RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A shop sells bicycles and tricycles. In total there are 7 cycles (cycles include both bicycles and tricycles) and 19 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.
A.b=2,t=3
B.b=5,t=3
C.b=6,t=2
D.b=2,t=5
Answer: D.b=2,t=5
Explanation: Let b be the number of bicycles and let t be the number of tricycles.
Set up the equations
b+t=7............(1)
2b+3t=19............(2)
Rearrange equation (1) and substitute into equation (2)
t=7-b
2b+21-3b=19
-b=-2
b=2
Calculate the number of tricycles t
t=7−b
=7−2
=5
There are 5 tricycles and 2 bicycles.
Answer is D.
Question: What is the lowest positive integer that is divisible by each of the odd integers between 9 and 15 inclusive?
A.3×17×19×21
B.5×17×19×23
C.7×15×17×19
D.15*11*13
Answer: D.15*11*13
Explanation: We should find the LCM of 9= 3*3,11,13 and 15 = 3*5 --> LCM = 15*11*13
Answer: D.
Question: In how many ways can the letters of the word CAREER be arranged?
A.180
B.2500
C.2000
D.2520
Answer: A.180
Explanation: CAREER has 6 words, but E and R are repeated two times. Thus ways = 6! / 2!*2! = 180 ways
A
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1250. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
A. 2480
B. 3490
C. 6785
D. 8225
Answer: D. 8225
Explanation: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:
16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2
Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.
= (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)
Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:
2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15 = 3600
So the sum must be 3375 + 1240 + 3600 = 8215
Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of
30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)
then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have
= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)
and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have
= 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)
In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals
15*15*62/2 = 6975
and adding back the 1250, we get the answer of 8225. (ANS D)
Question: A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most -.
A.216
B.243
C.215
D.729
Answer: C.215
Explanation: Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 - 1 = 215.
ANSWER:C
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
A.17 min
B.18 min
C.15 min
D.30 min
Answer: D.30 min
Explanation: Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
x/2 * 1/15 = 1 => x = 30 min.
Answer:D
Question: The length of rectangle is thrice its breadth and its perimeter is 40 m, find the area of the rectangle?
A.432
B.212
C.75
D.992
Answer: C.75
Explanation: 2(3x + x) = 40
l = 15 b = 5
lb = 15 * 5 = 75
Answer:C
Question: Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
A.s.1200
B.s.1542
C.s.1528
D.s.1540
Answer: A.s.1200
Explanation: A+B+C = 2600
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 2600 = Rs.1200
Answer: A
Question: Find the least number which when divided by 5,6,7,8 leaves a remainder 3 but when divided by 9 leaves no remainder
A.9632
B.7896
C.8741
D.1683
Answer: D.1683
Explanation: L.C.M Of 5,6,7,8=840
required number is of the form of 840K+3
least value of k for which (840k+3)is divided by 9 is k =2
required number=(840*2+3)=1683
Answer(D)
Question: A certain company charges $6 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. If the company charged $32 to ship a certain package, which of the following was the weight of the package, in pounds?
A.9
B.11
C.13
D.15
Answer: C.13
Explanation: Let the weight of the package be X.
2X + 6= 32
X = 13
The answer is C.
Question: A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 140 km downstream
A.3 hours
B.4 hours
C.5 hours
D.6 hours
Answer: C.5 hours
Explanation: Explanation:
Speed of the boat in still water = 24 km/hr
speed of the stream = 4 km/hr
Speed downstream = (22+5) = 28 km/hr
Distance travelled downstream = 140 km
Time taken = distance/speed = 140/28 = 5 hours
Answer: Option C
Question: 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?
A.11
B.17
C.18
D.21
Answer: D.21
Explanation: 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: D
Question: If v=4p where p is a prime number greater than 2, how many different positive even divisors does v have, including v?
A.two
B.three
C.four
D.six
Answer: C.four
Explanation: 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)=C
Question: 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?
A.20
B.22
C.25
D.26
Answer: A.20
Explanation: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Question: 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?
A.3:2
B.2:1
C.3:3
D.1:2
Answer: D.1:2
Explanation: 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
D
Question: 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
A.3
B.2
C.1
D.4
Answer: C.1
Explanation: 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 C
Question: 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?
A. 2 hr
B. 2hr 20 min
C. 2hr 40 min
D. 5 hr 40 min
Answer: C. 2hr 40 min
Explanation: Server J processes 480/4 files per hour = 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 per hour = 180 files per hour
480/180 = 2 2/3 hours=C
Question: 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
A.25:16
B.24:25
C.5:6
D.4:5
Answer: B.24:25
Explanation: 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 = 96 sq. units
Question asked = Area of the rectangle : Area of the square = 96:100 ==> 24:25=B
Question: A lady bought four books namely A,B,C,D to distribute her 6 children. How many ways she can distribute books?
A.6^3
B.6^4
C.6^5
D.6^6
Answer: B.6^4
Explanation: 6*6*6*6
6^4
ANSWER:B
Question: 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?
A.7000
B.7320
C.8000
D.9000
Answer: D.9000
Explanation: Let B's capital be Rs. x.
Then,(3500 / 12)/7x	=	2/3
14x = 126000
x = 9000.
answer :D
Question: 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?
A.8 ml
B.5 ml
C.14.5 ml
D.6 ml
Answer: C.14.5 ml
Explanation: 10.5 10.5
30% 70%
30% ----- 10.5
70% ------? => 24.5 - 10.5 = 14.5 ml
Answer:C
Question: Sum of ages of two friends is 30 while difference is 2 then their ages are
A.15 years, 17 years
B.16 years, 14 years
C.24 years, 1 years
D.18 years, 16 years
Answer: B.16 years, 14 years
Explanation: 16,14
ANSWER:B
Question: 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?
A.5/12
B.7/12
C.12/5
D.7/5
Answer: C.12/5
Explanation: 1/R = 1/x + 1/y
1/R = 1/4+1/6 = 5/12
R = 12/5
The answer is C.
Question: 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)?
A.45; 8.
B.20; 7.
C.30; 9.
D.80; 12.
Answer: C.30; 9.
Explanation: 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 = 6 square feet of yard per dog
Question: 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…?
A.1
B.2
C.4
D.6
Answer: B.2
Explanation: 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=4 C is out
1+3+....15= 81 A is out
1+3+5+7=16 D is out
1+3+5=9 E i out
Answer: B
Question: 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?
A.700 m
B.500 m
C.670 m
D.600 m
Answer: D.600 m
Explanation: Distance covered by Amar
= 18/4.8 (1.6km)
= 3/8(1600) = 600 m
Answer: D
Question: 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?
A.9.37 p.m
B.9.20 p.m
C.9.30 p.m
D.9.38 p.m
Answer: C.9.30 p.m
Explanation: D = 60 * 1 Â½ = 90 km
RS = 75 â€“ 60 = 15
T = 90/15 = 6 h
3.30 + 6 h = 9.30 p.m.
Answer: C
Question: Simplify: 500 x 500- 200 x 200
A.761200
B.761400
C.761800
D.210000
Answer: D.210000
Explanation: (500)^2 - (200)^2 = (500 + 200) (500 - 200) = 700 x 300 = 210000.
Answer is D.
Question: 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:
A.6 hours
B.10 hours
C.15 hours
D.30 hours
Answer: C.15 hours
Explanation: 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:C
Question: Look at this series: (1/9), (1/3), 1, ____ , 9, ... What number should fill the blank?
A.(2/3)
B.3
C.6
D.27
Answer: B.3
Explanation: Explanation: This is a multiplication series; each number is 3 times the previous number.
Answer: Option B
Question: A palindrome is a number that reads the same forward and backward, such as 120. How many odd, 4-digit numbers are palindromes?
A.40
B.55
C.50
D.90
Answer: B.55
Explanation: 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 = 55 ways
B
Question: 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?
A.4
B.3
C.2
D.1
Answer: A.4
Explanation: 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 = 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 = 4%
Answer: A
Question: 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?
A.14300
B.24883
C.14500
D.14600
Answer: B.24883
Explanation: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100^5 = 24883
B)
Question: 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)
A.288,000,000
B.240,000
C.2,400,000
D.24,000,000
Answer: A.288,000,000
Explanation: A. 288,000,000
12*100*6*100*4*100 = 288,000,000
Question: 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?
A.20
B.30
C.40
D.60
Answer: D.60
Explanation: If each side is 120 feet..then total perimeter is 150*4=600
poles every 10 feet hence no of poles= 600/10=60
ANSWER:D
Question: Look at this series: 53, 53, 43, 43, 33, 33, ... What number should come next?
A.A)23
B.B)14
C.C)27
D.D)53
Answer: A.A)23
Explanation: In this series, each number is repeated, then 10 is subtracted to arrive at the next number.
Answer: A
Question: 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?
A.2
B.3
C.4
D.5
Answer: D.5
Explanation: 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 D.
Question: 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?
A. 340
B. 304
C. 352
D. 300
Answer: C. 352
Explanation: 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 C.
Question: In a simultaneous throw of two dice, what is the probability of getting a total of 7?
A.1/6
B.1/4
C.2/3
D.3/4
Answer: A.1/6
Explanation: 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.
Answer A.
Question: 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, ...)?
A.(a) 80
B.(b) 55
C.(c) 82
D.(d) 83
Answer: B.(b) 55
Explanation: 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=11 such multiples.
So, final number of sets is 11*5=55
Answer : B
Question: 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?
A.237
B.268
C.132
D.827
Answer: C.132
Explanation: 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 = 12C2 ×2 = 132
Answer: C
Question: 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?
A.176 m
B.178 m
C.120 m
D.187 m
Answer: C.120 m
Explanation: Speed = (12/10 * 60) km/hr
= (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Question: How many ways are there to arrange the letters in the word Settees ?
A.210
B.1260
C.3780
D.7560
Answer: A.210
Explanation: 7 total words, 3E, 2S, 2T
= 9! / 3! 2! 2! = 210. Answer A
Question: 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?
A.a. 3/5
B.b.2/3
C.c.7/10
D.d.3/4
Answer: A.a. 3/5
Explanation: X(10) --- Net(0) --- T(-15) = -15/-10 = 3/2.
So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).
Question: 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?
A.40 km/hr
B.55 km/hr
C.65 km/hr
D.70 km/hr
Answer: A.40 km/hr
Explanation: 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.
Ans A
Question: 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?
A. 18.0%
B. 62.0%
C. 79.2%
D. 82.22%
Answer: D. 82.22%
Explanation: 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 D)
Question: 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?
A.52 sec
B.50 sec
C.51 sec
D.55 sec
Answer: B.50 sec
Explanation: B
50 sec
The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Question: 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?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: 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:B
Question: The fourth proportional to 12, 14 and 18 is?
A.21
B.66
C.88
D.99
Answer: A.21
Explanation: (14*18)/12 = 21
Answer: A
Question: If x + y = 0 and x =/ 0,then what is the value of
x2007/y2007?
A.-2007
B.-1
C.0
D.1
Answer: B.-1
Explanation: x = −y=/0,so x/y=-1
correct answer B
Question: 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?
A.1/6
B.2/9
C.6/11
D.9/16
Answer: A.1/6
Explanation: 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
Answer: option A
Question: 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?
A.$408
B.$816
C.$1224
D.$800
Answer: A.$408
Explanation: 1.04*1.04*5000 = $5408
The answer is A.
Question: The average of first three prime numbers greater than 20 is?
A.10
B.20
C.30
D.27.7
Answer: D.27.7
Explanation: 23 + 29 + 31 = 83/3 = 27.7
ANSWER:D
Question: 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?
A.300
B.250
C.230
D.250
Answer: B.250
Explanation: 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 B
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
A.3944
B.2999
C.2666
D.2888
Answer: A.3944
Explanation: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58
= Rs.3944.
Answer: A
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
A.150
B.180
C.190
D.200
Answer: B.180
Explanation: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
ANSWER B