MU-NLPC/Calc-aqua_rat huggingface dataset:
A teacher gave the same test to three history classes: M, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?  Choose the correct choice from the following answers:
A) 74  B) 75  C) 76  D) 77  E) 78

Solution: Ans : B (75)   lets say class M indeed has 4 children, B has 6 children and C has 5 children.   now, if the average of class M is 65, hence total marks awarded in the class = 65*4= 
65*4 = 260
260   Similarly,   class B= 80*6= 
80*6 = 480
480   class C= 77*5= 
77*5 = 385
385   total marks provided= M+B+C = 260+480+385= 
260+480+385 = 1_125
1125   avg. marks= 1125 / 15 (total no. of students) = 75=75
Answer: B
The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?  Choose the correct answer.
A) 16 2/9% B) 16 2/4% C) 16 2/3% D) 16 2/1% E) 16 2/6%

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 seamstress sells 200 metres of ribbon for Rs. 10000 at a loss of Rs. 7 per metre. Find her cost price for one metre of ribbon?
Choose the correct option.
A) 20	B) 43	C) 26	D) 34	E) 57

Solution: SP per metre = 10000/200 = Rs. 50 Loss per metre = Rs. 5 CP per metre = 50 + 7= Rs. 57Answer:57
Answer: E
X and Y are both integers. If X/Y = 57.40, then what is the sum of all the possible two digit remainders of X/Y? Choose the correct choice from the following.
A) 560	B) 616	C) 450	D) 900	E) 1024

Solution: Remainder = 0.40 --> 40/100 --> Can be written as (40/4) / (100/4) = 10/25   So remainders can be 10, 20, 30, 40, ..... 90.   We need the sum of only 2 digit remainders --> 10 + 20 + 30 + 40 + 50 + 60 + 70+ 80 + 90 =450   Answer: 450--  10 + 20 + 30 + 40 + 50 + 60 + 70+ 80 + 90= 
--  10 + 20 + 30 + 40 + 50 + 60 + 70+ 80 + 90 = 450
450   Answer: 450
Answer: C
In the xy plane line m has the equation 4x + y = w. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
Answers:
A) -4/3
B) 1/4
C) -4
D) 3/4
E) 4/3

Solution: The equation of line m is y=-4x+w. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.   Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r( +1)= 
( +1) = 1
1/4*r --> r=-4/3.   -4/3nswer: -4/3.
Answer: A
If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?  Choose the correct option
A) 2888
B) 1000
C) 2878
D) 27878
E) 2112

Solution: 6 * 5 * 4 = 60/100 * 50/100 * 40/100 * x   1 = 1/10 * 1/10 * 1/10 * x => x = 1000   Answer:1000
Answer: B
By selling a book for 300, 20% profit was earned. What is the cost price of the book?	Choose the correct answer
A) A)215	B) B)250	C) C)230	D) D)235	E) E)240

Solution: SP = 120% of CP; :. CP = 300 × 100/120 = 250   Option '250'
Answer: B
How many of the following numbers are divisible by 21 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
Choose the correct choice from the following answers:
A) 3
B) 4
C) 5
D) 1
E) 7

Solution: By using your calculator you can calculate that the following numbers are divisible by 21 : 462   Required number of number = 1.   1
Answer: D
Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6069, how much amount did Raghu invest ?
Choose the correct answer.
A) 1287	B) 2887	C) 2100	D) 1129	E) 1192

Solution: Let money invested by Raghu = Rs. x   Money invested by Trishul = 9/10= 
9/10 = 9/10 = around 0.9
0.9x   Money invested by Vishal= 9/10x * 110/100 = 0.99x   Also, x+0.9x+0.99x 9/10  * 110/100= 
9/10  * 110/100 = 99/100 = around 0.99
0.99x   Also, x+0.9x+0.99x= 6069   = x= 6069/2.89= 
6069/2.89 = 2_100
2100   Therefore, amount invested by Raghu is Rs. 2100.   Answer: 2100
Answer: C
If xy=4, x/y=16, for positive numbers x and y, y=?
Pick one:
A) 1/2
B) 2
C) 1/3
D) 3
E) 1/6

Solution: Very easy question. 2 variables and 2 easy equations.   xy=4 ---> x=4/y - (i)   x/y=16 ---> replacing (i) here ---> 4/(y^2)=16 ---> y^2=4/16=1/4 ---> y=1/2 or -1/2   The question states that x and y are positive integers. Therefore, y=1/2 is the answer.   1/2nswer 1/2.
Answer: A
A theater box office sold an average (arithmetic mean) of 63 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 78, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?  Choose the correct choice from the following choices
A) 2:3  B) 1:4  C) 1:5  D) 6:11  E) 4:7

Solution: Deviation from the mean for the daytime staff = 78 - 63= 
78 - 63 = 15
15.   Deviation from the mean for the evening staff= 63 - 60= 
63 - 60 = 3
3.   Thus, the ratio of the number of daytime staff members to the number of evening staff members is 3:15= 1:5.   The answer is 1:5.
Answer: C
A boy has 9 trousers and 9 shirts. In how many different ways can he select a trouser and a shirt? Choose one.
A) 100 B) 81 C) 104 D) 94 E) 110

Solution: The boy can select one trouser in nine ways.   The boy can select one shirt in 12 ways.   The number of ways in which he can select one trouser and one shirt is   9 * 9= 
  9 * 9 = 81
81 ways.   81
Answer: B
When a jogger moves at an average speed of 6 kmph, they reach their destination on time. When their average speed becomes 4 kmph, they reach their destination 15 minutes late. Find the length of journey.
Choose the correct choice from the following answers
A) 3 km B) 5 km C) 7 km D) 6 km E) None

Solution: Sol.   Difference between timings = 15 min = 1/4 hr.   Let the length of journey be x km.   Then, x/4 - x/6 = 1/4   â‡” 3x - 2x = 3   â‡” x = 3 km.   3 kmnswer 3 km
Answer: A
The average of 100,200,300 and x is 250 and the average of 300,150,100,x and y is 200. What is the value of y?
Select the correct option:
A) 100
B) 150
C) 50
D) 200
E) 250

Solution: We have : (100+200+300+x) /4 = 250   600+x = 1000   x = 400   (300+150+100+x+y)/5 = 200   550+400+y = 1000   y = 50   Answer is 50
Answer: C
An express traveled at an average speed of 200 km/hr, stopping for 3 min after every 125 kn. How long did it take to reach its destination 800 km from the starting point? Options.
A) 5 hrs 21 min B) 4 hrs 18 min C) 6 hrs 41 min D) 6 hrs 21 min E) 4 hrs 34 min

Solution: B   4 hrs 18 min   Time taken to cover 800 km = 800/200= 
800/200 = 4
4 hrs.   Number of stoppages= 800/125 - 1 = 6   Total time of stoppages = 3 * 6= 
3 * 6 = 18
18 min   Hence, total time taken= 4 hrs 18 min.
Answer: B
A rower whose speed is 6 km/hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 3 km/hr. What is the rower's average speed (in km/hr) for the total journey? Choose the correct answer:
A) 3.9 B) 4.2 C) 4.5 D) 4.8 E) 5.1

Solution: time upstream = d / 3   time downstream = d / 9   total time = d/3 + d/9 = 4d/9   average speed = 2d / (4d/9) = 4.5 km/hr   The answer is 4.5.2  / (4 /9)= 
2  / (4 /9) = 9/2 = around 4.5
4.5 km/hr   The answer is 4.5.
Answer: C
How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5 and 6 such that the numbers are divisible by 9?  Choose the correct choice from the following answers
A) 1  B) 2  C) 4  D) 6  E) 8

Solution: CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9   Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition   If sum of Digits = 9, No. =36, 45, 54, 63 --- 4 4ases   Answer: option 4
Answer: C
In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole? Options
A) 17 sec
B) 14 sec
C) 78 sec
D) 10 sec
E) 12 sec

Solution: Convert kmph to mps. 36 kmph = 36 * 5/18= 
36 * 5/18 = 10
10 mps.   The distance to be covered is equal to the length of the train.   Required time t= d/s = 100/10= 
100/10 = 10
10 sec.   Answer:10 sec:
Answer: D
A certain team consists of 4 professors and 6 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.) Choose the correct choice
A) 48
B) 100
C) 120
D) 288
E) 600

Solution: The groups can be formed as   PTT + PPT + PPP where P=professor and T=Teaching assistant   Number of different teams of 3 can be formed in which at least one member of the group is a professor   = 4C1* 6C2 + 4C2*6C1 + 4C3   = 4!/3! * 6*5/2 + 4*3/2 * 6 + 4   =60 +36 + 4   4 /3  * 6*5/2 + 4*3/2 * 6 + 4= 
4 /3  * 6*5/2 + 4*3/2 * 6 + 4 = 60
60 +36 + 4= 
60 +36 + 4 = 100
100   Answer 100
Answer: B
What is the probability that the sum of two dice will yield a 7, and then when both are thrown again, their sum will again yield a 7? assume that each die has 6 sides with faces numbered 1 to 6.
Choose the correct answer:
A) 1/144
B) 1/36
C) 1/12
D) 1/6
E) 1/3

Solution: In order to get the sum of the two dices to be 7, there are six combinations that satisfy this requirement.   1+6= 
1+6 = 7
7   2+5= 
2+5 = 7
7   3+4= 
3+4 = 7
7   4+3= 
4+3 = 7
7   5+2= 
5+2 = 7
7   6+1= 
6+1 = 7
7   Each combination has 1/36 of probability of occurrence, or in total 6/36 for the six combinations, which is 1/6.   In order to get the probability of this occurring twice in a row we multiply 1/6 *1/6 and we get 1/36.   The answer is 1/36.
Answer: B
In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 27 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?	Choose the correct option:
A) 12
B) 18
C) 24
D) 30
E) 36

Solution: 200 are sophomores.   The number of freshmen is 600 - 160 - 0.27(800) = 224   The answer is 24.
Answer: C
If x and y are nonnegative integers, both less than or equal to 2, then we say that (x; y) is a
friendly point. Compute the number of unordered triples of friendly points that form triangles
with positive area.	Choose the correct choice from the following choices
A) 32  B) 45  C) 67  D) 76  E) 82

Solution: There are   (9   3)= 84 unordered triples of friendly points. Instead of trying to count   the triples that yield triangles with positive area, we count the ones which have zero area. These   form line segments, of which there are 8 (three vertical, three horizontal, two diagonal), giving   us 76 desired unordered triples.   correct answer 76
Answer: D
If 15% of 30% of 50% of a number is 99, then what is the number?
Choose the correct choice from the following choices:
A) 4000	B) 3050	C) 4400	D) 4500	E) None of these

Solution: Let the number be a   Given, 15/100 * 30/100 * 50/100 * a = 99   => 3/20 * 3/10 * 1/2 * a = 99   => a = 10 * 20 * 10 * 2 = 4400.   ANSWER:4400
Answer: C
The ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8. If there are 52 black cars in the lot, how many red cars are there in the lot?
Choose one.
A) 11 B) 20 C) 24 D) 27 E) 32

Solution: 20 is correct   R/20 = 3/8 and 20 =52   R = 52*3/8 = 20
Answer: B
The original price of a suit is $200. The price increased 20%, and after this increase, the store published a 20% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 20% off the increased price, how much did these consumers pay for the suit?	Select.
A) $192  B) $198  C) $200  D) $208  E) $216

Solution: 0.8*(1.2*200)= 
0.8*(1.2*200) = 192
$192   The answer is $192.
Answer: A
Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?  Select
A) 19%	B) 68%	C) 18%	D) 48%	E) 64%

Solution: Total CP = Rs. 42000 + Rs. 13000   = Rs. 55000 and SP = Rs. 64900   Profit(%) = (64900 - 55000)/55000 * 100= 
(64900 - 55000)/55000 * 100 = 18
18%   Answer:18%
Answer: C
Look at this series: 52, 49, 54, 51, 56, 53, ... What number should come next?  Choose the correct choice from the following
A) 58 B) 60 C) 52 D) 50 E) 62

Solution: Explanation:   In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.   58nswer: Option 58
Answer: A
A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?  Options: A) Rs. 64 B) Rs. 69 C) Rs.72 D) Rs.75 E) Rs.90

Solution: C.P. = Rs. (100/122.5)x392   = Rs. (1000/1225)x392   = Rs. 320   Profit = Rs. (392 - 320) = Rs. 72.   Answer:Rs.72
Answer: C
A clock is started at noon. By 10 minutes past 5, the hour hand has turned through Choose the correct option:  A) 145 d  B) 150 d  C) 160 d  D) 155 d  E) 165 d

Solution: Angle traced by hour hand in 12 hrs = 360Âº.   5 hrs 10min = 31/6hrs = (360/12*31/6)= 
(360/12*31/6) = 155
155   ANSWER 155 d
Answer: D
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 56, the dividend is:
Select.
A) 5324
B) 6334
C) 7896
D) 8356
E) 8400

Solution: Divisor = (5 * 56)= 
(5 * 56) = 280
280= 10 * Quotient = Divisor   => Quotient = 280/10= 
280/10 = 28
28   Dividend= (Divisor * Quotient) + Remainder   Dividend = (280 * 28) + 56= 
(280 * 28) + 56 = 7_896
7896.   7896
Answer: C
When n is divided by 5 the remainder is 3. What is the remainder when (n + 1)^2 is divided by 5?	Choose the correct choice from the following options:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: n = 5x+3, for some integer x   (n+1)^2=(5x+4)^2=5y+16, for some integer y   When we divide this by 5, the remainder is 1.   The answer is 1.
Answer: B
Coins are to be put into 8 pockets so that each pocket contains at least one coin. At most 4 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?	Select the correct option:
A) 7
B) 18
C) 17
D) 22
E) 28

Solution: Since at most 3 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;   Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);   Total:   1+1+1+1+2+3+4+5= 
  1+1+1+1+2+3+4+5 = 18
18   Answer: 18
Answer: B
What is the greatest prime factor of 1+2+3+。。。+52?	Pick.
A) 53  B) 29  C) 31  D) 37  E) 41

Solution: find the sum from direct formula = n(n+1)/2 = 52(52+1)/2 = 26*53...   53 is a PRIME number, so ans is 53..   53 is the answer
Answer: A
The ratio, by volume, of soap to alcohol to water in a certain solution is 4:20:60. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?
Select.
A) 1200	B) 1250	C) 1300	D) 1400	E) 1450

Solution: soap:alcohol   Initial ratio soap:alcohol: water --> 4:20:60   Initial soap:alcohol = 4/20 =4:20   after doubled soap:alcohol =2* 4/20 = 8:20   Initial soap:water = 4/60=4:60   after halved soap:water: 1/2 * 4/60 = 2/60 = 2:60   After soap: alcohol:water --> 8:20:240-->2:5:60   given alcohol 100 cubic centimeter.   ratio is 40:100:1200(2:5:60)   For 100 cubic centimeter of 1200lcohol --- 1200cubic cm water is required.
Answer: A
The food in a camp lasts for 10 men for 50 days. If 10 more men join, how many days will the food last?  Choose the correct choice from the following choices
A) 22 days	B) 25 days	C) 50 days	D) 16 days	E) 17 days

Solution: one man can consume the same food in 10*50= 
10*50 = 500
500 days.   10 more men join, the total number of men= 20   The number of days the food will last = 500/20= 
500/20 = 25
25 days.   Answer:25 days
Answer: B
if x+y+z=9 and both y and z are positive integers greater than zero, then the maximum value x can take is?  Choose the correct choice from the following answers.
A) 7	B) 3	C) 8	D) 6	E) data insufficient

Solution: if y=z=1, then x will be equal to 7.   7NSWER:7
Answer: A
In a class there are 20 boys and 22 girls. In how many ways can a boy and a girl be selected?
Select the correct option
A) 508	B) 440	C) 800	D) 570	E) 503

Solution: We can select one boy from 20 boys in 20 ways.   We select one girl from 22 girls in 22 ways   We select a boy and girl in 20 * 22 ways i.e., = 440 ways.   Answer:440
Answer: B
In a dairy farm, 30 cows eat 30 bags of husk in 30 days. In how many days one cow will eat one bag of husk? Pick
A) 1
B) 40
C) 20
D) 26
E) 30

Solution: 30xplanation :   One bag of husk = 30 cows per day   ⇒ 30 × 1 × 30 = 1 × 30 × x   For one cow = 30 days   Answer : 30
Answer: E
The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10, then their difference is	Select the correct option:
A) 10
B) 46
C) 70
D) 90
E) None

Solution: Solution   Let the numbers be x and (100 - x) .   Then, x (100 - x) = 5 ×495   ‹=›x2 - 100x + 2475 = 0.   ‹=› (x -55) (x - 45) = 0.   x = 55 or x = 45.   Therefore, the numbers are 45 and 55.   Required difference = (55 - 45)= 
(55 - 45) = 10
10.   10nswer 10
Answer: A
If -2<= x <= 2 and 3 <= y <= 10, which of the following represents the range of all possible values of y-x? Options:
A) 5 <= y-x <= 6
B) 1 <= y-x <= 12
C) 1 <= y-x <= 6
D) 5 <= y-x <= 10
E) 1 <= y-x <= 10

Solution: Maximum value of y-x= 10 - (-2)= 
10 - (-2) = 12
12   Minimum value of y-x= 3-2= 
3-2 = 1
1   1 <= y-x <= 12 mentions the correct range
Answer: B
5 friends visited a fruit stall, and everyone decided to contribute equally to the total bill of $100. If one of the friends had a coupon for 6% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
Select the correct option.
A) 18 B) 18.8 C) 19 D) 17.8 E) 17.9

Solution: At the non-discounted price, each friend would pay $20, as $100 divided by 5 friends is $20 per friend. But if the bill is 6% off, then each friend would pay 6% less. 6% of $20 is $1.2, so each friend saves $1.2 and pays the remaining 18.8   CORRECT OPTION:OPTION 18.8
Answer: B
Dan can do a job alone in 15 hours. Annie, working alone, can do the same job in just 10 hours. If Dan works alone for 12 hours and then stops, how many hours will it take Annie, working alone, to complete the job?	Choose the correct choice from the following choices
A) 2
B) 4
C) 6
D) 8
E) 10

Solution: Dan can complete 1/15 of the job per hour.   In 12 hours, Dan completes 12(1/15) = 4/5 of the job.   Annie can complete 1/10 of the job per hour.   To complete the job, Annie will take 1/5 / 1/10 = 2 hours.   The answer is 2.
Answer: A
A positive number x is multiplied by 3, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?  Choose one: A) 9/4 B) 3/2 C) 4/3 D) 2/3 E) 1/2

Solution: We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:   2x/3   Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us   √(2x/3) = x   2x/3 = x^2   2x = 3x^2   3x^2 – 2x = 0   x(3x – 2) = 0   x = 0 or   3x – 2 = 0   3x = 2   x =4/3   Because x is positive, x = 4/3. The answer is 4/3.
Answer: C
How many zeros does 10! end with? Options:  A) 10  B) 4  C) 4  D) 3  E) 2

Solution: According to above 10! has 10/5= 
10/5 = 2
2=2 trailing zeros.   Answer: 2
Answer: E
Find the average of the series : 312, 162, 132, 142 and 122?
Select the correct option.
A) 299 B) 268 C) 276 D) 299 E) 174

Solution: Average   = (312 + 162 + 132 + 142 + 122)/5   = 870/5= 
870/5 = 174
174   Answer: 174
Answer: E
If the sum of 1/3 and 1/5 is converted to a decimal, what is the 3000th digit to the right of the decimal place?
Choose the correct choice from the following answers:
A) 2  B) 3  C) 5  D) 8  E) 9

Solution: 1/3 +1/5 =0.5333333...   hence, the 3000th digit would also be 3   Ans: 3
Answer: B
On the xy-plane, each point on circle C has coordinates such
that x 0 and y 0. If the center of circle C is the point (3; 7),
what is the maximum possible area of C?  Choose the correct choice:
A) 6  B) 9  C) 24  D) 32  E) 64

Solution: I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.   With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.   If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26   Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26   As it's written, none of the answers is clearly the correct one.   24
Answer: C
what is the sum of all even integers between 99 and 301?	Select:
A) 20200
B) 20000
C) 40400
D) 40000
E) 44000

Solution: a=100,tn=300   a+(n-1)d=300=>n=101   Sn=n/2(a+l)=101/2(100+300)   Sn=20200   20200NSWER:20200
Answer: A
The C.I. on a certain sum for 2 years at 10% per annum is Rs. 525. The S.I. on the same sum for double the time at half the rate percent per annum is? Select
A) 238
B) 500
C) 287
D) 197
E) 172

Solution: Explanation:   Let the sum be Rs. P. Then,   [P(1 + 10/100)2 - p] = 525   P[(11/10)2 - 1] = 525   P = (525 * 100) / 21= 
(525 * 100) / 21 = 2_500
2500   Sum= Rs. 2500   So, S.I. = (2500 * 5 * 4)/100 = Rs. 500   Answer:500
Answer: B
Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^3  Pick one.
A) 26
B) 22
C) 25
D) 30
E) 29

Solution: (4)^11x (7)^5 x (11)^3   = (2 x 2)^11 x (7)^5 x (11)^3   = 2^11 x 2^11 x7^5x 11^3   = 2^22 x 7^5 x11^3   Total number of prime factors = (22 + 5 + 3)= 
(22 + 5 + 3) = 30
30.   Answer is 30.
Answer: D
How many odd numbers are possible between 1 to 100000? find out the number of odd number of digits? Choices.
A) 2999	B) 3500	C) 4000	D) 4599	E) 49999

Solution: There are always one odd and one even no. And the question is odd no. Between 1 to 100000   So we have to find no. Between 1 to 100000 so we should not includes 1   100000/2 -1= 
100000/2 -1 = 49_999
49999   ANSW49999R:49999
Answer: E
On a scale of map, 0.4 cm represents 5.3 km. If the distance between the points on the map is 64 cm, the actual distance between these points is: Pick
A) 9 km
B) 72.5 km
C) 190.75 km
D) 848 km
E) None of these

Solution: Explanation :   Let the actual distance be x km. Then,   More distance on the map, More is the actual distance (848 kmirect Proportion)   => 0.4 : 64 :: 5.3 : x   => 0.4x = 64 x 5.3   => x = 64 x 5.3 /0.4   => x = 848   Answer : 848 km
Answer: D
If three sides of the triangle are 8 , 15 and S respectively then the how many values can S ? Choose one:  A) [A] 6  B) [B] 7  C) [C] 8  D) [D]9  E) [E] infinite number of values

Solution: Needed: How many Values can S take   Concept: Sum of any two sides of a triangle is greater then the third side.   Case 1: 8+5 > S => S<13   Case 2: 5+S > 8 => S >3   Case 3: 8+S > 5 =>S > -3 (Always true since S is one side of a Triangle)   Finally, 3 < S < 13. So, we can have infinite number of sides between 3 and 13.   Answer = E   PS: If question said S can take only integer value, the S = 9. Answer choice [D]9.
Answer: D