MU-NLPC/Calc-aqua_rat huggingface dataset:
HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 15%	Answers.
A) 36  B) 108  C) 32  D) 42  E) 45

Solution: (x+30)*30=(115/100)(25x+30*30)   Solving we get 108.   Answer is 108.
Answer: B
The value of x is one quarter of z. The sum of x, y, and z is equal to 26. If the value of y is twice the value of z, what is the largest factor of the sum of y and z? Pick:	A) 2	B) 3	C) 8	D) 12	E) 24 IS ANSWER

Solution: While most Test Takers would treat this as a 'system' algebra question and solve it that way, there are some interesting Number Property patterns in this prompt that will actually allow you to use the answer choices (and some pattern-matching) to get to the solution.   To start, I'm going to deal with the last piece of information first:   Y is twice Z   The prompt asks for the BIGGEST factor of the SUM of Y and Z. Since Y = 2Z, the sum of Y and Z is (2Z) + Z = 3Z. This means that the BIGGEST factor is a MULTIPLE OF 3 (and likely one of the larger multiples of 3 in the answer choices).   The second piece of information tells us...   X+Y+Z = 26   By extension...   X+(Y+Z) = 26   X+(larger multiple of 3) = 26   From the answer choices, there are really only 2 options that make any sense: Answers D and E....   With Answer D:   IF....Y+Z = 12, then X= 14, but....   The first piece of information tells us that X = 1/4 of Z, so X has to be relatively small....In this example, it's LARGER than Z, so D is NOT the answer. At this point, the answer would have to be E, but here's the proof...   IF...Y+Z = 24 and Y= 2Z....   Y = 16   Z = 8   X is 1/4 of Z, so X = (1/4)(8) = 2   X+Y+Z=26   2+16+8= 
2+16+8 = 26
26   All of the numbers 'fit' what we were told, so this MUST be the answer.   24 IS ANSWER
Answer: E
A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture? Choose one:  A) 1 kgs  B) 3 kgs  C) 5 kgs  D) 6 kgs  E) None of these

Solution: Explanation :   If the selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture = 30/1.2 = Rs.25/kg.   We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg.   Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg. The mean desired price falls between B and C.   Step 1:   Find out the ratio Qa:Qc using alligation rule.   Qa/Qc=(30−25)/(25−20)=1/1.   Step 2:   Find out the ratio Qb:Qc using alligation rule.   Qb/Qc=30−25/(25−24)=5/1.   Step 3:   Qc is found by adding the value of Qc in step 1 and step 2 =1+1= 
1+1 = 2
2.   Therefore, the required ratio=1:5:2.   If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture.   Answer : 5 kgs
Answer: C
Find the area of a parallelogram with base 24 cm and height 12 cm?  Choose the correct choice from the following choices
A) 198 cm2 B) 288 cm2 C) 279 cm2 D) 128 cm2 E) 297 cm2

Solution: Area of a parallelogram   = base * height   = 24 * 12= 
24 * 12 = 288
288 cm2   Answer:288 cm2
Answer: B
Arjun started a business with Rs. 20,000 and is joined afterwards by Anoop with Rs.40, 000. After how many months did Anoop join if the profits at the end of the year are divided equally?	Choose the correct choice from the following choices: A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Suppose Anoop joined after 3 months.   Then, 20000 * 12 = 40000 * (12 – x)   =>   => x = 6.   ANSWER:6
Answer: D
If a is a positive integer, which of the following could NOT be the square of a?  Choose the correct choice
A) 2432	B) 7426	C) 5966	D) 3415	E) 2155

Solution: A number ending in 2 cannot be a perfect square.   2432 ends in a number 2, making that the correct answer   (2432) 2432
Answer: A
The difference between the simple interest received from two different sources on Rs. 1400 for 3 years is Rs. 13.50. The difference between their rates of interest is? Pick:
A) A)2.4%	B) B)2.6%	C) C)0.2%	D) D)2.0%	E) E)1.3%

Solution: (1400 * R1 * 3)/100 - (1400 * R2 * 3)/100 = 13.50 4200(R1 - R2) = 1350   R1 - R2 = 0.2%   Answer:0.2%
Answer: C
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 600 m long?
Select.
A) 176 Sec
B) 180 Sec
C) 178 Sec
D) 267 Sec
E) 276 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1800 m   T = D/S   T = 1800/10= 
1800/10 = 180
180 Sec   Answer:180 Sec
Answer: B
A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 25 percent of the pack would be outfielder cards? Select
A) 10
B) 5
C) 6
D) 7
E) 8

Solution: let the number of O card to be removed=X   then remaning cards=12-X   now this 12-X cards should count less than 25% of toatal Ocards   12-X<.25*12   X>12-3   X>9   X=10   10ns 10
Answer: A
The average of the marks of 10 students in a class is 80. If the marks of each student are doubled, find the new average?
Choose the correct choice from the following options:
A) 80
B) 120
C) 160
D) 270
E) 110

Solution: Sum of the marks for the 10 students   = 10 * 80= 
10 * 80 = 800
800. The marks of each student are doubled, the sum also will be doubled.   The new sum= 800 * 2= 
800 * 2 = 1_600
1600. So, the new average= 1600/10= 
1600/10 = 160
160.   Answer:160
Answer: C
What least number must be subtracted from 427398 so that remaining no.is divisible by 11	Answers.
A) 3 B) 4 C) 6 D) 7 E) 8

Solution: Explanation:   On dividing 427398 by 11 we get the remainder 4, so 4 should be subtracted   Answer: Option 4
Answer: B
Water tax is increased by 20% but its consumption is decreased by 20%. Then, the increase or decrease in the expenditure of the money is : Choose the correct choice from the following choices:
A) No change	B) 5% decrease	C) 4% increase	D) 4% decrease	E) None

Solution: Explanation:   Let tax=Rs.100 and   Consumption=100 units   Original expenditure = Rs.(100×100)=Rs.10000(100×100)=Rs.10000   New expenditure = Rs.(120×80)=Rs.9600(120×80)=Rs.9600   4% decreaseecrease in expenditure   = (400/10000×100)%=4%   Correct Option: 4% decrease
Answer: D
A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?  Choose the correct choice from the following answers:
A) 66 2/3 %
B) 33 7/3 %
C) 33 1/3 %
D) 33 5/8 %
E) 34 1/3 %

Solution: The total number of mangoes bought by the shopkeeper be 15.   If he buys 5 a rupee, his CP = 3   He selling at 3 a rupee, his SP = 5   Profit = SP - CP = 5 - 3= 
5 - 3 = 2
2   Profit Percent= 2/3 * 100 = 66 2/3 %   66 2/3 %nswer: 66 2/3 %
Answer: A
For real number x, int(x) denotes integer part of x.int(x) is the largest integer less than or equal to x.int(1,2)=1,int(-2,4)=-3. Find the value of int(1/2)+int(1/2+ 100)+int(1/2+2/100)+....+int(1/2+99/100)	Choose the correct choice from the following.
A) 150	B) 98	C) 278	D) 277	E) 1811

Solution: int (1/2) = 0   int (1/2 + 100 ) = 100   into (1/2 + 2/100) = 0   ......   int  ( 1/2 + 50/100 )= 
 ( 1/2 + 50/100 ) = 1
1   int (1/2 + 51 /100)= 1   .......   int (1/2 + 99/100) = 1   So 100 + 1 + 1 + .....50 times = 150   150nswer:150
Answer: A
when fair coin is tossed 9 times find the probability of getting head at least once.	Choose the correct choice from the following answers:	A) 1/512	B) 511/512	C) 9/512	D) 503/51	E) 503/510

Solution: 1-1/2^9= 1-1/512 = 511/512   ANSWER:511/512
Answer: B
A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $2040 had it been put at the rate of interest compounded annually?
Choose one:  A) 5  B) 4  C) 3  D) 2  E) 1

Solution: We can form equations as following:   Initial amount = P, Total amount after interest = T, Interest per year = I   T = P+I   Given T1 = P+2I = 1400T2 = P+ 5I = 2000   From this we get, P = 1000I = 200 $   Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually)   consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ , after 3rd year it is 600$.and after 4rd year it is 800$.   To get a 640 $ compound interest the duration have to be > 2 year and < 4 years.   Only option fitting : Option 3.
Answer: C
If x and y are positive real numbers such that x + y = 1, which of the following could be the value of 100x + 600y?
I. 90
II. 250
III. 599  Choose the correct choice from the following:
A) II only	B) III only	C) I and II	D) I and III	E) II and III

Solution: We know that x and y are both between 0 and 1.   The minimum limit of 100x + 600y is 100, when x is close to 1 and y is close to 0.   The maximum limit of 100x + 600y is 600, when x is close to 0 and y is close to 1.   The expression can take on any value between 100 and 600.   The answer is II and III.
Answer: E
Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.57600? Options.
A) 81000 B) 81028 C) 27772 D) 72900 E) 22312

Solution: 57600* 9/8 * 9/8= 
57600* 9/8 * 9/8 = 72_900
72900.Answer:72900
Answer: D
In what time will a train 100 meters long cross an electric pole, if its speed is 360 km/hr	Choose the correct answer: A) 1 second B) 4.5 seconds C) 3 seconds D) 2.5 seconds E) None of these

Solution: Explanation:   First convert speed into m/sec   Speed = 360*(5/18)= 
360*(5/18) = 100
100 m/sec   Time= Distance/speed   = 100/100= 
100/100 = 1
1 second   1 secondnswer: 1 second
Answer: A
The tax on a commodity is diminished by 25% and its consumption increased by 13%. The effect on revenue is?
Answers: A) 18 B) 16 C) 10 D) 15 E) 14

Solution: 100 * 100= 
100 * 100 = 10_000
10000   75 * 113= 
75 * 113 = 8_475
8475   -----------   10000-----------1525   100-----------?=> 15% decrease   Answer:15
Answer: D
Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 120 percent of the sum paid to B, how much is B paid per week?	Choose one:
A) Rs.220
B) Rs.250
C) Rs.260
D) Rs.270
E) Rs.280

Solution: Let the amount paid to A per week = x   and the amount paid to Rs.250 per week = y   Then x + y = 550   Rs.250ut x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 550   ⇒ y[12/10 + 1] = 550   ⇒ 22y/10 = 550   ⇒ 22y = 5500   ⇒ y = 5500/22 = 500/2 = Rs.250   Rs.250
Answer: B
Machine A takes 100 hours to complete a certain job and starts that job at 7AM. After two hour of working alone, machine A is joined by machine B and together they complete the job at 12PM. How long would it have taken machine B to complete the jobif it had worked alone for the entire job?
Select
A) 100.11
B) 10.98
C) 18.07
D) 45.01
E) 35.09

Solution: Let us assume total job = 100 units   A finishes 100 units in 100 hrs(given)   Hence A (working rate)= 1 units /hr   Now Given that A works for 2 hr( so 2 units done) then A and B finish total work in 15 hours. Hence A and B finish 98 units in 15 hours. Of these 1x15=15 units were done by A. Hence B did 83units in 15 hours.   Hence B(working rate)= 83/15 units /hr   Hence B takes 100x15/83 = 18.07 hours to complete the job.   Answer 18.07.
Answer: C
A certain university will select 2 of 6 candidates eligible to fill a position in the mathematics department and 3 of 5 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Choose the correct choice from the following choices
A) 42
B) 70
C) 150
D) 165
E) 315

Solution: 61502*51503 = 15*10= 
15*10 = 150
150   the answer is (150)
Answer: C
If 0 < L < Y, L is an odd number and Y is a prime number, which of the following can be the value of L + Y ?  Choose the correct choice from the following answers:
A) 11.	B) 13.	C) 17.	D) 10.	E) 7.

Solution: If L is odd ,implies l(odd)+y(odd/even prime)=(Even/Odd)   If Y is even, the 2 is the even prime , therefore y=2l=1 since 0<L<Y therefore L+Y =3. But 3 is not an option   which implies y is odd,   Now L(odd)+Y(odd)=Even   10 is the only option that is even=10.
Answer: D
A sells a bicycle to B at a profit of 60% and B sells it to C at a loss of 60%. Find the resultant profit or loss.
Choose the correct answer: A) -4% B) 0% C) -5% D) 6% E) -36%

Solution: The resultant profit or loss = 60 - 60 - (60*60)/100 = -36%   loss = 36%   Answer is -36%
Answer: E
An amount of Rs.2,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?  Choices: A) 2378 B) 268 C) 269 D) 500 E) 6971

Solution: Explanation:   We have, P = 2Q & S = 4R   Further Q = R & P + Q + R + S = 2,000   Thus we get, 2Q + Q + Q + 4Q = 2,000   8Q = 2,000 or Q = Rs. 250   Thus, R = Rs. 250, P = 500 & S = Rs. 1000   Hence, the required difference = (S – P) = (1000 – 500) = Rs. 500   ANSWER:500
Answer: D
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed Z?	Choose the correct choice from the following answers.
A) 6  B) 8  C) 10  D) 12  E) 16

Solution: Let the current speed be x miles per hour.   Time taken if speed is 50% faster (i.e. 3x/2 = 1.5x) = 96/1.5x   Time taken if speed is reduced by 4 miles/hr (i.e. (x-4)) = 96/(x-4)   As per question, 96/(x-4) - 96/1.5x = 16   Solving this Z we get x = 8.   8.
Answer: B
A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?  Choose the correct option
A) 48 kmph B) 52 kmph C) 108 kmph D) 100 kmph E) 98 kmph

Solution: S = 180/6 * 18/5= 
180/6 * 18/5 = 108
108 kmph   answer :108 kmph
Answer: C
For some integer y, y^2 - 5 is divisible by all of the following EXCEPT Choose the correct choice from the following answers:
A) 29
B) 30
C) 31
D) 38
E) 41

Solution: Hint: y^2-5 (y is an integer) is never multiple of 3 (try to prove this), hence 30 is out.   Answer: 30
Answer: B
A searchlight on top of the watchtower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds?
Choose the most appropriate option.
A) 5/6
B) 5/12
C) 7/12
D) 11/12
E) 11/15

Solution: The searchlight completes one revolution every 30 seconds.   The probability that the man's area will be lit up is 5/30=1/6.   The probability that he will stay in the dark is 1-1/6=5/6   The answer is 5/6.
Answer: A
If t and y are different prime numbers less than ten, what must be true about the sum of t and y?	Pick
A) the sum is even  B) the sum is odd  C) the sum is less than ten  D) the sum is greater than ten  E) the sum is less than 13

Solution: This has to be solved by checking for each option:   Prime numbers less that 10 = 2, 3, 5, 7   A. the sum is even   May or may not be true. t = 3, y, = 5 -> True.   t = 2, y = 3 - True   B. the sum is odd   May or may not be true. t = 3, y, = 5 -> False.   t = 2, y = 3 - True   C. the sum is less than ten   May or may not be true t= 5, y = 7, Sum = 12   t = 2, y = 3. Sum = 5   D. the sum is greater than ten   May or may not be true t= 5, y = 7, Sum = 12   t = 2, y = 3. Sum = 5   E. the sum is less than 13   This will always be true.   Maximum sum = 7 + 5= 
7 + 5 = 12
12.   This is always less than 13.   Correct Option: the sum is less than 13
Answer: E
The height of the wall is 4 times its width and length of the wall is 3 times its height .if the volume of the wall be 10368 cu.m.its width is	Choose the correct choice from the following choices.
A) 4m B) 5m C) 6m D) 7m E) 8m

Solution: Explanation:   Let width = x   Then, height=4x and length=12x   12x Ã— 4x Ã— x = 10368   x = 6   Answer: 6m
Answer: C
A military garrison in a wild frontier has 500 men who have provisions to last 26 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?  Select.
A) 13 1/3  B) 12 1/3  C) 11 3/3  D) 12 1/2  E) 12 3/4

Solution: Total provisions=500*26*7= 
500*26*7 = 91_000
91000   Provisions used for in 6 weeks=6*7*500= 
6*7*500 = 21_000
21000   remaining provisions=70000   remaining provisions need to be split between 800(500+300) people.   Number of provisions per person= 70000/800   we need to find the answer in terms of weeks=(70000/800)/7=25/2   Answer:12 1/2
Answer: D
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Choose the correct choice from the following choices
A) 1000 B) 3783 C) 1837 D) 3799 E) 3786

Solution: 90%   104%   --------   14% ---- 140   100% ---- ? =>   Rs.1000   1000nswer: 1000
Answer: A
A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?  Choose one
A) 1/2 B) 1by3 C) 3/5 D) 3/7 E) 3/11

Solution: Let b stand for boy and g for girl. The sample space of the experiment is   S = {(g, g), (g, b), (b, g), (b, b)}   Let E and F denote the following events :   E : ‘both the children are girls’   F : ‘at least one of the child is a girl’   Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}   Now E n F = {(g,g)}   Thus P(F) = 3/4   and P (E n F )= 1/4   Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3   1by3)
Answer: B
There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
Choose the most appropriate option.
A) 120 B) 720 C) 1,060 D) 1,520 E) 1980 committees

Solution: these are two independent events. meaning picking men from a group of men has no effect on picking women from group of women. so you have to multiply here.   11c2*9c2 =1980   Answer is 1980 committees.
Answer: E
Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 25 hours respectively. The ratio of their speeds is Select
A) 4:1	B) 4:2	C) 3:5	D) 5:3	E) 4:6

Solution: Ratio of their speeds = Speed of first train : Speed of second train   = √25−−√9   = 5:3   Answer is 5:3.
Answer: D
What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 6?
Choices:
A) 0.12  B) 1  C) π/2  D) 2  E) 12

Solution: Maximum distance straight line is diameter   d = 2r = 12..   ANS option 12.
Answer: E
A sum was put at simple interest at a certain rate for 6 years Had it been put at 4% higher rate, it would have fetched 144 more. Find the sum.	Choose the correct choice from the following options:  A) 500  B) 600  C) 700  D) 800  E) 900

Solution: Difference in S.I. = P×T/100(R1−R2)   ⇒ 144 = P×6x4/100(∵ R1 - R2 = 2)   ⇒ P = 144×100/6×4=600   Answer 600
Answer: B
A bus travel 5/7 of its speed covers 42 km in 1 hr 40 min48 sec. What is theactual speed of the bus ? Choose the correct choice:
A) 25 km/hr B) 35 km/hr C) 42 km/hr D) 46 km/hr E) 55 km/hr

Solution: Time = 1 hr 40 min 48 sec = 1hr +4060hr+483600hr=1+23+175=12675hrdistance = 42 kmspeed=distancetime=42(12675)=42×75126⇒57 of the actual speed = 42×75126⇒actual speed = 42×75126×75=42×1518=7×153=7×5=35 km/hr   35 km/hr
Answer: B
Avg cost of 5 pens and 4 pencils isRs. 36.The avg cost of 5 pens and 9 pencils is Rs.56.Find the total cost of 25 pens and 25 pencils? Choose the correct choice from the following answers:
A) 80  B) 90  C) 100  D) 110  E) 120

Solution: Avg cost of 5 pens and 4 pencils is Rs. 36   (5 pen + 4 pencils) 9=36   therefore 1 pen cost is  36/9= 
 36/9 = 4
4, so 5 pen cost is 5x4=20 and 4 pencils cost is 4x4=16   Again, avg cost of 5 pens and 9 pencils is Rs.56   (5 pen + 9 pencils) 14=56   therefore 1 pen cost is  56/14= 
 56/14 = 4
4, so 5 pen cost is 5x4=20 and 9 pencils cost is 9x4=36   So 25 pen cost is (25/a)=100 and 25 pencils cost is (25x4)=100   ANSWER:100
Answer: C
The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?	Select the correct option.
A) 4 B) 5 C) 6 D) 7 E) 9

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35   So 30x + 35 + 31(x + 1) = > x = 4.   4nswer: 4
Answer: A
Three coins are tossed. Find the probability of at least 1 head and 1 tail ?  Pick one.
A) 1/2 B) 1/4 C) 3/4 D) 7/8 E) 1/8

Solution: n(s) = 2^3 = 8 ....(3 coins tossed)   let E is the event of getting at least 1 head and 1 tail   n(E) = TTH , HTT, THT, HHT, HTH, THH = 6   P(E) = n(E) / n(s)   = 6/8   = 3/4   Ans- 3/4
Answer: C
Calculate the value of 5.11 x 10^8 ?  Answers
A) 511000000
B) 5110000
C) 511000
D) 51100000
E) 51100

Solution: 5.11 x 10^6 = 5.11 x 100000000 = 511000000.   511000000nswer = 511000000
Answer: A
The ratio of two quantities is 5 to 6. If each of the quantities is increased by 15, what is the ratio of these 2 new quantities?
Select the correct option:
A) 5:6 B) 25:27 C) 15:16 D) 20:21 E) It cannot be determined from the information given

Solution: The ratio cannot be straight way added any quantity...   5:6 means 5x:6x...   So when you add a quantity, it becomes 5x + 15 : 6x +15..   So value of x is must..   Ans It cannot be determined from the information given
Answer: E
In how many ways a committee, Consisting of 3 men and 5 women can be formed from 8 men and 10 women?	Answers.
A) 266 B) 86400 C) 11760 D) 14112 E) 14720

Solution: To choose Required number of ways to form a committee:   Select 3 men out of 8 men and 5 women out of 10 women.   That is 8C3 * 10C6.   8C3=8!/3!*5!   =56   10C5=10!/5!*5!   =252   The Required number of ways=252*56= 
252*56 = 14_112
14112   14112
Answer: D
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron
weighs 8g/ cm^3 , then the weight of the pipe is
Choose the correct choice from the following choices.
A) 4.996 kg B) 5.696 kg C) 3.796 kg D) 3.696 kg E) 3.996 kg

Solution: External radius = 4 cm,   Internal radius = 3 cm.   Volume of iron = [ 22/7 x (4 ^2 x 3 ^2) 21] cm^3 = 462 cm^3   Weight of iron = (462 x 8)gm = 3696 gm = 3.696 kg   ANSWER:3.696 kg
Answer: D
Mario and Nina each have a bag of marbles, each of which contains 10 blue marbles, 10 red marbles, an 10 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble?
Choices:
A) 3/4 B) 2/9 C) 1/4 D) 1/8 E) 1/16

Solution: Mario and Nina each select one marble from their respective bags.   Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble   Probability that either Mario or Nina select a red marble = (10/30)*(10/30) + (10/30)*(10/30) = 2*(1/9)   Probability that either Mario or Nina select a red marble = 2/9   Answer would be 2/9.
Answer: B
John tossed a fair coin 5 times. What is the probability that the coin landed heads up exactly twice?
Select the correct option:	A) 0.156	B) 0.256	C) 0.35	D) 0.456	E) 0.555

Solution: The probability is exactly same as the cion landed tail up once. That is 5*(1/2)^5 = 5/32 =0.156.   The answer is, therefore, (0.156).
Answer: A
The bankers discount and the true discount of a sum at 20% per annum simple interest for the same time are Rs.200 and Rs.150 respectively. What is the sum and the time?	Pick.
A) Sum = Rs.600 and Time = 1.6 years
B) Sum = Rs.500 and Time = 1.6 years
C) Sum = Rs.400 and Time = 1.6 years
D) Sum = Rs.600 and Time = 3 years
E) None of these

Solution: Explanation :   BD = Rs.200   TD = Rs.150   R = 20%   F = BD ×TD/(BD – TD)=200×150/(200–150)=200×150/50=Rs. 600   BD = Simple Interest on the face value of the bill for unexpired time =FTR/100   ⇒200 = (600×T×20)/100   ⇒200 = 6 × T × 20 ⇒20 = 12 × T   ⇒ T = 20/12 = 1.6 years Sum = Rs.600 and Time = 1.6 yearsnswer : Option Sum = Rs.600 and Time = 1.6 years
Answer: A