MU-NLPC/Calc-aqua_rat huggingface dataset:
Jackson has $313,192 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
Choose one
A) $1
B) $2
C) $3
D) $4
E) $5

Solution: In order to divide the sum in 9 parts, the amount must also be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 313,192 = 19 and 18 is divisible by 9.   Hence we need to subtract 1 to this number for it to be divisible by 9   Correct Option: $1
Answer: A
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat(in still water) and the stream is	Choose the correct choice from the following:
A) 1:2	B) 1:3	C) 2:1	D) 3:1	E) None

Solution: Sol.   Let man’s rate upstream be x kmph. Then, his rate downstream = 2x kmph.   ∴ (Speed in still water) : (Speed of stream)   = [2x + x / 2] : [2x - x / 2]   3x / 2 : x / 2 = 3:1.   Answer 3:1
Answer: D
How many words can be formed by using all letters of word ALIVE.  Answers:
A) 120 B) 236 C) 128 D) 261 E) 191

Solution: Explanation:   The word 120LIVE contains 5 different letters   Therefore,   Required number of words = 5p5 = 5!   = (5*4*3*2*1)= 
(5*4*3*2*1) = 120
120   120NSWER:120
Answer: A
one person Tharak speed with the current is 10 km/hr and the speed of the current is 4 km/hr. Tharak's speed against the current is: Choose the most appropriate option:
A) 0 km/hr	B) 1 km/hr	C) 2 km/hr	D) 3 km/hr	E) 4 km/hr

Solution: Man's speed with the current = 10 km/hr   => speed of the man + speed of the current = 10 km/hr   speed of the current is 4 km/hr   Hence, speed of the man = 10-4= 
10-4 = 6
6 km/hr   man's speed against the current= speed of the man - speed of the current   = 6-4= 
6-4 = 2
2 km/hr   ANSWER:2 km/hr
Answer: C
A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?	Choose one: A) 8% B) 2% C) 3% D) 4% E) 6%

Solution: SP of first article = 1000   Profit = 20%   CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3   SP of second article = 1000   Loss = 20%   CP = (SP)*[100/(100-L)] = 5000/4= 
5000/4 = 1_250
1250   Total SP= 2000   Total CP = 2500/3 + 1250 = 6250/3   CP is more than SP, he makes a loss.   Loss = CP-SP = (6250/3)- 2000 = 250/3   Loss Percent = [(250/3)/(6250/3)]*100   =0.04 * 100= 
0.04 * 100 = 4
4%   Answer:4%
Answer: D
The smallest number when increased by " 1 " is exactly divisible by 6,18,36,48, 60 is:
Select:  A) 724  B) 721  C) 720  D) 719  E) 700

Solution: LCM = 720   720 - 1= 
720 - 1 = 719
719   ANSWER:719
Answer: D
A cyclist traveled for two days. On the second day the cyclist traveled 3 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling, what was her average speed on the second day?	Pick one:
A) 5 mph
B) 10 mph
C) 20 mph
D) 30 mph
E) 40 mph

Solution: SOLUTION:   D = 280 Mi   T = 12 hrs   Day 1 time = T1   Day 2 time = T2   T2 - T1 = 4 hrs ----- (I)   T1 + T2 = 12 hrs ----- (II)   Adding I and II, T2 = 8 hrs and T1 = 4 hrs   Day 1 Rate = R1   Day 2 Rate = R2   R1 - R2 = 10 mph   i.e. R1 = 10 + R2   280 = 8R2 + 4R1   i.e. 280 = 8R2 + 4 (10 + R2)   i.e. R2 = 20 mph   ANSWER: 10 mph
Answer: B
In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 161 hats in this group, how many of these hats are not blue?	Choose the correct choice from the following answers.
A) 28	B) 42	C) 48	D) 112	E) 76

Solution: Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be   7x+4x+12x=161 or 23x=161...here 7x,4x and 12x represent hats of each type   23x=161 so x=7...Blue hats =7*7=49...Not blue will be   161-49= 
  161-49 = 112
112.   Ans 112
Answer: D
By selling an article at Rs.600, a profit of 25% is made. Find its cost price? Choose the most appropriate option:
A) 288
B) 992
C) 678
D) 480
E) 131

Solution: SP = 600   CP = (SP)*[100/(100+P)]   = 600 * [100/(100+25)]   = 600 * [100/125] = Rs.480   Answer:480
Answer: D
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km? Pick.
A) 3
B) 6
C) 7
D) 8
E) 9

Solution: M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 6   T = 6/2= 
6/2 = 3
3   3nswer: 3
Answer: A
X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
Choose the correct choice from the following.
A) 1:2	B) 1:3	C) 2:1	D) 1:4	E) 1:5

Solution: Ratio in which they should share the profit   = Ratio of the investments multiplied by the time period   =45000×12:30000×9   =45×12:30×9   =3×12:2×9   =2:1   Answer is 2:1.
Answer: C
54.327 × 357.2 × 0.0057 is the same as :	Select the correct option:
A) 5.4327 × 3.572 × 5.7
B) 5.4327 × 3.572 × 0.57
C) 5.4327 × 3.572 × 0.0000057
D) None of these
E) Cannot be determined

Solution: Solution   Number of Decimal places in the given expression =8 .   Number of Decimal places in (a) = 8 .   Number of Decimal places in (b) =9 .   Number of Decimal places in (c) = 7 .   Number of Decimal places in (a) is the same as the given expression . 5.4327 × 3.572 × 5.7nswer 5.4327 × 3.572 × 5.7
Answer: A
A bag contains 4 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is	Choices
A) 8/15
B) 2/5
C) 3/5
D) 11/15
E) 17/33

Solution: Drawing two balls of same color from four green balls can be done in 4C₂ ways.   Similarly from eight white balls two can be drawn in ⁸C₂ ways.   P = 4C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 17/33   ANSW17/33R:17/33
Answer: E
If 100<x<190 and 10<y<100, then the product xy CANNOT be equal to: Choose the most appropriate option:  A) 18,104  B) 18,303  C) 18,356.732  D) 19,502  E) 18,909

Solution: Correct Answer: (D)   Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 100 * 10. The largest value must be less than 190 * 100. This means that 1000 < xy < 19,000. (19,502) is outside of this range, so it is not a possible product of xy.
Answer: D
A teacher prepares a test. She gives 6 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 3 questions have 3 choices and the last 3 have 4 choices.  Choose the correct choice from the following.
A) 255 B) 1816 C) 1872 D) 100 E) 144

Solution: Two cases.   First 1872ase: 2 Questions - 3 1872hoices, 2 Questions - 4 1872hoices   318722 * 318722 ways to select the questions   318721 * 318721 * 418721 * 418721 ways to answer the questions   = 3 * 3 * 3 * 3 * 4 * 4= 
3 * 3 * 3 * 3 * 4 * 4 = 1_296
1296   Second 1872ase: 1 Question - 3 1872hoices, 3 Questions - 4 1872hoices   318721 * 318723 ways to select the questions   318721 * 418721 * 418721 * 418721 ways to answer the questions= 3 * 1 * 3 * 4 * 4 * 4= 
3 * 1 * 3 * 4 * 4 * 4 = 576
576   Total= 1296 + 576= 
1296 + 576 = 1_872
1872   1872
Answer: C
The milk level in a rectangular box measuring 64 feet by 25 feet is to be lowered by 6 inches. How many gallons of milk must be removed? (1 cu ft = 7.5 gallons)  Choose the correct choice from the following choices.
A) 100  B) 250  C) 750  D) 5625  E) 6000

Solution: 6 inches = 1/2 feet (there are 12 inches in a foot.), so  64*25*1/2= 
 64*25*1/2 = 800
800 feet^3 of milk must be removed, which equals to   800*7.5= 
  800*7.5 = 6_000
6000 gallons.   Answer: 6000.
Answer: E
7 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? Select the correct option:  A) 40  B) 48  C) 45  D) 42  E) 22

Solution: Though 2*(7C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.   The first guy has to play 2 matches with the rest of 6, so he'll play 12matches.   Similarly, second guy has to play with the rest of 5 as his 2 games with the first guy are already played. So he plays 10 matches.   This continues like this and the total matches are 12+10+8...+2   12+10+...+2 = 2(6+5+...+1) = 2((6*7)/2) = 6*7= 
6*7 = 42
42.   ANSWER:42
Answer: D
P can do a certain work in 16 days. Q is 60% more efficient than P. How many days does Q alone take to do the same job? Choose the correct choice from the following answers:
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: Each day, P can do 1/16 of the work.   Each day, Q can do 1.6/16 of the work = 16/160 of the work   The time taken by B alone to complete the total work is   160/16= 
  160/16 = 10
10 days.   The answer is 10.
Answer: C
A can do a piece of work in 15 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?  Choices
A) 11 3/9 B) 19 3/7 C) 11 3/5 D) 11 3/7 E) 11 3/1

Solution: (x – 5)/15 + x/20 = 1   x = 11 3/7 days   Answer:11 3/7
Answer: D
If KING is coded as 17 and MASS is coded as 29 Then DON is coded as  Choose the correct choice from the following answers:
A) 21  B) 20  C) 18  D) 16  E) None of these

Solution: KING = 11+9+14+7= 
11+9+14+7 = 41
41 i.e (4*4)+(1*1)=17   MASS = 13+1+19+19= 
13+1+19+19 = 52
52 i.e (5*5)+(2*2)=29   DON = 4+14+15= 
4+14+15 = 33
33 i.e(3*3)+(3*3)=18   ANSWER:18
Answer: C
In March, Kurt ran an average of 1.2 miles an hour. If by June he had increased his pace by 20 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June?	Choices:	A) 3590/60^2	B) 2980/60^2	C) 2390/60^2	D) 3586/60	E) 60^2/3590

Solution: Kurt ran at an average of 1.2 miles/hour in march. So to run 1 mile he would take 1/1.2 hours = (60 * 60)/1.2= 
(60 * 60)/1.2 = 3_000
3000 seconds.   If he increases his speed by 20 seconds, he will complete a mile in 2980 seconds. Converting in hours= 2980/(60 * 60) = 2980/(60^2)   ANSWER: 2980/60^2
Answer: B
A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $19 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item?
Pick:
A) $27.50 B) $28.50 C) $29.50 D) $30.50 E) $31.50

Solution: Let x be the price that buyers see online.   The distributor wants to receive 1.2(original price) which should be 80% of x.   1.2(19) = 0.8x   x = 1.2(19) / 0.8 = 1.5(19) = $28.50   The answer is $28.50.
Answer: B
A person takes 5 hrs 45 min in walking to a place and riding back. He would have gained 4 hrs by riding both ways. The time he would take to walk both ways is?
Select the correct option.
A) 5 hours 45 min	B) 5 hours 55 min	C) 6 hours 45 min	D) 9 hours 45 min	E) 10 hours

Solution: ----------------------------------------------------------------   Solution 1   ----------------------------------------------------------------   Given that time taken for riding both ways will be 4 hours lesser than   the time needed for waking one way and riding back   From this, we can understand that   time needed for riding one way = time needed for waking one way - 4 hours   Given that time taken in walking one way and riding back = 5 hours 45 min   Hence The time he would take to walk both ways = 5 hours 45 min + 4 hours = 9 hours 45 min   9 hours 45 min
Answer: D
Find the area of a parallelogram with base 12 cm and height 8 cm?
Select the correct option:
A) 96 cm2	B) 104 cm2	C) 78 cm2	D) 86 cm2	E) 76 cm2

Solution: 96 cm2rea of a parallelogram = base * height = 12 * 8= 
12 * 8 = 96
96 cm2   96 cm2nswer:96 cm2
Answer: A
In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 25 p coins are there?  Choose the correct choice from the following answers.
A) 20	B) 30	C) 25	D) 50	E) 40

Solution: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.   Then, sum of their values = (25 x/100) + (20 x/100) + (15 x/100)   = 60 x /100   30 = 60 x / 100   x = 50 = 25 p coin   Ans - 50
Answer: D
A train 200 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line in seconds  Choices
A) 12 sec	B) 6 sec	C) 7 sec	D) 8 sec	E) 9 sec

Solution: Explanation:   Speed of the train = (60 x 5/18m / sec = 50/3 m/ sec.   Distance moved in passing the standing man = 100 m.   Required time taken = 200/(50/3) = (200 Ã—(3/50)) sec =12 sec   12 secnswer: Option 12 sec
Answer: A
In a store, the profit is 320% of the cost. If the cost increases by 25% but the SP remains constant, approximately what %of the sp is the profit?
Pick
A) 50%	B) 70%	C) 90%	D) 100%	E) 140%

Solution: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420   New C.P. = 125% of Rs. 100 = Rs. 125.   New S.P. = Rs. 420   Profit = 420 - 125 = Rs. 295   Required percentage = 295/420 * 100 = 1475/21 = 70%   70%
Answer: B
If a - b = 5 and a2 + b2 = 29, find the value of ab.	Choose the correct choice.
A) A)2  B) B)12  C) C)15  D) D)18  E) E)20

Solution: Explanation:   2ab = (a2 + b2) - (a - b)2   = 29 - 25= 
29 - 25 = 4
4   ab= 2.   2nswer: 2
Answer: A
The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one year old child. What is the average age of the family ? Choose the correct choice from the following choices
A) 21 years
B) 20 years
C) 18 years
D) 19 years
E) 17 years

Solution: after 5 years the average age of the two will be 28.   now the child is one year old ,   total age = 28*2 + 1= 
28*2 + 1 = 57
57   average age= total age/family members(3)   => 57/3= 
57/3 = 19
19   ANSWER:19 years
Answer: D
9.009/5.005 =
Choices: A) 1.08 B) 1.4 C) 1.8018 D) 1.4014 E) 1.8

Solution: 9.009/5.005 = 9009/5005 = 9(1001)/5(1001) = 9/5= 
9/5 = 9/5 = around 1.8
1.8   The answer is 1.8.
Answer: E
Which of the following describes all values of x for which 36–x^2 >= 0? Choose the correct choice from the following:
A) x >= 1	B) x <= –1	C) -6 <= x <= 6	D) x <= –1 or x >= 1	E) –1 <= x <= 1

Solution: 36 - x^2 >=0   means x^2 - 36 <=0   => (x-6)(x+6) <= 0   => -6 <= x <= 6   Answer - -6 <= x <= 6
Answer: C
In a certain accounting class of 100 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 55%, and the students on the make-up date had an average score of 95%, what was the average score for the entire class?	Choose the correct choice from the following:
A) 60%	B) 65%	C) 67%	D) 70%	E) 75%

Solution: 70% of the class scored 55% and 30% of the class scored 95%.   The difference between 55% and 95% is 40%.   The average will be 55% + 0.3(40%) = 67%.   The answer is 67%.
Answer: C
If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day?  Pick one:
A) 10 B) 15 C) 20 D) 25 E) None of them

Solution: Let the required number of days be x.   More men, Less days (indirect proportion)   Less hours per day, More days (indirect proportion)   Men 18 : 15   Hours per day 8: 9 } : :16 : x   (18 x 8 x x)=(15 x 9 x 16)= x=(44 x 15)144 = 15   Hence, required number of days = 15.   Answer is 15.
Answer: B
The average of 50 numbers id 44. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :  Pick one: A) 22.35 B) 33.25 C) 22.25 D) 11.35 E) 43.75

Solution: 43.75xplanation:   Total of 50 numbers = (50×44)=2200   Total of 48 numbers =(2200-(45+55)]=2100   Required average = 2100/48= 
2100/48 = 175/4 = around 43.75
43.75   Answer:43.75
Answer: E
10% of inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants let the village. The population is then reduced to 4050. Find the original inhabitants
Options:  A) 5500  B) 6000  C) 6500  D) 7000  E) 8000

Solution: Explanation:   Let the total number is x,   then,   (100-25)% of (100 - 10)% x = 4050   => 75% of 90% of x = 4050   => 75/100 * 90/100 * x = 4050   => x = (4050*50)/27 = 6000   Answer: Option 6000
Answer: B
The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is?  Choose the correct answer:
A) 9	B) 11	C) 15	D) 12	E) 20

Solution: Age of the 15th student = 15*15 - (14*5+16*9) = 225-214= 
225-214 = 11
11 years   Answer is 11
Answer: B
Which of the following is a multiply of 4 number ?
Choose the correct choice from the following:
A) 120
B) 130
C) 45
D) 82
E) 17

Solution: Explanation :   120 is a perfect multiply of 4   120nswer : Option 120
Answer: A
There is a group of persons each of whom can completea piece of work in 16 days, when they are working individually. On the 1st day 1 person works, on the second day another person joins him, on the third day one more person joins them & this process continues till the work is completed. How many days are needed to complete the work? Choose the correct choice:
A) 5 1⁄2 days
B) 5 1⁄3 days
C) 5 1⁄6 days
D) 6 1⁄6 days
E) 7 1⁄6 days

Solution: Work completed in 1st day = 1/16   Work completed in 2nd day = (1/16) + (1/16) = 2/16   Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16   …   An easy way to attack such problems is from the choices. You can see the choices are   very close to each other. So just see one by one.   For instance, The first choice given in 3 1⁄4   The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16   The work done in 4 days = (1+2+3+4)/16 = 10/16   The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?   The work done in 6 days = (1+2+3+4+5+6)/16 > 1   Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days.   (Just for your reference, work done in 5 days = 15/16.   Pending work in 6th day = 1 – 15/16 = 1/16.   In 6th day, 6 people are working and work done = 6/16.   To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.   Hence total time required = 5 + 1/6 = 5 1⁄6 days   5 1⁄6 days
Answer: C
What is the units digit of 6^m(2^7+1), for a positive integer m?
Choose the most appropriate option.
A) 1	B) 3	C) 4	D) 7	E) 0

Solution: Equation can be re-written as   6^m( 2^7 + 1)   =6^m ( 128 + 1)   =6^m (129)   Now, putting m= 0 ; Eqn = 129   putting m= 1 ; Eqn = 129. 6   putting m= 2 ; Eqn = 129 .36   putting m= 3 ; Eqn = 129 .216   We can see that there lies a pattern while multiplying 129 with multiples of 6 , units digit is always going to be 4   ANSWER:4
Answer: C
Bill has a collection of new and used trading cards that he stores in two albums. His first album contains 200 cards, 60% of which are used. If 90% of the cards in his second album are used, and 65% of all of his cards are used, what is the total number of trading cards in Bill’s collection?
Choices:	A) 290	B) 260	C) 254	D) 240	E) 156

Solution: Let, Total Cards in second collection = B   (60/100)*200 + (90/100)*B = (65/100)*(200+B)   i.e. B = 40   i.e Total cards = 200+B = 240   Answer: OPtion 240
Answer: D
Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 20 days.
Choose the correct choice from the following choices:
A) 12 days.
B) 17 days.
C) 18 days.
D) 19 days.
E) 20 days.

Solution: They together completed 4/10 work in 4 days.   balance 6/10 work will be completed by Arun alone in   20*6/10= 
  20*6/10 = 12
12 days.   12 days.NSWER:12 days.
Answer: A
9, 35, 91, 189, 341, ?	Options.
A) 502  B) 521  C) 559  D) 611  E) 712

Solution: Explanation :   13 + 23 = 9   23 + 33 = 35   33 + 43 = 91   43 + 53 = 189   53 + 63 = 341   63 + 73 = 559   Answer : Option 559
Answer: C
A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance? Choose the correct choice from the following:
A) 21 (1/8)kmph
B) 21 (1/3)kmph
C) 21 (7/3)kmph
D) 27 (1/3)kmph
E) 21 (1/8)kmph

Solution: Let the total distance be x km   total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64   Average speed = x/(3x/64) = 64/3kmph   = 21 (1/3)kmph.   Answer:21 (1/3)kmph
Answer: B
A team of four entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
Choices: A) 288 B) 329 C) 168 D) 127 E) 664

Solution: Explanation:   4 * 84= 
4 * 84 = 336
336 - 7= 
336 - 7 = 329
329   Answer:329
Answer: B
Product of two natural numbers is 5. Then, the sum of reciprocals of their squares is Choose the correct choice from the following choices: A) 290/289 B) 26/25 C) 290/90 D) 290/19 E) None of these

Solution: Explanation:   If the numbers are a, b, then ab = 5,   as 17 is a prime number, so a = 1, b = 5.   1/a2+1/b2=1/1(2)+1/5(2)   1/ 2+1/ 2= 
1/ 2+1/ 2 = 1
1/1(2)+1/5(2)=26/25   Option 26/25
Answer: B
In how many ways can the letters of the word WORDS be arranged in a row so that the vowels appear in alphabetic order?	Choose the correct choice from the following answers
A) 210  B) 120  C) 180  D) 220  E) 160

Solution: three letters can be arranged in ! ways.   only one combination AEI is required.   5 letters can be arranged in 5! ways.   thus 5!/ 1! * 1 = 120.   120
Answer: B
Raj and Roshan has some money with them in the ratio 5:4 respectively. If Raj has Rs. 45. How much money Raj has more than Roshan? Choices:
A) 5  B) 9  C) 16  D) 12  E) 18

Solution: Let the money Roshan has be x then (45/x)=5/4   Upon cross multiplication and solving for x we get x=36   So Raj has Rs. 9 more than Roshan   Answer:9
Answer: B
The average of seven numbers is 20. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?  Options:  A) 27  B) 29  C) 31  D) 41  E) 35

Solution: The total of seven numbers = 7X20 = 140   The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99   So, the middle number is  (140 - 99 )= 
 (140 - 99 ) = 41
41   41
Answer: D
An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,395, what was the total number of pairs of contact lenses that she sold?	Pick
A) 11	B) 13	C) 15	D) 17	E) 19

Solution: (x+5)*150 +x*85=2395   =>x=7   total lens=7+(7+5)= 
7+(7+5) = 19
19   Answer 19
Answer: E
A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 km/h and the speed of the boat in still water is 14 km/h, what is the distance between A and B?
Choices:	A) 200 km	B) 180 km	C) 160 km	D) 220 km	E) None of these

Solution: Speed of boat for downstream = 14 + 4= 
14 + 4 = 18
18 km/hr   Speed of boat for upstream= 14 – 4 = 10 km/hr   Distance = x   x / 18 + (x /2)/10 = 19   x = 180 km   Answer: 180 km
Answer: B
With the money I have , I can buy 50 pens or 150 pencils. I kept 10% aside for taxi fare. With the remaining , I purchased 54 pencils and P pens. What is the value of P?
Select the correct option:
A) 32
B) 30
C) 27
D) 25
E) 23

Solution: Since cost of, 50 pens = 150 pencils, With the cost of 3 pencils I can buy 1 pen. After   putting aside 10% for taxi I was left with 90% of the money , with which I can buy 135   pencils (90% of 150) or 45(90% of 50) pens, I bought 54 pencils and P pens, or I could have   bought ( 54 +3P ) pencils ,   54 +3P =135, 3P = 135-54= 
135-54 = 81
81, P=27   ANSWER:27
Answer: C