MU-NLPC/Calc-aqua_rat huggingface dataset:
In the number 10,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 55, what is the greatest possible value of B × A?
Select the correct option.
A) 0  B) 5  C) 10  D) 15  E) 25

Solution: You should notice that 55*2= 
55*2 = 110
110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0= 
0*0 = 0
0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*5=15 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).   Answer: E.   !   Please post PS questions in the PS subforum:gmat-problem-solving-ps-140/   Please post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/   No posting of PS/DS questions is allowed in the mainMath forum.   15
Answer: D
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is Choose the most appropriate option:
A) 75 cu. m
B) 750 cu. m
C) 7500 cu. m
D) 75000 cu. m
E) None of these

Solution: Solution   Area = (1.5 × 10000) m2 = 45000 m2.   Depth = m = m.   ∴ Volume = (area × depth) = m3 = 750 m3.   Answer 750 cu. m
Answer: B
If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are
the Q odds that x^2+y^2>1?	Choices.
A) 1. pi/4	B) 2. pi/16	C) 3. Q=1-pi/4	D) 4. Q=1-pi/16	E) 5.4-pi

Solution: area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi.   then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1)   total outcomes = 4   therefore probability = (4-pi)/4   3. Q=1-pi/4
Answer: C
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train? Choose the correct choice from the following answers:
A) 50 m B) 80 m C) 76 m D) 58 m E) 90 m

Solution: let length of each train = x m   total distance while passing the slower train = (x+x) = 2x m   relative speed = (46-36)= 
(46-36) = 10
10 km/hr=10*5/18 = 50/18 m/s   time = 36 sec   2x/36 = 50/18 => x=50   50 mNSWER 50 m
Answer: A
The probability that A speaks truth is 23/35 and that of B speaking truth is 35/47. What is the probability that they agree in stating the same fact?  Choose the correct answer:
A) 1553/1645	B) 1262/2535	C) 1257/1835	D) 1903/1735	E) None of these

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 23/35 * 35/47 + 22/35 * 34/47   = 805/1645 + 748/1645 = 1553/1645   1553/1645NSWER:1553/1645
Answer: A
The measures of the 2 acute angles of a triangle are in the ratio of 4 : 6. What arethe measures of the 2 angles? Select
A) 20° B) 70° C) 110° D) 120° E) 54°

Solution: If the ratio of the two angles is 4:6, then the measures of two angles can be written as 4x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence   4x + 6x = 90   10x = 90   x = 9   Measures of the two acute angles are   4x = 4 × 9 = 36°   6x = 6 × 9 = 54°   54°
Answer: E
Car Z travels 51 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?	Options.
A) 320  B) 375.2  C) 400  D) 408  E) 440

Solution: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.   The stem tells us that at 45 miles/hour, the car will run 51 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 40.8 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 40.8 miles/gallon * 10 gallons = 408 miles.   Answer 408.
Answer: D
Find the value of y from (12)^3 x 6^4 ÷ 432 = y? Select.
A) 2356 B) 3454 C) 4656 D) 3456 E) 5184

Solution: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184   432 12 x 62   5184
Answer: E
The proportion of water to alcohol in Solution A is 4:1 and the proportion of water to alcohol in Solution B is 2:3. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution?  Pick one
A) 39%
B) 40%
C) 41%
D) 42%
E) 43%

Solution: Let V be the total volume of the new solution.   Then a volume of V/2 was added from each solution A and B.   The amount of alcohol added to the new solution was:   (1/5)(V/2)+(3/5)(V/2)=V/10+3V/10=4V/10=2V/5.   The concentration of alcohol is 2/5=40%   The answer is 40%.
Answer: B
The average marks scored by Ganesh in English, Science, Mathematics and History is less than 17 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
Choices:	A) 40	B) 50	C) 60	D) 68	E) None of these

Solution: E+H+G+M/4âˆ’E+S+M+H/4=17   â‡’ G - S = 68   Answer 68
Answer: D
Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.133 per kg, the price of the third variety per kg will be
Answers:
A) Rs.169.50	B) Rs.1700	C) Rs. 175.50	D) Rs. 155.50	E) None

Solution: Solution   Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50   So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.   x-133/22.50 = 1 =â€º x - 133 = 22.50 =â€º x=155.50.   Hence, price of the third variety = Rs.155.50 per kg.   Answer Rs. 155.50
Answer: D
In an election, candidate A got 80% 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 choice.
A) 330000
B) 340000
C) 380800
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 = 80 %   Therefore, the number of valid votes polled in favour of candidate A = 80 % of 476000   = 80/100 × 476000   = 38080000/100= 
38080000/100 = 380_800
380800   380800)
Answer: C
Monica and Miya's age are in 2:5. Find teh age of Monica if the sum of their age is 28.  Choose the correct choice from the following choices:
A) 10 years
B) 14 years
C) 20 years
D) 8 years
E) 12 years

Solution: Let the age of Monica be 2x and Miya be 5x.   2x + 5x = 28   x = 4   Monica's age is 8 years   Answer : 8 years
Answer: D
A boy has twelve trousers and 14 shirts. In how many different ways can he select a trouser and a shirt? Choose the correct answer: A) 238 ways B) 287 ways C) 266 ways D) 168 ways E) 121 ways

Solution: Explanation:   The boy can select one trouser in 12 ways.   The boy can select one shirt in 14 ways.   The number of ways in which he can select one trouser and one shirt is   12 * 14= 
  12 * 14 = 168
168 ways.   Answer: 168 ways
Answer: D
A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?  Choose the correct choice from the following options.
A) 21/145	B) 36/145	C) 3/145	D) 2/119	E) 2/189

Solution: The probability that first ball is white:   =12C130C1=12C130C1   =1230=1230   =25=25   Since, the ball is not replaced; hence the number of balls left in bag is 29.   Hence, the probability the second ball is black:   =18C129C1=18C129C1   =1829=1829   Required probability,   =(25)×(1829)=(25)×(1829)   =36/145   36/145
Answer: B
When all the students in a school are made to stand in rows of 45, 40 such rows are formed. If the students are made to stand in rows of 40, how many such rows will be formed ?  Answers:
A) 31
B) 36
C) 45
D) 40
E) 21

Solution: Explanation:   Total number of students = 45 x 40   When arranged in rows of 40, number of rows formed are,   = 45.   Answer: 45
Answer: C
Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/4 of the remaining paint. How many gallons of paint has Joe used?
Choose the correct choice from the following answers.
A) 18  B) 157  C) 175  D) 216  E) 250

Solution: Total paint initially = 360 gallons   Paint used in the first week = (1/4)*360= 
(1/4)*360 = 90
90 gallons.   Remaning paint= 270 gallons   Paint used in the second week = (1/4)*270 = 67 gallons   Total paint used = 157 gallons.   Option 157
Answer: B
If Peter reads at a constant rate of 1 pages every 5 minutes, how many seconds will it take him to read N pages?
Select:	A) 300	B) 2N	C) 5/2*N	D) 24N	E) 150

Solution: Peter would read 1 page in 5/1 minutes   Peter would read N page in (5/1)*N min i.e. (5/2)*N*60 Seconds = 300N Seconds.   Option 300 is the correct 300nswer.
Answer: A
If y is 60 percent greater than x, then x is what percent less than y?
Choose the correct choice from the following options:  A) 30%  B) 37.5%  C) 45.5%  D) 50%  E) 55.5%

Solution: y = 1.6x   x = y/1.6 = 10y/16 = y - (3/8)*y   3/8 is 37.5%.   The answer is 37.5%.
Answer: B
A reduction of 40% in the price of apples would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? Choose the most appropriate option.
A) 1
B) 3
C) 6
D) 7
E) 10

Solution: 3   40*(40/100)= 
40*(40/100) = 16
16 --- 64   ? --- 12=> Rs.3
Answer: B
A merchant has 100 lbs of sugar, part of which he sells at 6% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 6% profit? Select the correct option
A) 70 lbs B) 40 lbs C) 30 lbs D) 50 lbs E) 64 lbs

Solution: These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:   A = # of pounds sold at 6% profit   B = # of pounds sold at 17% profit   A+B = 100 pounds   (.06A + .17B)/(A+B) = .10   .06A + .17B = .1A + .1B   .07B = .04A   7B = 4A   7/4 = A/B   So, for every 7 pounds of A, we have 4 pounds of B.   With 100 pounds total, we have 64 pounds of A and 36 pounds of B.   option 64 lbs
Answer: E
When the positive integer x is divided by 9,the remainder is 5.What is the remainder when 6x is divided by 9? Choices:
A) 0	B) 1	C) 3	D) 4	E) 6

Solution: i tried plugging in numbers   x = 9q+5   x = 14   6x 9 +5= 
9 +5 = 14
14   6x= 84   6x/9= 9*9 + 3   remainder is 3.   Answer is 3.
Answer: C
Find the one which does not belong to that group?  Answers.
A) 16 B) 36 C) 22 D) 64 E) 4

Solution: Explanation:   16, 36, 64 and 4 are perfect squares but not 22.   Answer:22
Answer: C
In a certain province in France there are 17 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
Choose the correct choice from the following answers
A) 30	B) 105	C) 330	D) 136	E) 156

Solution: 1 city needs 16 roads to connect directly to the rest => 17 city needs 17*14 roads.   One road is counted twice => the number of road needed is 17*16/2= 
17*16/2 = 136
136   Answer 136
Answer: D
A woman has $252,125 in her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to split this money evenly among her nine children?
Choose the most appropriate option:  A) $1  B) $2  C) $3  D) $4  E) $11

Solution: To find the least amount the woman should add to her saving account to split the money evenly among her 9 children,   she needs to make the total divisible by 9   Simply add the individual digits of the total = 2+5+2+1+2+5= 
2+5+2+1+2+5 = 17
17   If you add 1 , the number is divisible by 9 (17+ 1)   Correct Option : $1
Answer: A
If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?  Select the correct option: A) 1/12 B) 1/18 C) 1/42 D) 1/15 E) 1/17

Solution: X * (120/100)   ---------------- = 2/15   Y * (75/100)   X/Y = 1/12   1/12nswer: 1/12
Answer: A
how many number x (x being an integer) with 10<=x<=99 are 18 more than sum of their digits?
Choose the correct choice from the following answers:  A) 12  B) 9  C) 8  D) 18  E) 10

Solution: Let the no. be 10y+z.   then,   10y+z= y+z+18   => Y=2   So the no. are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. Total nos. 10   ANSW10R:10
Answer: E
x+(1/x) = 3.5 find x^2 + (1/x^2)  Select the correct option.
A) 2.25 B) 3.25 C) 10.25 D) 5.25 E) 6.25

Solution: squaring on both sides (x+1/x)^2=3.5^2   x^2+1/X^2=12.25-2   x^2+1/X^2=10.25   ANSWER:10.25
Answer: C
What will be the compound interest on a sum of Rs. 35,000 after 3 years at the rate of 12% p.a.? Choose the correct option
A) s:10123.19
B) s:14172.48
C) s:10123.20
D) s:10123.28
E) s:10123.12

Solution: Amount   = [35000 * (1 + 12/100)3]   = 35000 * 28/25 * 28/25 * 28/25   = Rs. 49172.48   C.I. = (49172.48 - 35000)= 
(49172.48 - 35000) = 14_172.48
Rs:14172.48   Answer: s:14172.48
Answer: B
Tom drives his car at a speed of 40kmph and reaches his destination in 5hrs and John covers the same distance in 8 hours. If speed of Tomis increased by 10kmph and speed of Ram is increased by 15kmph, what would be the difference between the times taken by them to cover the distance? Choose the most appropriate option
A) 2 hour  B) 1 hour  C) 3 hour  D) 4 hour  E) 5 hour

Solution: Distance covered by Ravi at a speed of 40 kmph in 5 hours   ð Distance= Speed x Time = 40 x 5= 200 km   Ram covers same distance in 8 hours => Speed of Rama =   Distance   Time   = 200/8= 
200/8 = 25
25 kmph.   Ravi speed is increased by 10 kmph=> New speed of Ravi = 40+10= 
40+10 = 50
50 kmph   Ram speed is increased by 15 kmph=>New speed of Ram = 25+15= 
25+15 = 40
40 kmph.   Therefore, time taken by Ravi to cover 200 km at 50 kmph= 200/50= 
200/50 = 4
4 hours   Time taken by Ram to cover 200 km at 40 kmph= 200/40= 
200/40 = 5
5 hours 1 hour)   Required time difference= 5 hours – 4 hours = 1 hour   1 hour
Answer: B
A train 490 m long, running with a speed of 63 km/hr will pass a tree in?  Choose the correct choice from the following answers.
A) 18 sec  B) 16 sec  C) 76 sec  D) 15 sec  E) 28 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 490 * 2/35= 
490 * 2/35 = 28
28 sec   Answer:28 sec
Answer: E
In how many ways the word ENGINEERING can be arranged so that no vowel come together???	Choose the correct choice from the following options.
A) 273000
B) 283000
C) 293000
D) 263000
E) 253000

Solution: Total no. of ways ENGINEERING can be arranged is   E=3, N=3, G=2, I=2, R=1   => 11!/(3!*3!*2!*2!) => 277200   No. of ways vowels come together   Vowels ==> (eieei)ngnrng =>   eieei can be considered as 1 letter ... so 1!   ngnrng = 6!   eieei can be arranged as 5!/(3!*2!)   ngnrng can be arranged as 6!/(3!*2!)   So (1!+6 !)*5!/(3!*2!*3!*2!)   => 4200   So no. of ways vowels not come together   => 277200 - 4200= 
277200 - 4200 = 273_000
273000   273000NSWER:273000
Answer: A
Car A takes 10 min lesser than Car B which is travelling at an average speed of 40mph to cover a distance of 60 miles. What is the average speed of car A?  Select:
A) 30
B) 35
C) 45
D) 50
E) 55

Solution: Time taken by Car B to cover 60 miles=60/40= 
60/40 = 3/2 = around 1.5
1.5 hrs=90 min   Time taken by Car A to cover 60 miles=80min   Average speed of Car A=60/80= 
60/80 = 3/4 = around 0.75
0.75 miles per min= 45 miles per hour.   Answer: 45
Answer: C
In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?  Choose the correct choice from the following options:
A) 9:3
B) 2:1
C) 1:3
D) 2:3
E) 2:5

Solution: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3   Answer: Option 1:3
Answer: C
In a throw of dice what is the probability of geÆ«ng number greater than 2	Choose the correct choice from the following.
A) 1/2	B) 2/3	C) 1/5	D) 1/6	E) None of these

Solution: Explanation:   Number greater than 2 is 3, 4, 5 & 6, so only 4 number   Total cases of dice = [1,2,3,4,5,6]   So probability = 4/6 = 2/3   Answer: 2/3
Answer: B
Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 350 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?	Choose one:
A) 1,300
B) 1,000
C) 900
D) 700
E) 550

Solution: Given: Atleast 1 juice was liked by the participants. --> Neither = 0   Assume, I -->No overlap between the sets   II --> Overlap between 2 sets   III --> Overlap between 3 sets   I + 2*(II) + 3*(III) = 100 + 200 + 700   I + 2*(350) + 3*(50) = 1000   I = 150   Total number of shoppers who took the taste test = I + II + III = 150 + 350 + 50= 
150 + 350 + 50 = 550
550   Answer: 550
Answer: E
A man is riding a bike downhill at 18 Km/hr, and uphill at 4 Km/hr, what is his rate? Choose the correct option:  A) 1 Km/Hr  B) 3 Km/Hr  C) 5 Km/Hr  D) 7 Km/Hr  E) 9 Km/Hr

Solution: 7 Km/Hrh = 18   Uh = 4   s=?   s=(18-4)/2 = 14/2= 
14/2 = 7
7   Answer= 7 Km/Hr
Answer: D
In an examination 40% failed in Hindi, 45% failed in English. If 25% students failed in both the subjects. Then the percentage of failed students is? Choices:
A) 59% B) 50% C) 90% D) 60% E) 20%

Solution: Male = 45,000* 5/9 = 25,000   Female = 45,000* 4/9 = 20,000   Married Male = 25,000* 40/100 = 10,000   Married Female = 10,000   20,000 ------------ 10,000   100 ------------- ? => 50%   Answer: 50%
Answer: B
If Jan 1, 2006 was a Sunday, What was the day of the week Jan 1, 2010?  Choose one.
A) Friday B) Thursday C) Tuesday D) Saturday E) None of these

Solution: Explanation :   Given that Jan 1 2006 was a Sunday   Number of odd days in the period 2006-2009   = 3 normal years + 1 leap year   = 3 x 1 + 1 x 2 = 5 (note that we have taken the complete year 2006 because the period in 2006 is from 01-Jan-2006 to 31-Dec-2006, which is the whole year 2006. Then the complete years 2007, 2008 and 2009 are also involved)   Hence Jan 1 2010 = (Sunday + 5 odd days) = Friday.. Fridaynswer : Option Friday
Answer: A
The daytime telephone rate between two cities is 60 cents for the first 3 minutes and c cents for each additional minute. The total charge is reduced 50 percent on calls made after 10:00 P.M. The cost, in dollars, of a 35-minute call made at 10:30 P.M. between these two cities is: Choose one:
A) 0.4(0.60) + 35c B) 0.5(0.60 + 32c) C) 0.4(0.60 + 9c) D) 0.5(0.60 + 0.32c) E) 0.6(0.60 + 0.35c)

Solution: For first three minutes = 60 cents   Remaining minutes = 35 -3= 
35 -3 = 32
32   charge for 32 minutes= 32c   total cost (if the call was made in daytime) = 0.60 + 32c   50% chargereducedon night calls => 50% charge   =>0.5(0.60 + 32c)   Hence, Answer is 0.5(0.60 + 0.32c)
Answer: D
A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?
Pick one:
A) 5 km/hr  B) 3 km/hr  C) 6 km/hr  D) 9 km/hr  E) 2 km/hr

Solution: Let A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.   So, 24/x + 24/(7 - x) = 14   x2 - 98x + 168 = 0   (x - 3)(x - 4) = 0 => x = 3 or 4.   Since, A is faster than B, so A's speed = 4 km/hr and B's speed   = 3 km/hr.   Answer: 3 km/hr
Answer: B
A committee of 3 people is to be chosen from the president and vice president of four different companies. What is the number of different committees that can be chosen if two people who work for the same company cannot both serve on the committee?  Choose the correct option:
A) 16
B) 24
C) 28
D) 32
E) 40

Solution: i just did the total number of possibilities first:   ab cd ef gh are the 4 companies for example   8c3. this will include the problem counts of a pres/vp of the same company   how many ways did we over count = How many ways can a president and VP of the same company be part of this group?   choose the group, 4c1, then take both the president and vp, 2c2, then a remaining member from one of the other 3, 6c1   4c1 * 2c2 * 6c1   4 * 1 * 6= 
4 * 1 * 6 = 24
24   8c3 - 24= 56 - 24= 
56 - 24 = 32
32 answer is 32
Answer: D
A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.140 where as B does not. In what ratio should they divide the second year's profit?
Choose one
A) 8:7 B) 7:5 C) 1:3 D) 8:7 E) 9:10

Solution: 9:10xplanation:   3: 4   A = 3/7*140= 
3/7*140 = 60
60   360: 400   39:40   Answer:9:10
Answer: E
A, B and C rents a pasture for Rs.841. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?
Pick:
A) 270	B) 279	C) 348	D) 371	E) 372

Solution: 12*8 :16*9 = 18*6   8: 12: 9   12/29 * 841= 
12/29 * 841 = 348
348   Answer: 348
Answer: C
2/5 of the fish in an aquarium is red and 1/4 of the fish is brown. 1/4of the red fish and 1/5 of the brown fish is male. If the rest of the fish in the aquarium is female, what is the probability that a fish randomly picked from the aquarium is male?  Choose the correct choice from the following.
A) 3/20	B) 7/30	C) 5/16	D) 1/3	E) 2/5

Solution: Straight method....   1/4 of 2/5 + 1/5 of 1/4 = 2/20 +1/20 =3/20   3/20NSWER:3/20
Answer: A
If a^2+b^2=177and ab=54 then find the value of a+b/a-b?	Pick:
A) 1	B) 3	C) 5	D) 7	E) 9

Solution: (a+b)^2=a^2+b^2+2ab=117+2*24=225   a+b=15   (a-b)^2=a^2+b^2-2ab=117-2*54   a-b=3   a+b/a-b=15/3= 
15/3 = 5
5   Answer is 5.
Answer: C
The bankerâ€™s discount of a certain sum of money is Rs. 60 and the true discount on the same sum for the same time is Rs.54. The sum due is	Choose the correct answer.
A) 210 B) 280 C) 360 D) 720 E) None

Solution: Sol.   Sum = B.D. * T.D. / B.D. - T.D. = Rs.[60 *54 / 60 - 54] = Rs. [72 * 60 / 6] = Rs. 720   Answer 720
Answer: D
Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?  Choose one:
A) 46 B) 42 C) 56 D) 70 E) 58

Solution: I'm going in on this one.   So let's say that we have the following   So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is  200 - 60= 
 200 - 60 = 140
140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30= 
100 - 30 = 70
70.   Thus 70 is the correct answer choice
Answer: D
M, N and O can do a piece of work in 60, 30 and 20 days respectively. Inhow many days can M do the work if he is assisted by N and O on every third day? Choose the correct option.
A) 10 days  B) 12 days  C) 15 days  D) 25 days  E) 30 days

Solution: M's 2 day's work = 1	x 2 =	1	.   20	10   (M + N + O)'s 1 day's work = 1	+	1	+	1 =	6	=	1	.   20	30	60	60	10   Work done in 3 days = 1	+	1 =	1	.   10	10	5   Now,	1	work is done in 3 days.   5   Whole work will be done in (3 x 5) = 15 days.   15 days
Answer: C