MU-NLPC/Calc-aqua_rat huggingface dataset:
Two cubes of tire sides ratio 2 : 3. Find its cube volumes ratio?
Choices:
A) 2:27  B) 3:27  C) 1:27  D) 8:27  E) 5:27

Solution: a(power3) : b(power3) = 2(power3) : 3(power3)   = 8 : 27   Answer is 8:27.
Answer: D
A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?	Choose the correct choice from the following answers:  A) 250  B) 882  C) 772  D) 512  E) 211

Solution: CP1 = 100 SP1 = 90   CP2 = 80 SP2 = 80 * (140/100)= 
80 * (140/100) = 112
112   22 ----- 100   55 ----- ?=> Rs.250   250nswer: 250
Answer: A
An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 50 cm, find the sum of the perimeters of all the triangles. Choose the correct choice.
A) 180 cm
B) 220 cm
C) 240 cm
D) 270 cm
E) 300 cm

Solution: We have 50 for first triangle, when we join mid-points of first triangle we get the second equilateral triangle then the length of second one is 25 and continues.   So we have 50,25,12.5,...   We have ratio = 1/2, and it is GP type.   Sum of infinite triangle is a/1-r = 50/1-(1/2) = 100   Equilateral triangle perimeter is 3a = 3*100= 
3*100 = 300
300.   So option 300 cm.
Answer: E
How many numbers between 11 and 90 are divisible by 7 ?
Choose the correct choice from the following answers:
A) 23
B) 11
C) 22
D) 32
E) 15

Solution: The required numbers are 14, 21, 28, 35, .... 77, 84.   This is an A.P. with a = 14 and d = (21 - 14)= 
(21 - 14) = 7
7.   Let it contain n terms.   Then, Tn= 84 => a + (n - 1) d = 84   => 14 + (n - 1) x 7 = 84 or n = 11.   Required number of terms = 11   ANSWER 11 11
Answer: B
How many integer values Y are there for x such that 1 < 3x + 5 < 17?	Options:
A) Two
B) Three
C) Four
D) Five
E) Six

Solution: 1 < 3x + 5 < 17   => -4 < 3x < 12   => -4/3 < x < 4   x can take integer values Y -1,0 , 1 , 2 , 3   Answer Five
Answer: D
A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
Choose the correct choice from the following options.
A) 60% B) 23% C) 30% D) 56% E) 73%

Solution: Let C.P. be Rs. 100.   Then, S.P. = Rs. 123.50   Let marked price be Rs. x. Then, 95/100 x = 123.50   x = 12350/95 = Rs. 130   Now, S.P. = Rs. 130, C.P. = Rs. 100   Profit % = 30%.   Answer: 30%
Answer: C
The average of five numbers id 27. If one number is excluded, the average becomes 22. What is the excluded number?	Choose the correct choice: A) 30 B) 40 C) 32.5 D) 35 E) 47

Solution: 47xplanation:   Sum of 5 numbers = 5 × 27   Sum of 4 numbers after excluding one number = 4 × 22   47xcluded number   = 5 × 27 - 4 × 22   = 135 - 88= 
135 - 88 = 47
47   Answer: Option 47
Answer: E
Which of the following points falls outside of the region defined by 2y≤6x−8?  Choose the correct choice from the following answers.
A) (5, 1)  B) (3, -8)  C) (1, 0)  D) (2, 0)  E) (0, -14)

Solution: Equation given is 2y<=6x-8   Simplifying this; y<=3x-4   Plug in the values provided in the options,   A. 1<=11   B. -8<=3   C. 0<=-1   D.0<=0   E. -14<=-12   Option (1, 0) is the answer.
Answer: C
A farmer has enough food to feed her 1000 cows for 50 days. After 10 days some of the cows run away and the food was now enough for the same period of 50 days as before. How many cows ran away?	Answers:
A) 300	B) 200	C) 500	D) 400	E) 250

Solution: 1000 ---- 50   1000 ---- 40   x ---- 50   x*50 = 1000*40   x = 800   1000   -------   200   Answer = 200
Answer: B
Find the L.C.M of 15, 18, 28 and 30.	Choose the correct answer:  A) 1800  B) 1260  C) 1460  D) 1600  E) 960

Solution: Explanation:   2 x 3 x 5 x 3 x 14 = 1260   Answer: Option 1260
Answer: B
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 36 years now, the son's age five years back was:  Select:  A) 13  B) 15  C) 20  D) 25  E) 30

Solution: Let the son's present age be x years. Then, (36 - x) = x   2x = 36.   x = 18.   Son's age 5 years back (18 - 5)= 
(18 - 5) = 13
13 years.   13nswer: Option 13
Answer: A
A train 310 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Choose the correct choice from the following options
A) 40
B) 56
C) 41
D) 36
E) 34

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 310 + 140= 
310 + 140 = 450
450 m   Required time= 450 * 2/25= 
450 * 2/25 = 36
36 sec   Answer: Option 36
Answer: D
A sum fetched a total simple interest of $4241.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?	Pick one
A) $8829  B) $2840  C) $6578  D) $7782  E) $8930

Solution: $8930   8930   Principal   = $100 x 4241.25/9 x 5   = $424125/45   = $8930.
Answer: E
9 3/4 + 8 2/17 - 9 1/15=?	Pick
A) 7 719/1020  B) 9 817/1020  C) 9 719/1020  D) 8 817/1020  E) None of them

Solution: Given sum=9+3/4+8+2/17-(9+1/15)   =(9+8-9)+(3/4+2/17-1/15)   =8+(765+120-68/1020   =8 817/1020   Answer is 8 817/1020
Answer: D
There are 10 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?  Choose the correct choice from the following options
A) 10 B) 30 C) 45 D) 60 E) 90

Solution: 10 players are there.   two players play one game with one another.   so 10452=10*9/2= 
10*9/2 = 45
45   SO OPTION 45 is correct
Answer: C
The sum of three consecutive even numbers is 42. Find the middle number of the three? Pick
A) 14	B) 66	C) 88	D) 99	E) 12

Solution: Three consecutive even numbers (2P - 2), 2P, (2P + 2).   (2P - 2) + 2P + (2P + 2) = 42   6P = 42 => P = 7.   The middle number is: 2P = 14.14nswer:14
Answer: A
The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the numbers is 480, then the other is: Choose one.
A) 11
B) 10
C) 8
D) 15
E) 12

Solution: Other number =	(12 x 600)/480 = 15.   ANSWER :15
Answer: D
Lake A has a duck population of 36 females and 30 males. Lake B’s duck population consists of the same ratio of females to males. If 6 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following?	Choose the most appropriate option: A) 144 B) 105 C) 78 D) 51 E) 77

Solution: Lake A has a duck population of 36 females and 35 males --> the ratio is F:M = 36:30 = 6:5.   Lake B’s duck population consists of the same ratio of females to males --> F:M = 6:5.   77
Answer: E
The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is?
Pick one:
A) 7! * ⁷P₆  B) 6! * ⁷P₆  C) 8! * ⁷P₆  D) 2! * ⁷P₆  E) 5! * ⁷P₆

Solution: We can initially arrange the six boys in 6! ways.   Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.   Hence required number of ways   = 6! * ⁷P₆   Answer: 6! * ⁷P₆
Answer: B
The instructions state that Cheryl needs 3/8 square yards of one type of material and 1/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 15/40 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?  Choose the correct choice.
A) 1/12	B) 1/9	C) 2/3	D) 1/3	E) 2 1/9

Solution: total bought = 3/8+1/3   left part 15/40--->3/8   so used part 3/8+1/3-3/8=1/3   Ans 1/3
Answer: D
In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of that of his mother. The wife is 9 years younger to her husband and the brother is seven years older than his sister. What is the age of the mother ?  Choices
A) 40 years B) 45 years C) 50 years D) 60 years E) 70 years

Solution: let daughter age x then father age will be 3x   let mother age is y then son age will be y/2   accor. to que.   3x-y=9 ....................1   y/2-x=7 =>2x-y = -14......2   solve the both eqe.   y=60   ANSWER:60 years
Answer: D
Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 4 minutes the first is turned off. How much longer will the cistern take to fill?  Choose the correct choice.
A) 10 1/7	B) 10 1/4	C) 10 1/3	D) 10 1/2	E) 10

Solution: 4/12 + x/15 = 1   x= 10.Answer: 10
Answer: E
In how many different number of ways 3 men and 2 women can sit on a shopa which can accommodate persons?
Select.
A) 170 B) 180 C) 200 D) 5 E) 220

Solution: Option '5'   5p1 = 5 = 5
Answer: D
Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 153 per Kg , the price of the third variety per Kg will be? Select.
A) Rs. 147.50
B) Rs. 785.50
C) Rs. 175.50
D) Rs. 258.50
E) None of these

Solution: Explanation :   Since first and 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.   By the rule of alligation, we have:   Cost of 1 kg Cost of 1 kg   of 1st kind of 2nd kind   (Rs. 130.50) (Rs. x)   \ /   Mean Price   (Rs. 153)   / \   x−153 22.50   =>x−(153/22.50)=1.   =>x−153=22.50.   =>x= 175.50 Rs.   Answer : Rs. 175.50
Answer: C
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? Choose the correct choice from the following options:
A) 81 B) 66 C) 55 D) 42 E) 30

Solution: 4.5 km /hr = (4.5*5/18) = 5/4 m/sec = 1.25 m/sec   5.4 km/hr = (5.4*5/18) = 3/2= 
3/2 = 3/2 = around 1.5
1.5 m/sec   speed= (x-1.25)*8.4=(x-1.5)*8.5   x=22.5   speed = 22.5*18/5= 
22.5*18/5 = 81
81 km/hr   81NSWER 81
Answer: A
A certain quantity of 55% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced? Answers.
A) 1:3 B) 1:2 C) 2:3 D) 2:1 E) 3:1

Solution: 25% - - - - - - - - - 35% - - - - - - 55%   From 25 to 35 =10   From 35 to 55 = 20   So the ratio is 10/20 = 1 to 2   2:1 it is
Answer: D
Ram's age and Shyam's age are in the ratio 3:4. Seven years ago the ratio of their ages was 2:3. Find the ratio of their ages five years hence?	Choose the correct choice from the following answers:
A) 26/37
B) 26/35
C) 26/39
D) 26/33
E) 26/31

Solution: Let ages of Ramu and Shyam be x and y respectively.   x/y = 3/4 => x = 3/4 y   (x- 7)/(y - 7) = 2/3   => 3x - 21 = 2y - 14 => 3x = 2y + 7   But x = 3/4 y   3 * 3/4 y = 2y + 7   9y = 8y + 28 => y = 28years   => x = 21 years   Ratio of their ages five years hence, (21 + 5)/(28 + 5) = 26/33.   Answer:26/33
Answer: D
The average of 1st 3 of 4 numbers is 7 and of the last 3 are 5. If the sum of the first and the last number is 13. What is the last numbers?	Pick one
A) 4 B) 5 C) 3.5 D) 7 E) 8

Solution: A + B + 3.5 = 21   B + 3.5 + D = 15   A + D = 13   A – D = 6   A + D = 13   2D = 7   D = 3.5   ANSWER:3.5
Answer: C
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 60 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?	Choose the correct choice from the following:	A) 480	B) 96	C) 160	D) 192	E) 320

Solution: A:B:C:D=2x:3x:5x:6x, for some positive number x. Total time 2x+3x+5x+6x=16x.   If 2x 2 +3 +5 +6= 
2 +3 +5 +6 = 16
16x.   If 2x= 60 then 16x = 480;   If 3x = 60 then 16x = 320;   If 5x = 60 then 16x = 192;   If 6x = 60 then 16x = 160;   Only answer choices which is not obtained is 96.   Answer: 96.
Answer: B
An object thrown directly upward is at a height of h feet after t seconds, where h = -15 (t-3)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
Select the correct option
A) 90	B) 98	C) 106	D) 120	E) 136

Solution: We see that h will be a maximum h=150 when t-3=0, that is when t=3.   90t t=5, h = -15(5-3)^2 + 150 = -15(4) + 150 = 90   The answer is 90.
Answer: A
A Locomo's train rails across an open track at 250 kilometers per hour. A regular passenger train travels at 68% of the Locomo's train speed. If the two trains start moving from the same station at the same time, how much time longer will it take the passenger train than the Locomo's to travel 850 kilometers? Select the correct option
A) 1 hour and 24 minutes.	B) 1 hour and 36 minutes.	C) 2 hours and 24 minutes.	D) 2 hours and 36 minutes.	E) 5 hours.

Solution: Difference in time = time taken by passenger train- time taken by Locomo's train   850/(250*68) *100 - 850/250   850 (100/ 250*68 - 1/250)   850*32/ (250*68)   1.6 hrs or 1 hr and 36 mins   1 hour and 36 minutes. is the answer
Answer: B
At a monthly meeting, 2/3 of the attendees were males and 3/4 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time? Choose the correct option:
A) 1/3
B) 1/4
C) 3/8
D) 2/9
E) 5/18

Solution: Males who did not arrive on time are 1/4*2/3 = 1/6 of the attendees.   Females who did not arrive on time are 1/6*1/3 = 1/18 of the attendees.   The fraction of all attendees who did not arrive on time is 1/6 + 1/18 = 2/9   The answer is 2/9.
Answer: D
Four friends, Peter, John, Quincy, and Andrew, are pooling their money to buy a $1200 item. Peter has twice as much money as John. Quincy has $20 more than Peter. Andrew has 15% more than Quincy. If they put all their money together and spend the $1200, they will have $11 left. How much money does Peter have?	Options
A) $320	B) $160	C) $200	D) $410	E) $325

Solution: P= 2J ; Q= P+20 ; $320= 1.15(Q)   P+J+Q+R-1200=11   P+0.5P+P+20+1.15(P+20) = 1211   P+0.5P+P+20+1.15P+23=1211   P+0.5P+P+1.15P+43=1211   P+0.5P+P+1.15P=1168   3.65P=1168   P=320   $320nswer:$320
Answer: A
If log 27 = 1.431, then the value of log 9 is:	Choose one:  A) 0.934  B) 0.945  C) 0.954  D) 0.958  E) 0.944

Solution: Explanation:   log 27 = 1.431   =log (33 ) = 1.431   =3 log 3 = 1.431   =log 3 = 0.477   log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.   ANSWER IS 0.954
Answer: C
Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/2 of the students who took physics left school; the chemistry students did not leave, and no fresh students came in. What fraction of all students either took biology or physics?	Choices.
A) 7/12
B) 4/9
C) 5/9
D) 1/4
E) 2/3

Solution: Lets pick smart numbers. Total number of students: 12   Biology (1/2): 6   5/9hemistry (1/3): 4   Physics (1/6): 2   After leaving school   Biology: 4   5/9hemistry: 4   Physics: 1   New Total number of students: 9   Biology and Physics: 5   Answer 5/9 or 5/9
Answer: C
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Dollar 5400 interest only for the period. The principal amount borrowed by him was:  Pick.
A) $ 18000 B) $ 13000 C) $ 14000 D) $ 15000 E) $ 19000

Solution: $ 15000   $ 15000   Principal = $ 15000ollar (100 x 5400)/(12x3) = $ 15000.
Answer: D
The salary of Mr. X is 30% more than that of Mr. Y . Find what percent of Mr. Y’s salary is less than Mr. X’s?	Choose the most appropriate option
A) 23 1/2% B) 23 1/1% C) 23 1/3% D) 23 1/8% E) 23 1/9%

Solution: y=100	x=130   130---------30   100---------? => 23 1/3%   Answer: 23 1/3%
Answer: C
Find the value of √(25/16).  Choose the correct choice.
A) 5/2	B) 3/4	C) 2/3	D) 1/3	E) 5/4

Solution: √( 25 / 16)   = √ 25 / √ 16   = 5 / 4   Answer is 5/4.
Answer: E
A can do a work in 8 days. B can do the same work in 16 days. If both A & B are working together in how many days they will finish the work?  Choose one: A) 3 days B) 16/3 days C) 3/4 days D) 9/12 days E) 5/7 days

Solution: A rate = 1/8   16/3 days rate = 1/16   (A+16/3 days) rate = (1/8)+(1/16) = 3/16   A & 16/3 days finish the work in 16/3days   correct option is 16/3 days
Answer: B
Two trains are running in opposite directions with the same speed. If the length of each train is 300 m and they cross each other in 10sec, then the speed of each train is? Choose the correct choice from the following options:
A) 30  B) 108  C) 36  D) 25  E) 24

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (300 + 300)/10 => x = 30   Speed of each train = 30 m/sec.   = 30 * 18/5= 
30 * 18/5 = 108
108km/hr.   Answer: Option 108
Answer: B
From 6 positive numbers and 6 negative numbers, how many groups S of 4 numbers, yielding a positive product, can be formed? Choose the correct choice from the following.
A) 720
B) 625
C) 30
D) 960
E) 255

Solution: Potential combinations of 4 numbers that will yield positive product   ++++ 4C6   ---- 4C6   ++-- 2C6*2C6   4C6 + 4C6 + 2C6*2C6   S=15 +15 + 15*15= 
15 +15 + 15*15 = 255
255=255
Answer: E
Julie drives to her sister’s house and back. She takes the exact same route both ways. On the trip out she drives an average speed of 80 miles per hour. On the trip back she drives an average speed of 40 miles per hour. What is her approximate average speed for the round trip in miles per hour?	Choose the correct choice from the following options
A) 40 B) 48.3 C) 53.33 D) 61.7 E) 70

Solution: Average speed = total distance/total time   Here distance to Julie's sister house and back is same as she takes the same route.   D = 80T1 and D=40T2   Therefore, T1 = D/80 and T2 = D/40   T1+T2 = 3d/80   Therefore, average speed  1+ 2= 
 1+ 2 = 3
3d/80   Therefore, average speed= 2d/3d/80   =2d * 80/3d   Answer is 53.3 Since, the options are far away we need not solve till the decimal points   So correct answer is option 53.33
Answer: C
4 dices are thrown at the same time. What is the probability of getting ONLY 2 dices showing the same face? Choose the correct choice from the following:
A) 4/9
B) 5/9
C) 11/18
D) 7/9
E) none of the above

Solution: Probability of getting two same faces: 1 and 1/6   For other two faces, probabilities: 5/6 and 4/6 respectively.   The dice combinations can be arranged in 4!/2! ways   Total probability = 1*1/6*5/6*4/6*4!/2! = 5/9   Answer:5/9
Answer: B
250 hundred multiples of seven are chosen at random, and 250 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?
Choose the correct choice from the following options:
A) 25.5%
B) 26%
C) 30%
D) 25%
E) 40%

Solution: --> Multiples of 7 are 7, 14, 21, 28, 35, 42....   Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.   So approx. 50 % of the 250 multiples are odd i.e 125 multiples.   --> Similalrly, for 8 multiples are:8,16,24...   All are even so 0 % are odd.   Total odd= (125+0)/(250+250)= 125/500=1/4 = 25%   Answer 25%
Answer: D
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 27 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?  Choose the correct answer.
A) 457 km
B) 444 km
C) 547 km
D) 645 km
E) 576 km

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 27 + 21= 
27 + 21 = 48
48   T= 12   D = 48 * 12= 
48 * 12 = 576
576   Answer:576 km
Answer: E
A man sells an article at 5% loss. Had he sold it for Rs.60 more he could have gained 10%. What is the cost price of the article?  Choose the correct option.
A) Rs.200/-  B) Rs.400/-  C) Rs.450/-  D) Rs.500/-  E) Rs.550/-

Solution: Short cut method:   Loss =====> 5 %   Profit ====> 10 %   ~   ----------------   15 % ---------> Rs.60/-   100 % --------> Rs.400/-   Option Rs.400/-)
Answer: B
If N is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT Choose the correct choice from the following answers:
A) z - w = 3(y - x)
B) N is divisible by 8
C) The average of w, x, y, and z is odd
D) N is divisible by 4
E) w + x + 8 = y + z

Solution: Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.   N = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12   Focus on the easiest options first. You see that N is not divisible by 8. Answer (N is divisible by 8)
Answer: B
by combining number of small cubes, a larger cube is produced. the ratio between volume of larger cube and small cube is 1000:8 then how many small cubes are required to produce a larger cube?  Choose one.
A) 100
B) 2
C) 5
D) 125
E) 80

Solution: the ratio is a13:a23=1000:8   then number small cubes requiered is  1000/8= 
 1000/8 = 125
125   so the answre is 125
Answer: D
If 6Pr = 360 and If 6Cr = 15, find r ?	Choose the most appropriate option:
A) 5	B) 6	C) 4	D) 3	E) 2

Solution: Solution:   nPr = nCr�r!   6Pr = 15 *r!   360 =15 *r!   r! =360 /15= 
360 /15 = 24
24   r!= 4*3*2*1   => r! =4!   Therefore, r = 4.   Answer: Option 4
Answer: C
An uneducated retailer marks all its goods at 50% above the cost price and thinking that he will still make 25% profit,offers a discount of 25% on the market price.what is the actual profit on the sales?
Choose the correct choice from the following answers.
A) 14.23%
B) 56.32%
C) 54.25%
D) 63.45%
E) 12.50%

Solution: Let C.P =Rs 100.   then ,marked price =Rs100   S.P=75% of Rs 150=Rs112.50   Hence,gain%=12.50%   Ans: 12.50%
Answer: E
Area of square with side x is equal to the area of a triangle with base x . The altitude of the triangle is
Pick one.
A) x/2  B) x  C) 2x  D) 4x  E) 3x

Solution: x^2 =1/2 Ãƒâ€” x Ãƒâ€” h or h = 2x^2/x = 2x   Answer : 2x
Answer: C
The number of bacteria in a petri dish increased by 20 percent every 2 hours. If there were 72 million bacteria in the dish at 6: 00 p.m., at what time were there 50 million bacteria in the dish? Choose the most appropriate option:
A) 6: 00 p.m.
B) 8: 00 p.m.
C) 2: 00 p.m.
D) 8: 00 a.m.
E) 12: 00 p.m.

Solution: Given:   he number of bacteria in a petri dish increased by 20 percent every 2 hours   There were 72 million bacteria in the dish at 6: 00 p.m   Since the bacteria is increasing by 20% every 2 hours, this means that the number is multiplied by 1.2 every 2 hours.   Required: At what time were there 50 million bacteria in the dish?   Assume that there were n intervals of 2 hours between 50 million and 72 million.   50 * (1.2)^n = 72   (12/10)^n = 72/50 = 144/100 = (12/10)^2   Hence n = 2 intervals.   Each interval was of 2 hours. Therefore, the number of hours = 4   Subtracting 4 hours from 6 PM, we get 2 PM as the answer.   Option 2: 00 p.m.
Answer: C
10 books are placed at random in a shelf. The probability that a pair of books will always be together is?  Choose the correct choice:
A) 1/6 B) 1/7 C) 1/5 D) 1/9 E) 1/2

Solution: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!   Required probability = 1/5   Answer:1/5
Answer: C