MU-NLPC/Calc-aqua_rat huggingface dataset:
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 1323 sq m, then what is the breadth of the rectangular plot?  Select.
A) 11 B) 17 C) 18 D) 21 E) 1322

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 1323   3b2 = 1323   b2 = 441 = 21 (b > 0)   b = 21 m.   Answer: 21
Answer: D
If v=4p where p is a prime number greater than 2, how many different positive even divisors does v have, including v?
Answers:  A) two  B) three  C) four  D) six  E) eight

Solution: v=2, 2, p (p is in the prime factorization since were told it is a prime number in the question)   2   4 (because of 2*2)   2p (because of 2 * p)   4p (because of 2 * 2 * p)=four
Answer: C
Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?  Choose the correct choice from the following answers:	A) 20	B) 22	C) 25	D) 26	E) 29

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131   a + b + c = √400 = 20   20
Answer: A
If 8 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
Choose the correct choice:
A) 3:2
B) 2:1
C) 3:3
D) 1:2
E) 6:1

Solution: 8M + 2B = 4(1M + 1B)   8M + 2B = 4M + 4B   4M = 2B   The required ratio of work done by a man and a boy = 2:4=1:2   1:2
Answer: D
If the following is true, can you find the value of (4 + 9)?
7 + 7 = 2
8 + 8 = 4
8 + 5 = 1
6 + 9 = 3
10 + 11 = 9
Select the correct option: A) 3 B) 2 C) 1 D) 4 E) 5

Solution: Solution:   1   Explanation:   4 + 9 = 1   The trick to solve is to assume the first number as the time in AM and the second number is the number of hours you have to add to it. You'll find the time in PM when you do that.   For example   7 AM + 7 hours = 14:00 or 2 PM   4 AM + 9 hours = 13:00 or 1 PM.   Answer 1
Answer: C
While working alone at their respective constant rates, server J uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files?
Pick one.
A) 2 hr B) 2hr 20 min C) 2hr 40 min D) 5 hr 40 min E) 6hr

Solution: Server J processes 480/4= 
480/4 = 120
120 per hour   Server Y processes 180/8 files per hour= 60 per hour   Total files processed per hour when J and Y work together = 120+60= 
120+60 = 180
180 files per hour   480/180= 2 2/3 hours=2hr 40 min
Answer: C
If the perimeter of square region Z and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of Z	Choose the correct choice from the following choices
A) 25:16	B) 24:25	C) 5:6	D) 4:5	E) 4:9

Solution: We know Perimeter of a square (Pz) = 4*side   Perimeter of a rectangle (Pr) = 2(length+breath)   Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)   Therefore,   Pz = Pr = 40   Area of the square = 100 sq. units   We know 2(length+breadth) = 40   i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)   Therefore length = 8, breath = 12   Area of the rectangle = 8*12= 
8*12 = 96
96 sq. units   Question asked= Area of the rectangle : Area of the square = 96:100 ==> 24:25=24:25
Answer: B
A lady bought four books namely A,B,C,D to distribute her 6 children. How many ways she can distribute books?  Choose the correct choice from the following answers:  A) 6^3  B) 6^4  C) 6^5  D) 6^6  E) 6^2

Solution: 6*6*6*6   6^4   ANSWER:6^4
Answer: B
A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?	Choose the correct choice
A) 7000  B) 7320  C) 8000  D) 9000  E) 9200

Solution: Let B's capital be Rs. x.   Then,(3500 / 12)/7x	=	2/3   14x = 126000   x = 9000.   answer :9000
Answer: D
The amount of water (in ml) that should be added to reduce 21 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is? Choose the correct choice:
A) 8 ml
B) 5 ml
C) 14.5 ml
D) 6 ml
E) 1 ml

Solution: 10.5 10.5   30% 70%   30% ----- 10.5   70% ------? => 24.5 - 10.5 = 14.5 ml   Answer:14.5 ml
Answer: C
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red? Choose the correct answer.
A) 12/428 B) 12/420 C) 12/455 D) 12/429 E) 12/413

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   When three marbles are drawn, the probability that one is yellow and two are red   = (212/4551)(412/4552)/1512/4553   = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)   = 12/455   Answer:12/455
Answer: C
Sum of ages of two friends is 30 while difference is 2 then their ages are Choose the correct choice from the following answers:
A) 15 years, 17 years
B) 16 years, 14 years
C) 24 years, 1 years
D) 18 years, 16 years
E) None

Solution: 16,14   ANSWER:16 years, 14 years
Answer: B
In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 4 Ohms and y is 6 Ohms?	Answers:
A) 5/12
B) 7/12
C) 12/5
D) 7/5
E) 11/5

Solution: 1/R = 1/x + 1/y   1/R = 1/4+1/6 = 5/12   R = 12/5   The answer is 12/5.
Answer: C
Lawrence is interested in dividing his backyard into equal pens for his dogs. Unfortunately, it does not divide equally. It turns out that in order for the yard to divide equally, Lawrence has to buy an additional six square feet of land and sell three of his dogs.. Which of the following can describe the number of square feet of the initial yard and the initial number of dogs (in the order square feet, dogs)?	Choose the correct choice
A) 45; 8.	B) 20; 7.	C) 30; 9.	D) 80; 12.	E) 35; 7

Solution: Option C) Initially 9 dogs then reduced to 6 dogs; and Initially 30 square feet of yard increased to 36 square feet of yard fits the requirement.   36 / 6= 
36 / 6 = 6
6 square feet of yard per dog
Answer: C
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...
For every positive integer n that is greater than 1, the function d(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The d(n) could have any of the following units digits except…?	Choose the correct choice
A) 1	B) 2	C) 4	D) 6	E) 9

Solution: For every positive integer n that is greater than 1, the function d(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The d(n) could have any of the following units digits except…?   Used brute force on this one to calculate. Not sure if there is a quicker way.   1+3= 
1+3 = 4
4 C is out   1+3+....15= 81 A is out   1+3+5+7= 
1+3+5+7 = 16
16 D is out   1+3+5= 
1+3+5 = 9
9 E i out   Answer: 2
Answer: B
Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km? Pick
A) 700 m B) 500 m C) 670 m D) 600 m E) 640 m

Solution: 600 mistance covered by Amar   = 18/4.8 (1.6km)   = 3/8(1600) = 600 m   Answer: 600 m
Answer: D
A train moves with a speed of 216 kmph. Its speed in metres per second is
Choose the correct choice from the following answers
A) 10.8	B) 18	C) 30	D) 38.8	E) 60

Solution: Solution   Speed	= 216 Kmph   = (216 x 5/18)m/sec   = 60 m/sec.   Answer 60
Answer: E
A train sets off at 2 p.m. at the speed of 60 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet? Choose the correct choice from the following.
A) 9.37 p.m
B) 9.20 p.m
C) 9.30 p.m
D) 9.38 p.m
E) 9.10 p.m

Solution: D = 60 * 1 Â½ = 90 km   RS = 75 â€“ 60 = 15   T = 90/15= 
90/15 = 6
6 h     3.30 + 6= 
  3.30 + 6 = 9.3
9.30 p.m.   Answer: 9.30 p.m
Answer: C
If the average costs of three colors of 20,40,60 chocolates respectively is 10,15,20 what is the average costs of all the chocolates? Choose the correct answer
A) 12.22	B) 13.33	C) 14.44	D) 15.55	E) 16.66

Solution: Average costs of group 1 =10   chocolates in group 1 = 20   Total costs of group 1 = 10*20   Average costs of group 2 = 15   chocolates in group 2 = 40   Total costs of group 2 = 15*40   Average costs of group 3 = 20   chocolates in group 3 = 60   Total costs of group 3 = 20*60   Total chocolates = 20+40+60= 
20+40+60 = 120
120   Average costs of all the chocolates=((10*20)+(15×40)+(20*60))/120   =50/3   =16.66   Answer is 16.66.
Answer: E
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:	Pick.
A) 6 hours	B) 10 hours	C) 15 hours	D) 30 hours	E) 35 hours

Solution: suppose first pipe filled the tank in x hour   so second in x-5 and third in x-9   1/x+1/(x-5)=1/(x-9)   by solving it we get x=15   ANSWER:15 hours
Answer: C
Rahul went to a shop and bought things worth Rs. 35, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  Choose the correct choice from the following options:	A) A)19.7	B) B)19.9	C) C)20.9	D) D)21.9	E) E)29.7

Solution: Total cost of the items he purchased = Rs.35   Given that out of this Rs.35, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (35−30/100−x)6/100 = 30/100   ⇒ 6(35 −0.3 −x) = 30   ⇒ (35 − 0.3 − x) = 5   ⇒ x = 35 − 0.3 − 5 = 29.7   29.7)
Answer: E
Look at this series: (1/9), (1/3), 1, ____ , 9, ... What number should fill the blank? Choose the correct option:  A) (2/3)  B) 3  C) 6  D) 27  E) 28

Solution: Explanation: This is a multiplication series; each number is 3 times the previous number.   Answer: Option 3
Answer: B
A palindrome is a number that reads the same forward and backward, such as 120. How many odd, 4-digit numbers are palindromes? Choose the correct choice from the following choices.
A) 40	B) 55	C) 50	D) 90	E) 2500

Solution: A palindrome is a number that reads the same forward and backward. Examples of four digit palindromes are 1221, 4334, 2222 etc   You basically get to choose the first two digits and you repeat them in opposite order. Say, you choose 45 as your first two digits. The next two digits are 54 and the number is 4554.   Also, you need only odd palindromes. This means that you need an odd digit at the end i.e. 1/3/5/7/9. This means that you need to start the number with an odd digit. Only then will it end with an odd digit.   In how many ways can you pick two digits such that the first one is an odd digit?   The first digit can be selected in 5 ways.(1/3/5/7/9)   The second digit can be selected in 10 ways.(0/1/2/3...8/9)   Total = 5*11= 
5*11 = 55
55 ways   55
Answer: B
For which of the following functions is f(r+b)=f(r)+f(b) for all positive numbers r and b?  Choose the correct choice from the following: A) a) f(x)=x^2 B) b) f(x)=x+1 C) c) f(x)=root x D) d) f(x)=2/x E) e) f(x)= -3x

Solution: f(r+b)=f(r)+f(b) Its e) f(x)= -3x
Answer: E
A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?  Choose the correct choice:
A) 4
B) 3
C) 2
D) 1
E) 8

Solution: SP of first article = 1000   Profit = 20%   CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3   SP of second article = 1000   Loss = 20%   CP = (SP)*[100/(100-L)] = 5000/4= 
5000/4 = 1_250
1250   Total SP= 2000   Total CP = 2500/3 + 1250 = 6250/3   CP is more than SP, he makes a loss.   Loss = CP-SP = (6250/3)- 2000 = 250/3   Loss Percent = [(250/3)/(6250/3)]*100   =0.04 * 100= 
0.04 * 100 = 4
4%   4nswer: 4
Answer: A
The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 5 years? Choose the correct choice from the following:
A) 14300
B) 24883
C) 14500
D) 14600
E) 15400

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   10000 × 120/100^5 = 24883   24883)
Answer: B
If a rectangular room measures 12 meters by 6 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter=100 centimeters)  Select the correct option:  A) 288,000,000  B) 240,000  C) 2,400,000  D) 24,000,000  E) 240,000,000

Solution: A. 288,000,000   12*100*6*100*4*100 = 288,000,000
Answer: A
Mr. loyd wants to fence his Square shaped land of 150Sqft each side.If a pole is laid every 10ft how many poles do he need?
Select
A) 20 B) 30 C) 40 D) 60 E) 65

Solution: If each side is 120 feet..then total perimeter is 150*4= 
150*4 = 600
600   poles every 10 feet hence no of poles= 600/10= 
600/10 = 60
60   ANSWER:60
Answer: D
Look at this series: 53, 53, 43, 43, 33, 33, ... What number should come next? Choose the correct choice
A) A)23
B) B)14
C) C)27
D) D)53
E) E)86

Solution: In this series, each number is repeated, then 10 is subtracted to arrive at the next number.   23nswer: 23
Answer: A
Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin
Choose the correct choice from the following choices:  A) 23.5  B) 24.5  C) 12.5  D) 14.5  E) 13.6

Solution: Explanation:   If Rahul age is x, then Sachin age is x-7,   so (x-7)/x = 7/9   => 9x-63 = 7x   => 2x = 63   => x = 31.5   So Sachin age is   31.5 - 7= 
  31.5 - 7 = 24.5
24.5   Answer: Option 24.5
Answer: B
A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 14,907,200,000 pounds, how many widgets have been unloaded?  Choose the correct choice from the following answers.
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: We need to know the number of widgets (which weigh 5 pounds each). The number of times that 5 divides the number is related to the number of times that 10 divides the number.   When we divide 14,907,200,000 by 100,000, we get 14,907,200,000 = 149,072 * 5^5 *2^5.   149,072 is not divisible by 5, thus there are 5 widgets.   The answer is 5.
Answer: D
The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 9000, brokerage being 1/4%, is:
Choose the correct answer:
A) 113.2  B) 114  C) 114.75  D) 124  E) 124.75

Solution: Face Value = Rs. 9000.   Dividend = 10.5%.   Annual Income = Rs. 756.   Brokerage per Rs. 100 = Rs. 0.25.   Dividend is always paid on the face value of a share.   Face Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income.   = 9000 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100.   = Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 125.   = Market Value of Rs. 100 stock = Rs. 125 - Re. 0.25.   = Market Value of Rs. 100 stock = Rs. 124.75.   answer : 124.75
Answer: E
A drought decreased the amount of water stored in State J reservoirs from 200 billion gallons to 150 billion gallons. If the drought decreased the amount of water in the reservoirs to 30 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the rain? Choose the correct option.
A) 340
B) 304
C) 352
D) 300
E) 350

Solution: After the reservoir is filled to 150 gallons the amount of water is at 30% - which means that 70% of the reservoir is empty. To figure out what that 70% is : 150 gallons /30 percent = x gallons /70 percent , therefore, x = 350 gallons , answer choices A,B,E,D are below 350 . We know that the reservoir must be short more than 350 gallons, therefore, the only possible choice is 352.
Answer: C
In a simultaneous throw of two dice, what is the probability of getting a total of 7? Pick one:	A) 1/6	B) 1/4	C) 2/3	D) 3/4	E) 4/5

Solution: We know that in simultaneous throw of two dice, n(S) = 6 x 6 = 36.   Let E = event of getting a total of 7 ={(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}   P(E) = n(E)/n(S) = 6/36 = 1/6.   1/6nswer 1/6.
Answer: A
Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 66. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?  Pick.
A) (a) 80 B) (b) 55 C) (c) 82 D) (d) 83 E) (e) 84

Solution: T1: 1,2,3,4,5   T2: 2,3,4,5,6   T3: 3,4,5,6,7   etc.   means that every multiple of 6 will be involved in 5 sets. We have (66-6)/6+1= 
(66-6)/6+1 = 11
11 such multiples.   So, final number of sets is  11*5= 
 11*5 = 55
55   Answer : (b) 55
Answer: B
12 members were present at a board meeting. Each member shake hands with all of the other members before and after the meeting .How many hand shakes were there?	Choose the correct choice from the following.
A) 237 B) 268 C) 132 D) 827 E) 261

Solution: Explanation:   In order to have a hand shake there must be two members. Therefore to select 2 out of 12 we have 12C2.   This happens twice that is before and after the meeting   Answer = 121322 ×2 = 132   Answer: 132
Answer: C
A group of students was interviewed for that if it was asked whether or not they speak French and / or English. Among those who speak French, 20 speak English well, while 60 of them do not speak English. If 60% of students do not speak French, how many students were surveyed?
Choose the correct choice from the following:
A) 250
B) 225
C) 175
D) 195
E) 200

Solution: Number of students who speak French are 60 + 20= 
60 + 20 = 80
80   Of total students, the percentage of students who do not speak French was 60% --> percentage of who do is 40%   80-------40%   x ------- 100%   x= 80*100/40= 
80*100/40 = 200
200= number of all students   Answer is 200
Answer: E
A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?  Choose the most appropriate option.
A) 176 m	B) 178 m	C) 120 m	D) 187 m	E) 144 m

Solution: Speed = (12/10 * 60) km/hr   = (72 * 5/18) m/sec   = 20 m/sec.   Length of the train = 20 * 6= 
20 * 6 = 120
120 m.   Answer: 120 m
Answer: C
How many ways are there to arrange the letters in the word Settees ?	Answers:
A) 210	B) 1260	C) 3780	D) 7560	E) 11340

Solution: 7 total words, 3E, 2S, 2T   = 9! / 3! 2! 2! = 210. 210nswer 210
Answer: A
John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment T that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?  Choose the correct choice.
A) a. 3/5
B) b.2/3
C) c.7/10
D) d.3/4
E) e.4/5

Solution: X(10) --- Net(0) --- T(-15) = -15/-10 = 3/2.   So, John invested 3/3+2= 
3/3+2 = 3
3/5 of his savings in investment X. a. 3/5ns (a. 3/5).
Answer: A
A retailer bought a machine at a wholesale price of $126 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?  Options
A) 81  B) 100  C) 120  D) 135  E) 168

Solution: My solution: Wholesale Price= 126   Retail Price, be = x   He provides 10 % discount on Retail price= x-10 x/100   This Retail price = 20 % profit on Wholesale price   x-10 x/100 = 126+ 1/5(126)   x=168;   ANSW168R:168
Answer: E
A train met with an accident 40km away from station A. It completed the remaining journey at 5/6th of the original speed and reached station B 1hr 12mins late. Had the accident taken place 60km further, it would have been only 1hr late. what was the original speed of the train?	Pick
A) 40 km/hr
B) 55 km/hr
C) 65 km/hr
D) 70 km/hr
E) 48 km/hr

Solution: let the original speed be 6x. A/q, traveling 40 km at 5/6th of original speed costs him 12 minutes etc   40/5x =40/6x +12/40 -> x =10 , 4x= 40.   40 km/hrns 40 km/hr
Answer: A
At a certain conference, 74% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance?	Choose the correct choice from the following answers
A) 18.0%	B) 62.0%	C) 79.2%	D) 82.22%	E) 82.0%

Solution: I do not think that Venn will be helpful here. A table will make more sense. But here is my approach.   74% regestered at least 2 weeks and paid full fee.   10% paid full fee and did not registered at least 2 weeks in advance. Then 90% paid full fee and registered at least 2 weeks before.   90% *X=74% where X is the number of people who registerd 2 weeks in advance and paid full fee. (ANSWER 82.22%)
Answer: D
How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?	Choose one.
A) 52 sec B) 50 sec C) 51 sec D) 55 sec E) 58 sec

Solution: B   50 sec   The distance to be covered = Sum of their lengths = 200 + 300= 
200 + 300 = 500
500 m.   Relative speed= 72 -36= 
72 -36 = 36
36 kmph= 36 * 5/18= 
36 * 5/18 = 10
10 mps.   Time required= d/s = 500/10= 
500/10 = 50
50 sec.
Answer: B
The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits? Choose the correct option:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: Let the two-digit number be 10a + b   a = b + 2 --- (1)   10a + b = 7(a + b) => a = 2b   Substituting a =   2b in equation (1), we get   2b = b + 2 => b = 2   Hence the units digit is: 2.   ANSWER:2
Answer: B
The fourth proportional to 12, 14 and 18 is? Choices.
A) 21
B) 66
C) 88
D) 99
E) 26

Solution: (14*18)/12= 
(14*18)/12 = 21
21   21nswer: 21
Answer: A
Which of the following describes all values of x for which 25-x^2 ≥ 0 ? Pick.
A) x ≥ 1
B) x ≤ -1
C) 0 ≤ x ≤ 1
D) x ≤ -1 or x ≥ 1
E) -5 ≤ x ≤ 5

Solution: 25-x^2 >= 0 ---> x^2-25<=0   --> (x+5)(x-5)<=0   Above equation true for   i) x+5<=0 and x-5>=0 ---> x<= -5 and x>=5 ---> this is not possible ---Strike out this solution   ii) x+5>=0 and x-5<=0 ---> x>=-5 and x<=5 --> -5<=x<=5   Answer -5 ≤ x ≤ 5
Answer: E
In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that both pen will be defective? Choose the correct answer:
A) 1/6
B) 2/9
C) 6/11
D) 9/16
E) 3/4

Solution: Method- 1   There are 9 fine pieces of pen and 3 defective in a lot of 12 pens   i.e. Probability of first pen being defective = (1/3)   i.e. Probability of Second pen being defective = (1/2)   Probability of Both pen being defective = (1/2)*(1/3) = 1/6   1/6nswer: option 1/6
Answer: A
An investor bought a 1-year $5,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?  Choose the correct option.
A) $408	B) $816	C) $1224	D) $800	E) $400

Solution: 1.04*1.04*5000= 
1.04*1.04*5000 = 5_408
$5408   The answer is $408.
Answer: A
The average of first three prime numbers greater than 20 is?
Choose the correct option.
A) 10  B) 20  C) 30  D) 27.7  E) 50

Solution: 23 + 29 + 31= 
23 + 29 + 31 = 83
83/3= 27.7   ANSWER:27.7
Answer: D
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?  Options
A) 300	B) 250	C) 230	D) 250	E) 260

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.   Answer: Option 250
Answer: B