer 55.39%
Answer: C
What will come in place of the x in the following Number series? 5,28,57,88  Choose the correct choice from the following choices.
A) 156	B) 159	C) 166	D) 125	E) 180

Solution: 28=23+5   57=29+28   88=31+57   125=37+88   125
Answer: D
Caleb won Bruce in a 100 m race by 0.35 m. If Bruce had given Caleb a 6 m head start how many meters more will it take for Bruce to overtake Caleb? Choose the most appropriate option
A) 7.2m	B) 5.2m	C) 8.2m	D) 4.2m	E) 6.2m

Solution: Distance Bruce ran before completion of race---100 m-0.35m=99.65m   Distance gained on Caleb over 99.65m---6m-0.35m=5.65   then Bruce gains 99.65/5.65m = 1m on Kelly every 17.64 meters.   Therefore 17.64 divided by 0.35 of 1 meter.   ANSWER: E. 6.2m
Answer: E
If (5)(x^2) has four different prime factors, at most how many different prime factors does x have? Pick one
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: x can have at most 4 prime factors, namely the prime factor 5 plus 3 others.   If x had more than this number of prime factors, then (5)(x^2) would have more than 4 prime factors.   The answer is 4.
Answer: D
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?  Choose the correct option:
A) 872 m	B) 278 m	C) 267 m	D) 150 m	E) 287 m

Solution: Speed=(60 * 5/18) m/sec   = (50/3) m/sec Length of the train   = (Speed x Time) = (50/3 * 9)= 
(50/3 * 9) = 150
150 m.   Answer: 150 m
Answer: D
In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 0) lies inside the circle and the point (2, -3) lies outside the circle. If the radius r of the circle r is an integer then r= Choose the correct choice from the following options.
A) 6 B) 5 C) 4 D) 3 E) 2

Solution: Can be solved without much calculations.   You are given that (-2,-3) is the center of the circle. Point (2,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (2,-3) ---> lesser than 5 units but the radius will also be greater than the distance of (-2,-3) from (-2,0) ----> greater than 3 units.   Thus the radius is >3 but <5and as it is an integer, the only possible value of radius = 4 units.   4 is the correct answer.
Answer: C
A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in.
Choose the correct option:
A) 2 days B) 6 days C) 3 days D) 4 days E) 5 days

Solution: 15/25 + 5/x = 1 => x = 25/4   1/25 + 4/25 = 5/25=1/5   5 days   ANSW5 daysR:5 days
Answer: E
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Choose one.
A) 656 sq.cm
B) 517 sq.cm
C) 657 sq.cm
D) 826 sq.cm
E) 600 sq.cm

Solution: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE = √(625 - 225)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 30= 
1/2 * 40 * 30 = 600
600 sq.cm.   Answer: 600 sq.cm
Answer: E
Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a orange cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?	Choices
A) 120  B) 140  C) 150  D) 160  E) 180

Solution: # ways to distribute Blue marbels(3) is :   1 in each cup= 1   2 in one cup and 1 in other=6   all 3 in one cup = 3   total 1+6+3= 
1+6+3 = 10
10 possibilities   # ways to distribute Red marbels(2) is :   1 in each cup= 3 ways   all in one cup = 3ways   total 6ways.   # ways to distribute Green marbels(1) is :   3 ways   total number of ways = 10*6 *3= 
10*6 *3 = 180
180   180
Answer: E
If 45% of z is 120% of y and y is 75% of x, what percent of x is z?
Pick one
A) 200
B) 160
C) 100
D) 65
E) 50

Solution: (45/100)z = (120/100)y   and y = (75/100)x i.e. y = (3/4)x   i.e. (45/100)z = (120/100)*(3/4)x   i.e. z = (120*3)x/(45*4)   i.e. z = (2)x = (200/100)x   i.e. z is 200% of x   200nswer: Option 200
Answer: A
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age fourteen years back was?	Options:	A) 5yr	B) 15yr	C) 20yr	D) 25yr	E) 30yr

Solution: Let the son's present age be x years   Then, 38-x = x   x = 19   Son's age 14 years back = 19-14= 
19-14 = 5
5 years   5yrnswer is 5yr
Answer: A
A bag contains 5 green balls and 8 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour?
Pick: A) 3/7 B) 6/11 C) 12/21 D) 19/39 E) 29/49

Solution: The total number of ways to draw two balls is 13C2 = 78   The number of ways to draw two green balls is 5C2 = 10   The number of ways to draw two white balls is 8C2 = 28   P(two balls of the same colour) = 38/78 = 19/39   The answer is 19/39.
Answer: D
If x, y, and z are positive integers such that x^2 - y^2 + z^2 = 36, which of the following could be the values of x, y, and z?
I)x=122,y=157,z=99
II)x=125,y=160,z=102
III)x=100,y=150,z=167	Choose the correct answer: A) I only B) II only C) III only D) I​ and II E) I and III

Solution: 10 sec answer if you know how to find the units digit of a number   The number given is of the form of square, so calculate the units digit - Here your objective is to find the sum where last digit is 0   x = 122, so x^2 will have units digit 4   y = 157, so y^2 will have units digit 9   z = 99, so z^2 will have units digit 1   Calculate the units digit , the units digit will be 0   Test with options II and III, only option I will satisfy the condition , hence this will be our answer is option I only.
Answer: A
If u r genius solve it:-
40 * 14 = 11
30 * 13 = 12
20 * 12 = ?	Choose the correct choice:
A) 2
B) 4
C) 6
D) 8
E) 10

Solution: Logic :   40*14= 
40*14 = 560
560=5+6+0= 
5+6+0 = 11
11   30*13= 
30*13 = 390
390=3+9+0= 
3+9+0 = 12
12   So 20*12= 
20*12 = 240
240=2+4+0= 
2+4+0 = 6
6   Answer : 6
Answer: C
A customer asks the clerk for a paintbrush and a bucket of whitewash for a total price of B dollars. If the paintbrush costs 300 cents less than twice the price of a bucket of whitewash, what is the price of half a bucket of whitewash in dollars?
Choose the correct choice from the following:  A) (B + 200)/2.  B) (B + 2)/6.  C) (2B + 200)/3.  D) (B + 2)/3.  E) (B - 2)/6.

Solution: P = 2w - 200   thus total price in cents as given should be   2w-200 +w = 100B   3w - 200 = 100 B   3w = 100 B+200   3w =b+2 (in dollars)   w/2 = (b+2)/6   Ans:(B + 2)/3.
Answer: D
A manufacturer sells a pair of plastics to a wholesale dealer at a profit of 18%. The wholesaler sells the same to retailer at a profit of 20%. The retailer in turn sells them to a customer for Rs. 30.09, there by earning a profit of 25%. The cost price for the manufacturer is: Choose the correct choice from the following answers:
A) 23
B) 16
C) 17
D) 45
E) 28

Solution: C   Let the cost price for the manufacturer be Rs. x. Then, 125% of 120% of 118% of x = 30.09.   125/100 * 120/100 * 118/100 * x = 3009/100   177/100 x = 3009/100 => x = 17
Answer: C
In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?	Select
A) 13/8
B) 21/13
C) 8/5
D) 5/8
E) 8/13

Solution: let five terms in the sequence be a,b,c,d,e   a=1   b= 1+1/1= 
1+1/1 = 2
2/1   c=1+1/2= 3/2   d= 1+2/3 = 5/3   e= 1+3/5 = 8/5   hence answer should be 8/5.
Answer: C
What is difference between biggest and smallest fraction among 2/3, 3/4, 4/5 and 5/3 Answers
A) 2/5 B) 3/5 C) 1/6 D) 1 E) None of these

Solution: Explanation:   2/3 = .66, 3/4 = .75, 4/5 = .8 and 5/3 = 1.66   So biggest is 5/3 and smallest is 2/3   Their difference is 5/3 - 2/3 = 3/3= 
3/3 = 1
1   Option 1
Answer: D
Which of the following numbers must be added to 5678 to give a remainder of 35 when divided by 460? Choose the correct choice from the following choices:
A) 955	B) 980	C) 797	D) 618	E) 718

Solution: (5678+x)=(460*y)+35   5678-35+x=460*y   5643+x=460*y   so in x last digit must be 7 so ans should be c   ANSWER:797
Answer: C
The total surface area of a solid hemisphere of diameter 14 cm is Choose the correct choice from the following answers
A) 308 cm2 B) 462 cm2 C) 1232 cm2 D) 1848 cm2 E) None

Solution: Solution   Total surface area	= 3ΠR2   = (3 x 22/7 x 7 x 7)cm2   = 462 cm2.   Answer 462 cm2
Answer: B
When positive integer x is divided by 7, the quotient is y and the remainder is 3. When 2x is divided by 6, the quotient is 3y and the remainder is 2. What is the value of 11y – x?
Choose the correct answer:	A) 4	B) 3	C) 2	D) 1	E) 0

Solution: (1) x = 7y+3   (2) 2x = 18y+2   (2)-(1): x=11y-1   11y-x=1   The answer is 1.
Answer: D
Pipe A can fill a tank in 30 minutes. Pipe B can fill the same tank 6 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow? Choose the correct choice from the following choices:  A) 4 minutes  B) 15/4 minutes  C) 192/7 minutes  D) 224/7 minutes  E) 28 minutes

Solution: Pipe A can fill a tank in 30 minutes --> the rate of A = 1/30tank/minute;   Pipe B can fill the same tank6 times fasterthan pipe A --> the rate of B = 1/30 + 6/30 = 7/30 tank/minute.   Their combined rate = 1/30 + 7/30 = 4/15 tank/minute;   Therefore, A and B can fill the tank in 15/4 minutes.   Answer: 15/4 minutes
Answer: B
What is the area inscribed by the lines y =3, x = 2, y = x+3 on an xy-coordinate plane?	Select:
A) a) 1 B) b) 2 C) c) 4 D) d) 6 E) e) 10

Solution: First, let's graph the lines y = 3 and x = 2   At this point, we need to find the points where the line y = x+3 INTERSECTS the other two lines.   For the vertical line, we know that x = 2, so we'll PLUG x = 2 into the equation y = x+3 to get y = 2+3= 
2+3 = 5
5   Perfect, when x= 2, y = 5, so one point of intersection is (2,5)   For the horizontal line, we know that y = 3, so we'll PLUG y = 3 into the equation y = x+3 to get 3 = x+3. Solve to get: x = 0   So, when y = 3, x = 0, so one point of intersection is (0,3)   Now add these points to our graph and sketch the line y = x+3   At this point, we can see that we have the following triangle.   The base has length 2 and the height is 2   Area = (1/2)(base)(height)   = (1/2)(2)(2)   = 2   Answer:   b) 2
Answer: B
John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?  Choose the correct option:
A) 16%	B) 16.66%	C) 18%	D) 21%	E) 23%

Solution: Increase = (10/60)*100 = (1/6)*100 = 16.66%.   16.66%
Answer: B
A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?	Pick:	A) 65 days	B) 85 days	C) 15 days	D) 45 days	E) 13 days

Solution: B's 1 day work = (1/12 - 1/20) = 1/30   Now, (A + B)'s 1 day work = (1/20 + 1/60) = 1/15   So, A and B together will complete the work in 15 days.   Answer:15 days
Answer: C
The average age of 6 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years. Find the average age of the women? Select the correct option.
A) 87  B) 12  C) 30  D) 28  E) 17

Solution: 10 + 12 + 6 * 2= 
10 + 12 + 6 * 2 = 34
34/2= 
34/2 = 17
17   Answer:17
Answer: E
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 5 years the amount to be paid is? Options:	A) 3377	B) 2688	C) 2688	D) 9125	E) 1268

Solution: A = 7500(26/25)^5 = 9125   Answer: 9125
Answer: D
Paulson spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%.Find the percentage increase in his savings .
Pick.
A) 25
B) 35
C) 50
D) 20
E) 15

Solution: Let the original income=$100. Then, expenditure=$75 and   savings =$25   New income =$120, New expenditure =   $((110/100)*75)=Rs.165/2   New savings = $(120-(165/2)) = $75/2   Increase in savings = $((75/2)-25)=$25/2   Increase %= ((25/2)*(1/25)*100)= 
((25/2)*(1/25)*100) = 50
50%.   Answer 50) 50.
Answer: C
A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?
Choose the most appropriate option
A) 1/5 B) 2/3 C) 3/7 D) 4/7 E) 5/11

Solution: |X||X| can take 7 values.   To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x   ⇒ P(|X|<2)= Favourable 3/7asesTotal 3/7asesP(|X|<2)= Favourable 3/7asesTotal 3/7ases   = 3/7   3/7
Answer: C
In an election, candidate A got 65% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate. Choose the correct answer.
A) 330000
B) 309400
C) 347000
D) 356000
E) 357000

Solution: Total number of invalid votes = 15 % of 560000   = 15/100 × 560000   = 8400000/100= 
8400000/100 = 84_000
84000   Total number of valid votes 560000 – 84000= 476000   Percentage of votes polled in favour of candidate A = 65 %   Therefore, the number of valid votes polled in favour of candidate A = 65 % of 476000   = 65/100 × 476000   = 30940000/100= 
30940000/100 = 309_400
309400   309400)
Answer: B
Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Pick one.
A) 11
B) 12
C) 77
D) 17
E) 19

Solution: Speed of the first train = 120/10= 
120/10 = 12
12 m/sec.   Speed of the second train= 120/5 = 8 m/sec.   Relative speed = 12 + 8= 
12 + 8 = 20
20 m/sec.   Required time= (120 + 120)/20= 
(120 + 120)/20 = 12
12 sec.   Answer:12
Answer: B
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them? Pick.
A) 5/6
B) 5/1
C) 5/8
D) 5/6
E) 5/2

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - 6C3/10C3   = 1 - (6 * 5 * 4)/(10 * 9 * 8)   5/6   Answer:5/6
Answer: D
log3 N+log7 N what is 3 digit number N that will be whole number Choices.
A) 343	B) 729	C) 829	D) 929	E) 727

Solution: No of values N can take is 1   7^3=343   343NSWER:343
Answer: A
A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?  Pick one
A) 7 PM B) 9 PM C) 4 PM D) 5 PM E) 6 PM

Solution: 1 to 2 = 1/4   2 to 3 = 1/4 + 1/5 = 9/20   After 3 AM = 1/4 + 1/5 - 1/2 = -1/20   1/4 + 9/20 = 14/20   1 h ---- 1/20   ? ----- 14/20   14 hours ==> 5 PM   Answer:5 PM
Answer: D
If a coin is tossed twice, what is the probability that on the first toss the coin lands heads and on the second toss the coin lands tails?
Answers
A) 1/6
B) 1/3
C) 1/4
D) 1/2
E) 1

Solution: first toss the coin lands heads = 1/2   the second toss the coin lands tails = 1/2   For independent even A and B, (A∩B) = A*B   probability that on the first toss the coin lands heads and on the second toss the coin lands tails = 1/2*1/2 = 1/4   Hence, answer will be 1/4.
Answer: C
Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?	Options:
A) 17.5%
B) 62.5%
C) 87.5%
D) 140%
E) 150%

Solution: You are mixing a collection consisting of 20% biographies with a collection consisting of 100% biographies to give a collection consisting of 37.5% biographies. The weights of the two collections will be:   w1/w2 = (A2 - Avg)/(Avg - A1) = (1 - 3/8)/(3/8 - 1/5) = (5/8)/(7/40) = 25/7   So if initial collection had a total of 25 books (including 1/5th biographies i.e. 5 biographies), 7 new biographies were added.   Biographies have increased by (7/5)*100= 
(7/5)*100 = 140
140%   Answer (140%)
Answer: D
If 6x^2 + x - 12 = (hx + b)(cx + d), then |h| + |b| + |c| + |d| =
For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/  Answers.
A) 10
B) 12
C) 15
D) 18
E) 20

Solution: 6x^2+x-12 = 6x^2 + 9x -8x -12   => 3x(2x+3) -4(2x+3)   => (2x+3)(3x-4) = (hx+b)(cx+d)   Hence h=2, b=c=3, d=-4   So, 2+3+3+ |-4| = 2+3+3+4= 
2+3+3+4 = 12
12   Answer 12.
Answer: B
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 40, the dividend is:
Select.
A) 5330 B) 5336 C) 5343 D) 5345 E) 4040

Solution: Divisor = (5 * 40)= 
(5 * 40) = 200
200= 10 * Quotient = Divisor   => Quotient = 200/10= 
200/10 = 20
20   Dividend= (Divisor * Quotient) + Remainder   Dividend = (200 * 20) + 40= 
(200 * 20) + 40 = 4_040
4040.   4040
Answer: E
In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 4 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?  Choose the correct choice from the following:
A) 30
B) 45
C) 60
D) 90
E) 120

Solution: Whole trip = distance by foot + distance by bus + distance by car   x = 1/5x + 2/3x + 4   x - 13/15x = 4   2/15x = 4 => so x = (15/2)*4= 
(15/2)*4 = 30
30Km   30nswer 30
Answer: A