MU-NLPC/Calc-aqua_rat huggingface dataset:
A reduction of 40% in the price of bananas would enable a man to obtain 66 more for Rs.40, what is reduced price per dozen? Choose the correct choice:
A) 1.91	B) 2.91	C) 4.91	D) 3.91	E) 5.91

Solution: 40*(40/100)= 
40*(40/100) = 16
16 --- 66   ? --- 12=> Rs.2.91   Answer: 2.91
Answer: B
A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number Q of tickets sold by the male members of the association	Pick one.
A) 50 B) 56 C) 58 D) 62 E) 66

Solution: Given that, Total average Q sold is 66, Male/Female = 1/2 and Female average is 70. Average of Male members isX.   (70*F+X*M)/(M+F) = 66 -> Solving this equation after substituting 2M=F, X = 58. ANS 58.
Answer: C
1370 , 1320 , 1070 , -180 ?
Options
A) -6430
B) -6530
C) -6630
D) -6730
E) -6830

Solution: 1370,1320,1070,-180,?   1370-50*(5^0)=1320   1320-50*(5^1)=1070   1070-50*(5^2)=-180   -180-50*(5^3)=-6430   -6430NSWER:-6430.
Answer: A
If Susan takes 11 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
Choose the correct choice from the following options
A) xy/11	B) 660x/y	C) 60xy/11	D) xy/660	E) 11x/(60y)

Solution: The answer is E.   She runs x yards in 11x/y seconds =11x/60y minutes.
Answer: E
A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train. Choose the correct choice from the following options:	A) 225 meter	B) 200 meter	C) 250 meter	D) 190 meter	E) 180 meter

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 12= 
  (50/3) * 12 = 200
200 meter   Answer:200 meter
Answer: B
If t, u, v, w, x, y, and z are seven different prime numbers, which of the following is the smallest possible value of t + u + v + w + x + y + z?  Choose the correct answer:  A) 50  B) 52  C) 54  D) 56  E) 58

Solution: The sum of the seven small smallest primes numbers is 2+3+5+7+11+13+17= 
2+3+5+7+11+13+17 = 58
58.   The answer is 58.
Answer: E
What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
Choose the most appropriate option:  A) 5%  B) 6%  C) 2%  D) 95%  E) 1%

Solution: 160 = (180*4*R)/100   R = 5%   5%nswer: 5%
Answer: A
Ratio of two numbers x and y is 2:5. If x is increased by 50% and y is increased by 8 then the new ratio becomes 3:10. what is the ratio 3y:(x+6)
Answers
A) 15:8
B) 8:15
C) 2:5
D) 5:2
E) 13:6

Solution: Let:   x = 2n   y = 5n   3n/(5n+5) = 3/10   30n = 3*(5n+5)   n = 1   So, x =2; y=5   3y/(x+6) = 15/8   15:8nswer = 15:8
Answer: A
A boy runs 200 metres in 72 seconds. What is his speed ? Choices.
A) 10 km/hr B) 14 km/hr C) 20 km/hr D) 12 km/hr E) 24 km/hr

Solution: 200/72 * 18/5= 
200/72 * 18/5 = 10
10 km/hr   10 km/hrNSWER:10 km/hr
Answer: A
Operation#is defined as adding a randomly selected two digit multiple of 10 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers? Choose the correct choice:	A) 0%	B) 10%	C) 20%	D) 30%	E) 40%

Solution: Any multiple of 10 is even.   Any two-digit prime number is odd.   (even+odd)/2 is not an integer. Thus # does not yield an integer at all.   Therefore P=0.   0%nswer: 0%.
Answer: A
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 100 metres?  Choose one.
A) 16 seconds B) 20 seconds C) 14 seconds D) 12 seconds E) 15 seconds

Solution: Speed of the boat downstream = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 100 m= 100/5= 
100/5 = 20
20 seconds.   Answer: 20 seconds
Answer: B
How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/4!?	Choose the correct choice from the following answers:
A) 1 B) 3 C) 5 D) 6 E) 9

Solution: 4! = 24   1/100 < 1/24 < 1/10   0.001 < 1/24 < 0.01   So 1/24 has 1 leading zeros   1nswer: 1
Answer: A
A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
Choose the correct option:
A) 11 B) 77 C) 16 D) 10 E) 88

Solution: lb = 150   2(l + b) = 50 => l + b = 25   l – b = 5   l = 15 b = 10   Answer: 10
Answer: D
The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
Pick one.
A) 21 years
B) 71 years
C) 51 years
D) 91 years
E) 11 years

Solution: Explanation:   Age of the teacher = (37 * 15 - 36 * 14)= 
(37 * 15 - 36 * 14) = 51
51 years.   Answer: 51 years
Answer: C
Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is?	Choose the correct choice from the following:
A) 5/15  B) 5/12  C) 5/19  D) 5/12  E) 5/11

Solution: Using question number 11 and 12, we get the probability as   1 - (1/36 + 5/9) = 5/12   Answer: 5/12
Answer: B
Find the odd man out
4,9,16,25,36,42,49
Answers
A) 4  B) 9  C) 16  D) 42  E) 49

Solution: 2*2= 
2*2 = 4
4   3*3= 
3*3 = 9
9   4*4= 
4*4 = 16
16   5*5= 
5*5 = 25
25   6*6= 
6*6 = 36
36   7*7= 
7*7 = 49
49   ANSWER:42
Answer: D
If Rs.10 be allowed as true discount on a bill of Rs.110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is Pick:
A) 18.20	B) 18.33	C) 18	D) 18.3	E) None of these

Solution: Explanation:   Present worth = Amount - TrueDiscount   = 110 -10 = Rs.100   SI on Rs.100 for a certain time = Rs.10   SI on Rs.100 for doube the time = Rs.20   TrueDiscount on Rs.120 = 120 - 100 = Rs.20   TrueDiscount on Rs.110 = (110x 20/120) = Rs.18.33   Answer: 18.33
Answer: B
A hostel had provisions for 250 men for 28 days. If 50 men left the hostel, how long will the food last at the same rate?
Choose the correct choice from the following answers:
A) 35  B) 40  C) 50  D) 60  E) 65

Solution: A hostel had provisions for 250 men for 28 days   If 50 men leaves the hostel, remaining men = 250 - 50= 
250 - 50 = 200
200   We need to find out how long the food will last for these 200 men.   Let the required number of days= x days   More men, Less days (Indirect Proportion)   (men) 250 : 200 :: x : 28   250×28=200x   5×28=4x   x=5×7=35   35NSWER 35
Answer: A
In a certain province in Japan there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?	Select the correct option:
A) 30
B) 105
C) 330
D) 14!
E) 15!

Solution: Method-1:   Japan has Total Cities = 15 and each city should be connected with every other city   So Total Roads required to connect 1st City with other 14 cities = 14   Now 1st City is connected with all other cities so,   So Total Roads required to connect 2nd City with 13 cities (Other than 1st) = 13   Now 1st and 2nd Cities are connected with all other cities so,   So Total Roads required to connect 3rd City with 12 cities (Other than 1st, and 2nd) = 12   ......and so on...   Total Roads required = 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1= 
14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105
105=105
Answer: B
A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Pick one:
A) 833 1/4	B) 833 1/3	C) 833 1/9	D) 833 1/2	E) 833 1/1

Solution: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.   If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.   How many grams he has to give instead of one kilogram(1000 gm).   120 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/120 = 2500/3 = 833 1/3 grams.Answer: 833 1/3
Answer: B
The ratio of the volumes of two cubes is 6859 : 1331. What is the ratio of their total surface areas?  Pick
A) 1:21	B) 12:7	C) 1:15	D) 21:17	E) 13:13

Solution: Ratio of the sides   = ³√6859 : ³√1331 = 19 : 11   Ratio of surface areas   = 192 : 112 = 12:7   Answer:12:7
Answer: B
Find the area of a parallelogram with base 24 cm and height 16 cm?	Select:
A) 761 cm2	B) 384 cm2	C) 157 cm2	D) 276 cm2	E) 672 cm2

Solution: Area of a parallelogram   = base * height   = 24 * 16= 
24 * 16 = 384
384 cm2   Answer: 384 cm2
Answer: B
How much is 90% of 40 is greater than 4/5 of 25?  Pick.
A) 29
B) 776
C) 66
D) 16
E) 99

Solution: (90/100) * 40 – (4/5) * 25   36 - 20= 
36 - 20 = 16
16   Answer: 16
Answer: D
(?) + 3699 + 1985 - 2047 = 31111 Answers
A) 27488
B) 27424
C) 27474
D) 27784
E) 27468

Solution: 27474   27474   x + 3699 + 1985 - 2047 = 31111   x + 3699 + 1985 = 31111 + 2047   x + 5684 = 33158   x = 33158 - 5684= 
33158 - 5684 = 27_474
27474.
Answer: C
A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:  Choose the correct option
A) 10 B) 20 C) 40 D) 73 E) 64

Solution: let x pupils in the class   by question   total increase in marks = x/2   so;x/2 = (83 - 63)   x = 2 * 20   40   ANSWER:40
Answer: C
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.	Choices.
A) 288 m  B) 704 m  C) 898 m  D) 556 m  E) 465 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.   = 500 * 2 * 22/7 * 22.4= 
500 * 2 * 22/7 * 22.4 = 70_400
70400 cm= 704 m   Answer: 704 m
Answer: B
If f(x)=x^2 and x is a positive integer, which of the following will not be the value of f(f(x))?	Options
A) 1	B) 16	C) 81	D) 256	E) 144

Solution: f(x)=x^2   f(f(x)) = (x^2)^2   =x^4   A. 1 , x=1   B. 16 , x=2   C. 81 , x=3   E. 144   f(x)=12   Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(x)) .   D. 256 , x=4   Answer 144
Answer: E
what is the unit digit in (7^95-3^58)?	Choose the correct choice
A) 0	B) 4	C) 6	D) 7	E) None of them

Solution: Unit digit n 7^95=Unit digit in [(7^4)^23 x 7^3]=(1x3)=3   Unit digit in 3^58=Unit digit in [(3^4)^14 x 3^2]=(1x9)=9   Unit digit in (7^95 - 3^58)=(13-9)= 
(13-9) = 4
4   Answer is 4.
Answer: B
You collect balls. Suppose you start out with 0. Neha gives you another 210 balls. How many balls do you have at the end?  Choose the correct choice
A) 201
B) 120
C) 200
D) 0
E) 210

Solution: Solution   Start with 0 balls.   Neha gives you 210 balls:   0 + 210= 
  0 + 210 = 210
210 balls.   So you have 210 at the end.   Correct answer: 210
Answer: E
Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Choose the correct choice from the following:  A) 10  B) 12  C) 15  D) 20  E) 25

Solution: Speed of the first train = 120/10= 
120/10 = 12
12 m/sec.   Speed of the second train= 120/5 = 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
Answer: B
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square. Choose the correct answer.
A) 18 : 5  B) 7 : 16  C) 5 : 14  D) 5 : 32  E) None of these

Solution: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.   a2 = 4096 = 212   a = (212)1/2 = 26 = 64   L = 2a and b = a - 24   b : l = a - 24 : 2a = 40 : 128 = 5 : 16   ANSWNone of theseR:None of these
Answer: E
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 40% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above? Choose the correct answer
A)  5%  B)  10%  C)  25%  D)  15%  E)  30%

Solution: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.   Neither is zero.   Hence 100 = 60 + 40 + 35 - n (Exactly 2 products) - 2*10   100 = 115 - n (Exactly 2 products) => n (Exactly 2 products) = 15.   Answer:  15%
Answer: D
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? Select:	A) 28	B) 26	C) 20	D) 87	E) 24

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   Answer: 20
Answer: C
A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss?  Choose the correct choice from the following options:  A) 9% loss  B) 400  C) 4000  D) 324  E) 8% LOSS

Solution: (30*30)/100= 
(30*30)/100 = 9
9%loss   9% lossNSWER:9% loss
Answer: A
In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
Choose the correct answer:
A) 50 B) 40 C) 25 D) 15 E) 10

Solution: A scores 60 while B score 40 and C scores 30.   The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3= 
25 * 3 = 75
75.   In a game of 100 points, B gives (100 - 75)= 
(100 - 75) = 25
25 points to C.   ANSWER:25
Answer: C
What ratio must a shopkeeper mix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.19 ?	Answers:
A) 10 : 7	B) 9 : 8	C) 2 : 1	D) 13 : 11	E) 14 : 8

Solution: 2 : 1orrect option: (2 : 1)   Use rule of alligation, to determine the ratio   The required ratio of Soybean and Peas = 6 : 3 =2 : 1
Answer: C
A 90 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?	Pick one.
A) 25  B) 20  C) 47  D) 36  E) 30

Solution: 1: 2/5 = 5: 2   2/7 * 90 =25   25nswer:25
Answer: A
A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number X is Choose the correct choice from the following answers.
A) 74  B) X=75  C) X=175  D) X=680  E) 690

Solution: I solved this question by plugging in numbers from the answer choices.   A.) 74   Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5.   B.) 75   I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7.   15-7= 
15-7 = 8
8 so I know the correct answer isX=75
Answer: B
1370 , X, 1070 , -180, -6430 Select.
A) 1320	B) 6530	C) 6630	D) 6730	E) 6830

Solution: 1370-50*(5^0)=1320   1320-50*(5^1)=1070   1070-50*(5^2)=-180   -180-50*(5^3)=-6430   1320NSWER:1320.
Answer: A
Coins are to be put into 9 pockets so that each pocket contains at least one coin. At most 5 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?  Answers
A) 7	B) 13	C) 16	D) 19	E) 28

Solution: Since at most 5 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+1+2+3+4+5= 
  1+1+1+1+1+2+3+4+5 = 19
19   Answer: 19
Answer: D
John is the owner of a company and for Thanksgiving he wants to give a Turkey to each employee to celebrate the holiday. Each turkey cost him $25. If he has 85 employees, how much would John need to spend?	Choose the correct choice from the following
A) $2,125
B) $1,320
C) $2,000
D) $1,580
E) $2,000.75

Solution: Answer is (A). If John wants to give each of his employees a turkey to help celebrate the Thanksgiving holiday and each one costs him $25 multiplied by the number of employees (85), he would have to pay a total of $2,125.
Answer: A
In how many ways letters of the word DATA be arranged?	Select:
A) 6
B) 18
C) 12
D) 6
E) 2

Solution: DATA has 4 letters, out of which A repeated 2 times. Hence total ways = 4! / 2!=12 ways   12
Answer: C
Two pipes a and b can fill a tank in 12 hours and 15 hours respectively.if both pipe open together in tank,then how much time it take to fill the tank?  Choose the most appropriate option.
A) 15	B) 18	C) 20/3	D) 19/4	E) 25/4

Solution: in 1 hour pipe a fill=1/12   in 1 hour pipe b fill=1/15   pipe(a+b) in 1 hour=[1/12+1/15]=3/20   total time taken to fill the tank=20/3 hour   answer 20/3
Answer: C
What distance will be covered by a bus moving at 72 kmph in 30 seconds? Choose the correct choice from the following answers
A) 877 m
B) 600 m
C) 167 m
D) 176 m
E) 546 m

Solution: Explanation:   72 kmph = 72 * 5/18= 
72 * 5/18 = 20
20 mps   D= Speed * time = 20 * 30= 
20 * 30 = 600
600 m.   Answer: 600 m
Answer: B
Which of the following is equal to the value of 2^3 + 2^3 + 3^3 + 3^3 + 3^3 ? Select
A) 2^3 + 3^3
B) 2^7 + 3^4
C) 2^8 + 3^4
D) 2^4 + 3^4
E) 2^4 + 3^6

Solution: 2^3 + 2^3 + 3^3 + 3^3 + 3^3   = 2 (2^3) + 3 (3^3)   = 2^1 (2^3) + 3^1 (3^3)   = 2^(1+3) + 3^(1+3)   = 2^4 + 3^4   Ans: 2^4 + 3^4
Answer: D
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race? Choose the correct option
A) 190 sec  B) 200 sec  C) 210 sec  D) 220 sec  E) 250 sec

Solution: Time taken by B run 1000 meters = (1000 * 10)/50= 
(1000 * 10)/50 = 200
200 sec.   Time taken by A= 200 - 10= 
200 - 10 = 190
190 sec.   190 secNSWER 190 sec
Answer: A
‘A’ and ‘B’ started a business in partnership investing Rs 20000/- and Rs 15000/- respectively. After six months ‘C’ jointed them with Rs 20000/-. What will beB’s share in the total profit of Rs 25000/- earned at the end of two years from the starting of the business?  Choose the correct choice from the following.
A) 6500  B) 7500  C) 8500  D) 9000  E) 9500

Solution: A:7500:C =(20000*24) : (15000*24) : (20000*18)   = 4 : 3 : 3   7500's Share = (3*25000)/(4+3+3)= 
(3*25000)/(4+3+3) = 7_500
7500Rs   ANSWER:7500
Answer: B
A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Answers:
A) 877m
B) 189m
C) 350m
D) 216m
E) 978m

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 39   = 50/3   3(x + 300) = 1950 è x   = 350m.   Answer: 350m
Answer: C
Anand and Deepak started a business investing Rs. 5,500 and Rs. 19,000 respectively. Out of a total profit of Rs. 20,800, Deepak's share is?  Select:
A) Rs. 9400	B) Rs. 16130.6	C) Rs. 8400	D) Rs. 3400	E) Rs. 8440

Solution: Ratio of their shares = 5500 : 19000 = 11 : 38   Deepak's share = 20800 * 38/49= Rs. 16130.6   Answer:Rs. 16130.6
Answer: B
A man can row with a speed of 12 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? Choose the correct choice from the following answers:
A) 33
B) 77
C) 20
D) 99
E) 17

Solution: M = 12   S = 5   DS = 12 + 5= 
12 + 5 = 17
17   Answer: 17
Answer: E
A train leaves New York City at 7.15 Am and arrives in Buffalo at 2.47 that afternoon. What total length of time does the trip take? Select the correct option.
A) 7 h 92 min.  B) 7 h 32 min.  C) 7 h 12 min.  D) 8 h 32 min.  E) 5 h 32 min.

Solution: Explanation:   2.47 PM = 14.47   Total time = 14.47 – 7.15 = 7 hrs 32 min   Answer:7 h 32 min.
Answer: B
A no.when divided by 158 gives a remainder 50, what remainder will be obtainedby dividingthe same no.16?	Choose the correct choice from the following answers
A) 10
B) 11
C) 12
D) 13
E) 14

Solution: 158 + 50= 
158 + 50 = 208
208/16= 
208/16 = 13
13 (Remainder)   13
Answer: D
In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?	Choose the correct choice:	A) 16 sec	B) 18 sec	C) 19 sec	D) 10 sec	E) 17 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
If selling price of 12 pens is equal to the cost price of 18 pens, find the profit percent. Choices
A) 50%  B) 58%  C) 59%  D) 51%  E) 55%

Solution: Explanation:   Selling price of 12 pens = cost price of 18 pens   Therefore, the profit is 6 pens and cost price is 12 pens.   % profit = profit/cost price * 100   = 6/12 * 100= 
6/12 * 100 = 50
50%   50%NSWER: 50%
Answer: A
The probability that a convenience store has no iced tea is 60%. If Karl is stopping by 3 convenience stores on his way to work, what is the probability thatat least oneof the stores will not have a can of iced tea?	Select:
A) 1/8
B) 1/4
C) 1/2
D) 3/4
E) 7/9

Solution: p=1-3/5^3(all stores have iced tea)=7/9   7/9
Answer: E
If a and b are the roots of the equation x2 - 9x + 9 = 0, then the value of a2 + b2 is:
Choose the correct choice from the following answers.
A) 63 B) 24 C) 17 D) 6 E) 5

Solution: Sol.(b) The sum of roots = a+ b = 9   Product of roots = ab = 9   Now, a2 + b2 = (a + b)2 - 2ab = 81 - 18= 
81 - 18 = 63
63   63nswer 63
Answer: A
A businessman earns $26800 in December, thus decreasing his average annual (January to December) earnings by $1200. His average annual earnings would be
Source: CMAT Preparation
Pick:
A) $29000  B) $33500  C) $40000  D) $41000  E) $42300

Solution: (x - 26,800)/11 - x/12 = 1,200   x = 480,000   x/12 = 40,000   Answer: $40000.
Answer: C
An insect leaps 72 centimeters in 1.5 seconds. What is its speed?	Pick one.
A) 90 centimeters per second  B) 10.8 centimeters per second  C) 1.08 meters per second  D) 4.8 centimeters per second  E) 0.48 meters per second

Solution: 72 / 1.5= 
72 / 1.5 = 48
48 cm/s= 0.48 m/s   The answer is 0.48 meters per second.
Answer: E
A room contains 200 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room? Select the correct option
A) 0 B) 05 C) 10 D) 15 E) 20

Solution: Say group of x people left the room.   # of women in the room was 0.15*200= 
0.15*200 = 30
30;   # of women in the group that left 0.3x;   # of women in the room after the group left it is 0.1(160-x);   So, 30-0.3x= 0.1(200-x) --> x=10.   Answer: 10.
Answer: C
A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 45% are drinking beer, 40% are drinking mixed drinks, and 15% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?
Choose the correct choice from the following choices:
A) 1/2 B) 4/7 C) 10/17 D) 7/24 E) 7/10

Solution: Suppose there are 100 students   Group 1/2 : 40% = 40 students   45% drink beer = 18   40% mixed = 16   15% both = 6   Group B 60% = 60   30% beer= 18   30% mixed = 18   20% both= 12   now we need both ( beer + mixed = both)   probability = total beer drinker = 18+18= 
18+18 = 36
36 and both= 20   thus 18/36 = 1/2   Hence 1/2
Answer: A
Which of these following integers is the square of an integer?  Pick one:
A) 20821304103	B) 20571304329	C) 20467304228	D) 20453304487	E) 20814304592

Solution: The unit digit of any perfect square can not be 2, 3, 7, or 8.   The answer is 20571304329.
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 38 years now, the son's age five years back was:	Choose the correct choice from the following.
A) 24 years	B) 33 years	C) 14 years	D) 18 years	E) 9 years

Solution: Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years.   answer :14 years
Answer: C