MU-NLPC/Calc-aqua_rat huggingface dataset:
Mangala completes a piece of work in 30 days, Raju completes the same work in 70 days. If both of them work together, then the number of days required to complete the work is Select
A) 4 days B) 21 days C) 8 days D) 10 days E) 11 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 30 × 70/100 = 21 days.   Answer : 21 days
Answer: B
Seats for Maths, Physics and Biology are in the ratio of 6 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?	Answers
A) 12 : 15 : 20
B) 6 : 7 : 8
C) 6 : 8 : 9
D) Cannot be determined
E) None of these

Solution: Reqd ratio 6 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100   = 6 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 12 : 15 : 20   12 : 15 : 20nswer 12 : 15 : 20
Answer: A
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:  Choose the correct choice from the following choices
A) 20 B) 80 C) 100 D) 200 E) None

Solution: EXPLANATION   Let the number of students in rooms A and B be x and y respectively.   Then, x – 10 = y + 10 x – y = 20 …. (i)   and x + 20 = 2(y – 20) x – 2y = -60 …. (ii)   Solving (i) and (ii) we get: x = 100 , y = 80.   The required answer A = 100.   Answer 100
Answer: C
If the probability that the Cleveland Browns win the Super Bowl is 1/100 and the probability that the Cleveland Indians win the World Series is 1/10, what is the probability that either the Browns win the Super Bowl or the Indians win the World Series (but not both)?	Choose the most appropriate option.
A) 9/50 B) 17/100 C) 27/250 D) 53/500 E) 101/1000

Solution: 99/100*1/10 + 1/100*9/10 = 108/1000 = 27/250   The answer is 27/250.
Answer: C
In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.	Choices
A) 10	B) 12	C) 16	D) 17	E) 18

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 24   => 2x = 24 => x = 12   12
Answer: B
Calculate how much time could be saved if the train would run at its usual speed, given that it ran at 5/7 of its own speed and got to its destination in 15 hours?	Choose the most appropriate option.
A) 1.29 hrs B) 2.29 hrs C) 4.29 hrs D) 5.29 hrs E) 3.29 hrs

Solution: New speed = 5/7 of usual speed   New time = 5/7 of usual time   5/7 of usual time = 15 hrs   Usual time = 15*5/7 = 10.71 hrs   Time saved = 15-10.71= 
15-10.71 = 4.29
4.29 hrs   Answer is 4.29 hrs
Answer: C
Find the average of all the numbers between 6 and 34 which are divisible by 5 Choose the correct choice.
A) 18
B) 20
C) 24
D) 30
E) 32

Solution: Multiples of 5 between 6 and 34 are 10,15,20,25,30   Average = (10+15+20+25+30)/5   =5(10+30)/2*5   =40/2= 
40/2 = 20
20   ANSWER:20
Answer: B
What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
Choose the correct choice from the following:
A) 1000 B) 2300 C) 3000 D) 4000 E) 4500

Solution: A.P.=(200X12900)/[4(200+5X3)]=3000 Ans   Alternative   100+105+110+115=12900   430=12900   100=12900/(430)X100=3000   3000
Answer: C
A gardener increased the length of a rectangle-shaped garden by 25 percent and decreased its width by 10 percent. The area of the new garden	Options.
A) has increased by 15 percent
B) has increased by 12.5 percent
C) has increased by 7.5 percent
D) is exactly the same as the old area
E) cannot be expressed in percentage terms without actual numbers

Solution: Let L be the original length and let W be the original width.   The original area was L*W.   The new area is 0.9W*1.25L = (0.9)(1.25)L*W = 1.125*L*W   The answer is has increased by 12.5 percent.
Answer: B
An employer pays 3 workers P, Q and R a total of $610 a week. p is paid 125% of the amount Q is paid and 80% of the amount R is paid. How much does P earn in a week?
Choose the correct choice from the following choices:
A) $150
B) $175
C) $180
D) $195
E) $200

Solution: Soln:-   p+q+r = 610   given p=1.25q and p=.80r   putting these values in the above equation we get p=$200   ANSW$200R:$200
Answer: E
√289 - √625 ÷ √25 is equal to ?
Pick one:
A) 17	B) 15	C) 12	D) -8/5	E) None

Solution: Answer   √289 - √625 ÷ √25   = √17 x 17 - √25 x 25 ÷ √5 x 5   = 17 - 25 ÷ 5 = 17 - 5= 
17 - 5 = 12
12   12orrect Option: 12
Answer: C
IF THE PROBABILITY is 0.6 that an “unfair” coin will turn up tails on any given toss. If the coin is tossed 3 times, what is the probability that at least one of the tosses will turn up tails?
Options:
A) 0.064
B) 0.36
C) 0.64
D) 0.784
E) 0.936

Solution: probability that at least one of the tosses will turn up tails = 1 - probability that all will be heads   = 1 - (0.4*0.4*0.4)   = 1 - 0.064= 
1 - 0.064 = 0.936
0.936 0.936
Answer: E
A train covers a distance of 12 km in 10 minutes. If it takes 5 seconds to pass a telegraph post, then the length of the train is  Choices.
A) 110m  B) 120m  C) 140m  D) 160m  E) 100cm

Solution: Explanation:   Speed =12/10x 60 km/hr = 72 x5/18m/sec = 20 m/sec.   Length of the train = (Speed x Time) = (20 x 5) m = 100 m   Answer: Option 100cm
Answer: E
If M:N = 3:5 and N:O = 5:8 then M:N:O is Choices.
A) 6:7:8	B) 2:7:8	C) 3:7:9	D) 4:7:8	E) 3:7:8

Solution: Solution:   M/N = 3/5;   N/O = 5/8;   M:N:O = 3*5:5*5:5*8 = 15:35:40 = 3:7:8   Answer: Option 3:7:8
Answer: E
Last year, the price of a vacation package was P. At the beginning of this year, the price went up 60%. Lucas used a travel voucher to purchase the vacation package at 25% off this year’s price. In terms of P, how much did Lucas pay?
Choices
A) P + 10  B) 1.1*P  C) 0.02*P  D) 0.20*P  E) 1.20*P

Solution: Last year price = P;   This year price = 1.6P;   Lucas used a travel voucher to purchase the vacation package at30%offthis year’s price, thus he paid   (1 - 0.25)*1.6= 
  (1 - 0.25)*1.6 = 1.2
1.20P.   Answer: 1.20*P.
Answer: E
At what price must an article costing Rs.47.50 be marked in order that after deducting 8% from the list price. It may be sold at a profit of 25% on the cost price? Choose the correct choice from the following:
A) 64.54
B) 62.6
C) 62.1
D) 62.7
E) 62.2

Solution: CP = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(92/100)= 59.375   MP = 64.54   64.54nswer: 64.54
Answer: A
Ten boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?  Pick one.
A) A)10^30	B) B)2^30	C) C)1^30	D) D)3^30	E) E)6^30

Solution: Each Mango can be given to any one of the Ten people or in other words..1 mango can be divided into 10 ways...so all 30 can be divided in 10^30 ways   10^30NS:10^30
Answer: A
Solve for x the equation log9(x3) = log2(8)  Choose the most appropriate option
A) 9
B) 8
C) 7
D) 6
E) 5

Solution: log9(x3) = log2(8) : given   log2(23) = 3 : simplify right hand side of given equation.   log9(x3) = 3 : rewrite the above equation   log9(x3) = log9(93) : rewite 3 as a log base 9.   x3 = 93 : obtain algebraic equation from eqaution D.   x = 9 : solve above for x   correct answer 9
Answer: A
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is: Answers:
A) 4830
B) 5120
C) 6420
D) 8960
E) None

Solution: EXPLANATION   Clearly, l = (48 – 16)m = 32 m,   b = (36 -16)= 
(36 -16) = 20
20 m,   h= 8 m.   Volume of the box = (32 x 20 x 8) m3 = 5120 m3.   Answer 5120
Answer: B
A sequence contains an alternation of positive and negative numbers. The sequence contains x numbers, and begins with a positive number. How many positive numbers are in it If x is an odd number?
Choose the most appropriate option:  A) (x+1)/2  B) x/3  C) x/(2-1)  D) x/(2+1)  E) (x-1)/2

Solution: Lets put values for x, say x=7 since it's odd   and first number is neg so sequence will be {pos,neg,pos,neg,pos,neg,pos} we can see that it has 4 positive terms   so putting x=7 in the options,   option (x+1)/2 = (x+1)/2 => (7+1)/2= 
(7+1)/2 = 4
4 , the number of positive integers   So, (x+1)/2 is the answer
Answer: A
The average length of 6 ropes is 80 cm. If the average length of one third of the ropes measure to 70 cm, what is the average of the other ropes?	Choices.
A) 75. B) 85. C) 90. D) 94. E) 100.

Solution: Edit:   Given ( X1 + X2 ... + X6 ) / 6 = 80   ( X1 + X2 ... + X6 ) = 480 --> Eq 1.   Now given avg length of one third ropes is 70. That means out  6 / 3= 
 6 / 3 = 2
2 ropes.   let the avg length of two ropes be ( X1 + X2 ) / 2= 70 .   ( X1 + X2 ) = 140. --> eq 2.   Now we are asked to find the average of the remaining i.e. ( X3 + X4 + X5 + X6 )   Substitute eq 2 in eq 1 then we get   140 + X3 + X4 + X5 + X6 = 480   => X3 + X4 + X5 + X6 = 340   Now divide 340 by 4 we get 85.   => ( X3 + X4 + X5 + X6) / 4 = 85 = avg length of remaining ropes.   IMO correct option is 85..
Answer: B
If x and y are even integers, which of the following is an odd integer? Choose the correct choice from the following choices:
A) xy + 2
B) x(y − 1)
C) x(x + 5)
D) 3x + 4y
E) (x + 3)(y − 1)

Solution: If x and y are even integers, then:   A. xy + 2: even + even = even   B. x(y − 1): even(odd) = even   C. x(x + 5): even(odd) = even   D. 3x + 4y: even + even = even   E. (x + 3)(y − 1): (odd)(odd) = odd.   Answer is (x + 3)(y − 1).
Answer: E
If the complement of a certain angle is five times the measure of that certain angle, then what is the measure of that certain angle? Answers.
A) 45°  B) 30°  C) 22.5°  D) 18°  E) 15°

Solution: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.   The original angle is x, so the complement is 5x, and together, these add up to 90 degrees.   x + 5x = 90   6x = 90   x = 15°   Answer = (15°)
Answer: E
Of the three numbers, the first is twice as second and three times the third. The average of the three numbers is 55, and the three numbers in order are?
Choose the correct choice from the following:
A) 116,58,36
B) 90,45,30
C) 126,63,36
D) 108,54,36
E) None of these

Solution: Explanation :   Solution: Let A =x,   B =x/2, C = x/3.   =x + x/2 + x/3 / 3 = 55   By solving we will get x = 90.   Hence A= 90   90,45,30= 90/2= 
90/2 = 45
45   C= 90/3= 
90/3 = 30
30   Answer : 90,45,30
Answer: B
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Choose one: A) 4 B) 8 C) 6 D) 2 E) 10

Solution: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50   5x = 20   x = 4.   So Age of the youngest child = x = 4 years.   4NSWER 4
Answer: A
In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?	Select the correct option:	A) 76	B) 42	C) 78	D) 26	E) 92

Solution: 5x 6x 2x   50 25 100   250x + 150x + 200x = 4200   600x = 4200   x = 7 => 6x = 42   Answer: 42
Answer: B
A group of 8 employees book a full row at a movie theater. There are 2 best buddies and a couple and the 2 people in both those cases must always sit together. in how many arrangements can the students sit?
Choose the correct choice from the following options:	A) A.1296	B) B.2880	C) C.1850	D) D.3546	E) E.4200

Solution: If we Glue the best buddy and couple together: {AB}, {CD}.   6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each couple within their unit can be arranged in 2! ways.   Therefore the final answer is 6!*2!*2!=2,880.   Answer: B.2880.
Answer: B
In seventeen given numbers, the average of first 9 numbers is 4 and that of the last 9 numbers is also 4. If the average of these 17 numbers is 3, the 9th number is Choose one.
A) 23  B) 4  C) 17  D) 21  E) 28

Solution: Explanation :   9th number = (9*4 + 9*4 - 17*3)= 
(9*4 + 9*4 - 17*3) = 21
21.   Answer : 21
Answer: D
A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?	Choose the most appropriate option:
A) 2888  B) 2778  C) 2500  D) 2818  E) 2871

Solution: A:B:2500 = 2/3:1/6:1/6 = 4:1:1   x * 2/100 * 2/3 = 200   B capital = 15000*1/6= 
15000*1/6 = 2_500
2500.Answer2500
Answer: C
The average of 6 no.'s is 3.95. The average of 2of them is 4.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? Choose the most appropriate option:
A) 4.2
B) 4.4
C) 3.6
D) 5.6
E) 5.7

Solution: Sum of the remaining two numbers = (3.95 * 6) - [(4.4 * 2) + (3.85 * 2)]   = 7.20.   Required average = (7.2 / 2) = 3.6.   3.6
Answer: C
A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.20,000 earned at the end of 2years from the startingof the business? Pick:
A) s. 5,000
B) s. 5,500
C) s. 5,700
D) s. 6,000
E) s. 7,500

Solution: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.   B's share = Rs. 20000 x	3/10	= Rs. 6,000.   s. 6,000
Answer: D
Diesel costs Rs.4 per lit and petrol costs 7.23 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol. Choose the most appropriate option:
A) 9 months	B) 5 months	C) 7 months	D) 3 months	E) 2 months

Solution: Explanation :   =>In the First Month the price of the diesel would be 4*110/100= 
4*110/100 = 22/5 = around 4.4
4.4=>In the Second Month the price of the diesel would be 4.4*110/100= 
4.4*110/100 = 4.84
4.84=>In the Third Month the price of the diesel would be 4.84*110/100= 
4.84*110/100 = 5.324
5.324=>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85   =>In the fifth Month the price of the diesel would be 5.85*110/100 = 6.44   =>In the sixth Month the price of the diesel would be 6.44*110/100 = 7.08   =>In the seventh Month the price of the diesel would be 7.08*110/100 = 7.79 which is higher than the price of petrol   Answer : 7 months
Answer: C
The ratio, by volume, of bleach to detergent to water in a certain solution is 2 : 25 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain? Choose the correct choice from the following answers:
A) 40  B) 45  C) 50  D) 75/2  E) 35

Solution: B:75/2:W = 2:25:100   Bnew / 75/2new = (1/3)*(2/25) = (2/75)   75/2new / Wnew = (1/2)*(25/100) = (1/8)   Wnew = 300   75/2new = Wnew/5 = 300/8 =75/2   So, answer will be 75/2
Answer: D
In digging a pond 20 m * 12 m * 5 m the volumes of the soil extracted will be? Pick one:
A) 3387  B) 1000  C) 1200  D) 2787  E) 1121

Solution: 20 * 12 * 5= 
20 * 12 * 5 = 1_200
1200   Answer: 1200
Answer: C
The average of 45 results is 10. The average of first 22 of them is 15 and that of last 22 is 20. Find the 23 result? Choose the correct choice from the following answers
A) 600  B) 480  C) 750  D) 650  E) 560

Solution: 23th result = sum of 45results - sum of 44 results   10*45-15*22+20*22 = 450-330+440= 
450-330+440 = 560
560   Answer is 560
Answer: E
Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction? Choose the correct choice from the following answers:
A) 8 sec
B) 12 sec
C) 15 sec
D) 10 sec
E) 11 sec

Solution: Speed of the first train = 120/10 m/sec = 12 m/sec.   Speed of the second train = 120/15 m/sec = 8 m/sec.   Relative speed = (12 + 8)= 
(12 + 8) = 20
20 m/sec.   Required time= (120 + 120)/20= 
(120 + 120)/20 = 12
12 sec.   Answer : 12 sec.
Answer: B
The average of a couple was 23Yrs when they were married 5Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 20Yrs now. How old is the
child now ? Choose one:
A) 2 Yrs B) 4 Yrs C) 3 Yrs D) 1 Yrs E) None of these

Solution: (a+b-5-5)/2=23;   a+b=56;   a+b+c/3=20;   solving both c=4   ANSWER:4 Yrs
Answer: B
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
Choose the correct choice from the following:
A) 38020
B) 38000
C) 38028
D) 38019
E) 38192

Solution: CP + CP/8 = 45000   CP = 40000   SP = 40000*(95/100)= 
40000*(95/100) = 38_000
38000   Answer: 38000
Answer: B
A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed? Choices.
A) 7 days
B) 9 days
C) 4 days
D) 6 days
E) 2 days

Solution: Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/4 + 1/12 = 1/3.   Total time required to complete the work = 2 * 3= 
2 * 3 = 6
6 days.   Answer: 6 days
Answer: D
What approximate value should come in place of the question mark (?) in the following equation?
95.245 + 25.912 × 7.2 + ? = 905.293	Choose the correct choice from the following:	A) 986.6	B) 936.6	C) 996.6	D) 995.6	E) 998.6

Solution: 95.245 + 25.912 × 7.2 + ? = 905.293   or, ? = 905.293 – 95.245 + 25.912 × 7.2   ? = 905.293 – 95.245 + 186.5664   ≈ 996.6   Answer 996.6
Answer: C
If a number between 10 and 30 (inclusive) at random. What is the probability that the tens digit is greater than ones digit?  Answers.
A) 31/41  B) 4/21  C) 14/41  D) 27/41  E) 11/41

Solution: If tens digi is 3 ---> ones digit : 0,   If tens digi is 2 ---> ones digit : 0, 1   If tens digi is 1 ---> ones digit : 0   So the number of numbers whose tens digit is greater than ones digit is 11.   The total number is   30-10+1= 
  30-10+1 = 21
21.   So the probability is 4/21.   The answer is (4/21).
Answer: B
Find the ones digit of 73^351
Answers.
A) 3
B) 5
C) 6
D) 7
E) 9

Solution: The units digit of 73^351 will be the same as the units digit of 3^351   3^1=3 --> the units digit is 3;   3^2=9 --> the units digit is 9;   3^3=27 --> the units digit is 7;   3^4=81 --> the units digit is 1;   3^5=243 --> the units digit is 3 AGAIN;   ...   So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 351=348+3=(multiple of 4)+3, then the units digit of 3^351 will be the third number in the pattern thus 7.   Answer: 7.
Answer: D
A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%? Choose one:
A) Rs.146  B) Rs.144  C) Rs.129  D) Rs.123  E) Rs.128

Solution: Given that SP = Rs. 102 and loss = 15%   CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.   To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100   = Rs.144   Answer:Rs.144
Answer: B
A man took some money for borrowed, for 2 years the total will be Rs.9000/- and 5 years it will be13, Rs.500/-. Then how much amount he borrowed?  Answers.
A) Rs.5000/-	B) Rs.5200/-	C) Rs.5500/-	D) Rs.5800/-	E) Rs.6000/-

Solution: 2 years --------> Rs.9000/-   5 years --------> Rs.13500/-   ~ ~   ------------------------------   3 years ---------> Rs.4500/-   1 year ----------> Rs.1500/-   2years * Rs.1500/- = Rs.3300/-   P = Rs.9000/- - Rs.30000/- = Rs.6000/-   P = Rs.6000/-   Rs.6000/-
Answer: E
A car travels at a speed of 10 miles per hour. How far will it travel in 5 hours?	Select the correct option:  A) 50 miles  B) 62 miles  C) 325 miles  D) 70 miles  E) 20 miles

Solution: During each hour, the car travels 65 miles. For 5 hours it will travel   10 + 10 + 10 + 10 + 10 = 5 *10= 
5 *10 = 50
50 miles correct answer 50 miles
Answer: A
Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 90kmph. When will Raghu overtake Anup?
Choose the correct choice from the following choices:
A) 9:00am
B) 9:40am
C) 10:00am
D) 12:00pm
E) 11:10am

Solution: Suppose bike is overtaken by car xhrs after 6am   Distance covered by the bike in x hrs = distance covered by the car in x-1 hr   60x = 90(x-1)   30x = 90   x = 3 hrs   Required time = 6+3= 
6+3 = 9
9:00am   9:00amnswer is 9:00am
Answer: A
A shopkeeper buys mangoes at the rate of 7 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Choose the most appropriate option:
A) 33 4/3 % B) 33 1/7 % C) 400/7 % D) 32 1/3 % E) 33 2/3 %

Solution: The total number of mangoes bought by the shopkeeper be 21.   If he buys 7 a rupee, his 400/7 %P = 3   He selling at 3 a rupee, his SP = 7   Profit = SP - 400/7 %P = 7 - 3= 
7 - 3 = 4
4   Profit Percent= 4/7 * 100 = 400/7 %   Answer:400/7 %
Answer: C
An apple tree has 30 apples. 10 apples have fallen off of the tree. How many apples remain on the tree?
Choose the correct choice from the following options.
A) 20	B) 1	C) 0	D) 5	E) 100

Solution: A. 20
Answer: A
In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case? Pick.
A) 537
B) 528
C) 645
D) 538
E) 538

Solution: Assume X soldiers join the fort. 1200 soldiers have provision for 1200(days for which provisions last them)(rate of consumption of each soldier)   = 1200(30)(3) kg   Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) kg   As the same provisions are available   => 1200(30)(3) = (1200 + x)(25)(2.5)   x = [1200(30)(3)]/[(25)(2.5)] - 1200   Answer:528   x = 528
Answer: B
What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 67.12 = ?
Choose the correct choice from the following options.
A) 230  B) 231  C) 235  D) 220  E) 240

Solution: ? = 33 1⁄3% of 768.9 + 25% of 161.2 – 67.12   = 1⁄3 of 768.9 + 1⁄4 of 161.2 – 67.12   = 256.3 + 40.3 – 67.12 ≈ 231   Answer 231
Answer: B
Find the least number by which (59)(36)(17) has to be multiplied to obtain a perfect square?  Choose the correct option:	A) 5	B) 17	C) 85	D) 221	E) 223

Solution: For any perfect square the index of the power of each of its prime factors is even. in the given number the power of 5 and 17 have odd indices, while 3 has an even index.   The least number = (5)(17) = 85.   ANSWER:85
Answer: C
What is the least value of x. So that 43x87 is divisible by 3? Answers
A) 4	B) 5	C) 2	D) 6	E) 7

Solution: The sum of the digits of the number is divisible by 3, then the number is divisible by3.   4 + 3 + x + 8 + 7 = 22 + x   Least value of x may be 2   Therefore  22+ 2= 
 22+ 2 = 24
24 is divisible by 3.   2
Answer: C
The average salary per head of the entire staff of an office including the officers and clerks is Rs.90. The average salary of officers is Rs.600 and that of the clerks is Rs.84. If the number of officers is 2, find the number of officers in the office?	Choose one
A) 1 B) 8 C) 7 D) 6 E) 2

Solution: 6 * 22= 
6 * 22 = 132
132   7 * 19= 
7 * 19 = 133
133   --------------   1.1nswer: 1
Answer: A
(1+0.0001)/(0.00004+1)
The value of the expression above is closet to which of the following?	Choose one:
A) 0.0001  B) 0.001  C) 0.1  D) 1  E) 10

Solution: Notice that we need approximate value of the fraction.   Now, the nominator is very close to 1 and the denominator is very close to 1, hence the value of the fraction is very close to   1/1= 
  1/1 = 1
1.   Answer: 1.
Answer: D
One fourth of a solution that was 10% salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent salt by weight?
Options:
A) 24% B) 34% C) 22% D) 18% E) 8.5%

Solution: Say the second solution (which was 1/4 th of total) was x% salt , then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.   Answer: 34%.
Answer: B