RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: One thief entered a cave where he found a pile of diamonds. At first he thought of taking all. But listening to his conscience he thought of taking only half of them. But while returning he picked up two more from the pile. After that Second thief entered the cave and bagged half of remaining diamonds and picked up two more while returning. Later third thief entered and did the same. Even the fourth thief did the same. When the fifth thief entered he found only one diamond in the cave. How many diamonds are there in the cave at first.
A.74
B.75
C.76
D.77
Answer: C.76
Explanation: When 5th thief entered-1 diamond
When 4th thief entered -(1+2)*2=6 diamonds
When 3rd thief entered -(6+2)*2=16 diamonds
When 2nd thief entered -(16+2)*2=36 diamonds
When 1st thief entered -(36+2)*2=76 diamonds
ANSWER:C
Question: If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 8 m of the same rod?
A.22.8 kg
B.25.6 kg
C.28 kg
D.30.4 kg
Answer: D.30.4 kg
Explanation: Explanation :
Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)
=> 11.25 : 8 :: 42.75 : x
=> 11.25 x x = 8 x 42.75
=> x = (8 x 42.75) / 11.25
=> x = 30.4
Answer : D
Question: Of the 10 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
A.22
B.50
C.56
D.70
Answer: B.50
Explanation: another approach :
one scenario : [WWWM]
now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.
and 5 ways to select one man
so 5*4*3*5 = 300
now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways
hence 300/3!= 300/6=50
B
Question: I had a certain amount of candies with me. I gave half of them with one more to my first son. Then, I gave the remaining half with one more to the younger son. Now I was left with just one candy.
How much candies did I have in the beginning?
A.10
B.15
C.22
D.25
Answer: A.10
Explanation: A
I had 10 candies in the beginning.
Explanation:
Let us take and solve this problem in the reverse direction.
At the end, I was left with 1 candy. Let me take the extra one candy back from my younger son. Now since I gave him half of what I had, we must be having the same number of candies. I have 2, which means he also have 2. This implies that I was left with 4 candies after I gave some to the elder son.
Let me take back the extra candy from my elder son now. Now I have 5 candies. Since I gave him half of what I had, he must be having 5 candies as well. Thus, I had 10 candies in the beginning.
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
A.Rs.250
B.Rs.280
C.Rs.290
D.Rs.299
Answer: A.Rs.250
Explanation: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But 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
A
Question: Three numbers are in the ratio 3:4:5 and their L.C.M. is 1800. Their H.C.F is?
A.20
B.30
C.40
D.50
Answer: B.30
Explanation: Let the numbers be 3x,4x and 5x
their L.C.M. = 60x
60x = 1800
x = 30
The numbers are 3*30 , 4*30 , 5*30
Hence required H.C.F. = 30
Answer is B
Question: A and B complete a work in 3 days. A alone can do it in 9 days. If both together can do the work in how many days?
A.3.75 days
B.4.75 days
C.3.25 days
D.3.15 days
Answer: B.4.75 days
Explanation: 1/3 + 1/9 = 4/9
9/4 = 4.75 days
Answer: B
Question: What is the probability, to 3 decimal places, that at least two people in a room share the same birthday if there are eleven people in the room? (Assume nobody was born on a leap year)
A.0.027
B.0.03
C.0.076
D.0.141
Answer: D.0.141
Explanation: First, find the probability that nobody has the same birthday: 364/365 * 363/365 * 362/365 * ... * 356/365 * 355/365 = 0.859. Then the correct answer is 1 - 0.859 = 0.141, so the correct answer is D
Question: The average of first 10 natural numbers is?
A.5.7
B.5.5
C.5.4
D.5.2
Answer: B.5.5
Explanation: Sum of 10 natural no. = 110/2
= 55
Average = 55/10
=5.5
Answer: B
Question: A farmer is planting a row consisting of 4 unique apple trees and 5 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?
A.512
B.5760
C.1,024
D.1,152
Answer: B.5760
Explanation: 2 possible arrangements are possible
AOAOAOAO
OAOAOAOA
2 unique type of trees are present consisting of 4 trees each
4 apple trees can be arranged in 4! ways
4 orange trees can be arranged in 4! ways
as 2 arrangements are possible
total arrangements = 2 *4! * 5! = 5760
correct answer option B
Question: A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
A.3 hrs 48 min
B.3 hrs 45 min
C.3 hrs 85 min
D.3 hrs 75 min
Answer: B.3 hrs 45 min
Explanation: Time taken by one tap to fill the tank = 3 hrs.
Part filled by the taps in 1 hour = 4 * 1/6 = 2/3
Remaining part = 1 - 1/2 = 1/2
2/3 : 1/2 :: 1 : x
x = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min
So, total time taken = 3 hrs 45 min.
Answer: B
Question: In an election between two candidates, the winner has a margin of 10% of the votes polled. If 4000 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?
A.16000
B.10000
C.40000
D.12000
Answer: C.40000
Explanation: Winner - Looser
55% - 45%
If 4000 people change their mind and vote for the loser:
Winner - Looser
45% - 55%
Thus 4,000 people compose 25% of all voters, which means that the total number of votes is
40,000
Answer: C
Question: 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 48 years now, the son's age five years back was:
A.A)14
B.B)67
C.C)19
D.D)89
Answer: C.C)19
Explanation: Let the son's present age be x years. Then, (48 - x) = x
2x = 48.
x = 24.
Son's age 5 years back (24 - 5) = 19 years.
Answer:C
Question: What is the probability for a family with four children to have a girl and three boys (assuming the probability of having a boy or a girl is equal)?
A.1/2
B.1/3
C.1/4
D.1/8
Answer: C.1/4
Explanation: One possible case is: girl - boy - boy - boy
The probability of this is 1/2*1/2*1/2*1/2 = 1/16
There are 4C3 = 4 such cases so we should multiply by 4.
P(one girl and three boys) = 4/16 = 1/4
The answer is C.
Question: Tom opened a shop investing Rs.3000. Jose joined him 2 months later, investing Rs.4000. They earned a profit of Rs.4230 after completion of one year. What will be Jose's share of profit?
A.2000
B.2200
C.2309
D.2350
Answer: D.2350
Explanation: SoL = ~s- So Anju’s share = [5/9] x 4230 = 2350
D
Question: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 40, and 50 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?
A. 4/11
B. 1/2
C. 15/22
D. 200/9
Answer: D. 200/9
Explanation: P1 takes 12 hrs
Rate for P2P3 together = 1/40 + 1/50 = 9/200
Therefore they take 200/9
Ratio = 200/9 = D
Question: If X is to be chosen at random from the integers between 1 to 7, inclusive, and Y is to be chosen at random from the integers between 8 and 12, inclusive, what is the probability that X + Y will be even?
A.2/5
B.3/7
C.5/7
D.17/35
Answer: D.17/35
Explanation: X+Y will be even if X and Y are both even or both odd.
P(X and Y are both even) = 3/7*3/5 = 9/35
P(X and Y are both odd) = 4/7*2/5 = 8/35
P(X+Y is even) = 9/35 + 8/35 = 17/35
The answer is D.
Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
A.33
B.77
C.66
D.11
Answer: D.11
Explanation: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10
Remaining work = 7/10
The number of days required for this initial work = 7 days.
The total number of days required = 4 + 7 = 11 days.
Answer:D
Question: A reduction of 30% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
A.46
B.47
C.48
D.49
Answer: C.48
Explanation: 800*(30/100) = 240 ---- 5
? ---- 1 => Rs.48
Answer: C
Question: The number of positive integer solutions for the equation x +y +z + t = 30 is
A.3854
B.3654
C.3764
D.3960
Answer: B.3654
Explanation: The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k
(k-1)C(n-1)- where k is the number and n is number of variable in the equation.
30-1 C 4-1 = 29C3 = 3654
Answer : B
Question: Michael cashed a check for $1,100 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?
A. $630
B. $800
C. $770
D. $730
Answer: A. $630
Explanation: 1. 15 bills spent
2. Number of $10 bills is one more or one less than number of $50 bills.
So, 2 choices
1. 7*10 + 8*50 = $470
2. 8*10 + 7*50 = $430
Least money lost implies most money spent. i.e $470
Therefore, lost money = 1100 - 470 = 630.
Answer A
Question: Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel five times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?
A.4
B.6
C.8
D.9
Answer: B.6
Explanation: W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/5 and W = 5S
Then we have 1/(5*S) + 1/S = 1/5<=> 6/(5*S) = 1/5 <=> S = 6
ANS: B
Question: Mrs. B. invested $30,000; part at 5%, and part at 8%. The total interest on the investment was $2,100. How much did she invest at each rate?
A.x = $1,000, y = $29,000
B.x = $5,000, y = $25,000.
C.x = $10,000, y = $20,000.
D.x = $15,000, y = $15,000
Answer: C.x = $10,000, y = $20,000.
Explanation: 2100 = (30000-x) 5/100 + 8x/100
Solving, we get x = 20000
So, answer is 10000 & 20000
Answer = C
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
A.289
B.190
C.277
D.266
Answer: B.190
Explanation: Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10
= 190 sec.
Answer:B
Question: Q=(429)^2 * 237 * (1243)^3 is thrice of ?
A.33605 * 31960 * (1243)^2
B.33654 * 538219 * (1243)^2
C.33891 * 533247 * (1243)^2
D.34122 * 532004 * (1243)^2
Answer: C.33891 * 533247 * (1243)^2
Explanation: Q=(429)^2*237*(1243)^3 is an odd number.
Among answer choices only C is an odd number, (so thrice C also will be an odd number).
Answer: C.
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
A.22
B.88
C.12
D.99
Answer: C.12
Explanation: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C
Question: If 6^w is a factor of (10!)^2, What is the greatest possible value of w ?
A.2
B.4
C.6
D.8
Answer: D.8
Explanation: w 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7
6= 2*3
Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D
Question: A library has an average of 500 visitors on Sundays and 140 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
A.100
B.200
C.300
D.400
Answer: B.200
Explanation: Explanation:
Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (500 * 5 + 140 * 25) / 30 = 6000/30 = 200
Answer: B) 200
Question: What is 35% of 4/13 of 650?
A.50
B.60
C.70
D.80
Answer: C.70
Explanation: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 650, or 1/9 of 650. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
The number 650 is a bit more than 630, so (1/9)*630 will be about 70.
Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
The answer is C.
Question: A starts a business with $3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the
ratio 2 : 3. B's contribution in the capital is
A.7000
B.9000
C.8000
D.9900
Answer: B.9000
Explanation: Ratio in which profit is divided =2:3
Assume that B's contribution to the capital=b
3500×12:b×7=2:3
⇒3500×12×3=2×b×7
⇒b = 3500×12×3 / 2×7
=500×6×3=9000
ANSWER:B
Question: Together, Victor and Tami Vargas earn $33,280 per year. Tami earns $4,160 more per
year than Victor earns. How much do Tami earn per year?
A.$28,720
B.$8,720
C.$18,720
D.$38,720
Answer: C.$18,720
Explanation: You are asked to find two unknown amounts. Victor’s earnings: x
Represent the amounts using algebra. Tami’s earnings: x 4,160
Write an equation showing that the sum of the
two amounts is $33,280. Solve the equation. x x 4,160 33,280
Combine like terms. 2x 4,160 33,280
Subtract 4,160 from both sides of the equation. 2x 4,160 4,160 33,280 4,160
2x 29,120
Divide both sides by 2.
x 14,560
Now go back to the beginning, when you first wrote the amounts in algebraic language. Since
x represents Victor’s earnings, you know that Victor earns $14,560 per year. Tami’s earnings are
represented by x+4,160. Add: 14,560+4,160=18,720. Tami earns $18,720 per year.
Answer: Victor earns $14,560, and Tami earns $18,720.
correct answer C
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 7% dividend at the end of the year,then how much does he get ?
A.Rs. 500
B.Rs. 840
C.Rs. 650
D.Rs. 720
Answer: B.Rs. 840
Explanation: Solution
Number of shares = (14400/120) = 120.
Face value = Rs. (100x120 ) = Rs. 12000.
Annual income = Rs.(7/100x12000) = Rs. 840.
Answer B
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.277
B.277
C.120
D.882
Answer: C.120
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: Four dice are thrown simultaneously. Find the probability that all of them show the same face.
A.1/216
B.1/215
C.5/300
D.1/415
Answer: A.1/216
Explanation: Total no of elementary events = 6^4
n(S) = 6^4
x={(1,1,1,1)(2,2,2,2).....(6,6,6,6)}
n(X)=6
n(X)/n(S) =6/6^4
=1/216
ANSWER A
Question: Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam?
A. 1/4
B. 12/47
C. 1/3
D. 5/12
Answer: B. 12/47
Explanation: Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.
adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work
R>( 60/47 *12)/60 =12/47
Answer B
Question: If five numbers are randomly selected without replacement from set {1, 2, 3, 4, 5}, what is the probability that the numbers are selected in ascending order?
A.1/256
B.1/120
C.1/480
D.1/240
Answer: B.1/120
Explanation: The total number of ways to arrange 5 numbers is 5! = 120.
There is only one way to arrange the numbers in ascending order.
P(ascending order) = 1/120
The answer is B.
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.
A.25years
B.45years
C.12years
D.6years
Answer: A.25years
Explanation: Total age of 39 persons = (39 x 15) years
= 585 years.
Average age of 40 persons= 15 yrs 3 months
= 61/4 years.
Total age of 40 persons = (_(61/4 )x 40) years= 610 years.
:. Age of the teacher = (610 - 585) years=25 years.
Ans: A
Question: In the first 10 overs of a cricket game, the run rate was only 3.6. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
A.6.25
B.6.5
C.6.15
D.7
Answer: C.6.15
Explanation: 10 overs - run rate = 3.6
runs scored in first 10 overs = 36
remaining overs 40
total runs to be scored= 282
32 runs already scored 282-36=246
246 runs to be scored in 40 overs
let required runrate be x
40*x=246
x=246/40
x=6.15
the required runrate is 6.15
ANSWER:C
Question: A cab driver 5days income was $25, $50, $60, $65 , $70. Then his average income is?
A.A)$58
B.B)$54
C.C)$65
D.D)$48
Answer: B.B)$54
Explanation: avg = sum of observations/number of observations
avg income=(25+50+60+65+70)/5 = 54
Answer is B
Question: What is the remainder when 14,456 × 15,657 × 16,788 is divided by 10?
A.6
B.8
C.4
D.3
Answer: A.6
Explanation: Only the unit's digit of the product will decide the remainder when divided by 10.
Hence, 6*7*8= will give units digit as 6
So, whatever be the number, if it ends in 6, the remainder after dividing with 10 will be 6.
OptionA
Question: In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,6). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?
A.1/5
B.1/3
C.1/2
D.2/3
Answer: D.2/3
Explanation: The area of the right triangle is (1/2)*4*6 = 12.
Only the points (a,b) below the line y=x satisfy a - b > 0.
The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.
P(a - b > 0) = 8/12 = 2/3
The answer is D.
Question: Rs. 6000 is lent out in two parts. One part is lent at 4% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
A.5:1
B.5:7
C.5:2
D.5:8
Answer: B.5:7
Explanation: Let the amount lent at 4% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 4/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 2500
Amount lent at 10% = 3500
Required ratio = 5:7
Answer:B
Question: 88% OF 370+24% OF 210-?=118
A.256
B.258
C.268
D.358
Answer: B.258
Explanation: LET 88% OF 370+240% OF 210-X=118
THEN, X=(88/100*370)+(24/100*210)-118-325.60+50.40-118=376-118=258
CORRECT OPTION: B
Question: The smallest number which when diminished by 8, is divisible 8, 16, 24, 32 and 40 is:
A.1008
B.1015
C.488
D.490
Answer: C.488
Explanation: Required number = (L.C.M. of 8, 16, 24, 32, 40) + 8
= 480 + 8
= 488
Answer: Option C
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 72.25, the number of the member is the group is:
A.57
B.67
C.77
D.85
Answer: D.85
Explanation: Explanation:
Money collected = (72.25 x 100) paise = 7225 paise.
∴ Number of members = √(7225) = 85.
Answer: D
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is
A.25/42
B.25/47
C.25/32
D.25/48
Answer: A.25/42
Explanation: :
Total fruits = 9
Since there must be at least two apples,
= 25/42.
Answer: A
Question: How many words can be formed by using all letters of the word ‘BIHAR’ ?
A.110
B.120
C.130
D.140
Answer: B.120
Explanation: Solution
The word BIHAR contains 5 different letters.
Required number of words = 5P5 = 5 ! = (5 x 4 x 3 x 2 x 1) = 120
Answer B
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 4 : 1 ?
A.6 months
B.3 months
C.2 months
D.8 months
Answer: A.6 months
Explanation: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 4. or x = (85000 * 12) / (42500 * 4) = 6.
So, B joined for 6 months.
Answer: A
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
A.1
B.3
C.5
D.6
Answer: A.1
Explanation: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Question: A, B and C rents a pasture for Rs.928. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
A.270
B.289
C.288
D.255
Answer: C.288
Explanation: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 928 = 288
Answer: C
Question: What is the difference between the place values of two sevens in the numeral 54707429 ?
A.699990
B.693000
C.99980
D.699930
Answer: B.693000
Explanation: Explanation:
Required Difference
= 700000 - 7000 = 693000
Answer is B
Question: In an election between two candidates first candidate got 65% of votes polled and second Candidate got 2800 votes. The total number of votes polled was?
A.7000 votes
B.8000 votes
C.9000 votes
D.9800 votes
Answer: B.8000 votes
Explanation: Total = 100 %,
First person got 65%
second person got remaining 35 % of votes.
than 35 % = 2800
35% = 35Ã—80 = 2800
100% =100Ã—80 =8000 votes
B
Question: Jason flips a coin three times. What is the probability W that the coin will land on the same side in all three tosses?
A.1/16
B.1/8
C.1/4
D.1/3
Answer: C.1/4
Explanation: Total outcome is 2^3=8
Favorable cases HHH or TTT
Therefore, probability W is 2/8 or 1/4.C
Question: From 5 positive numbers and 7 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?
A.720
B.625
C.250
D.960
Answer: C.250
Explanation: The number of ways to choose 4 positive numbers is 5C4 = 5.
The number of ways to choose 4 negative numbers is 7C4 = 35.
The number of ways to choose 2 positive and 2 negative is 5C2*7C2 = 10*21 = 210.
The total number of groups is 5+35+210 = 250.
The answer is C.
Question: If 2x^2 – y^2 = 2xy, then (x - y)^2 =
A.x^2
B.3x^2
C.4xy
D.2y^2-x^2
Answer: D.2y^2-x^2
Explanation: (x-y)^2 = x^2 + y^2 - 2xy = x^2 + y^2- 2x^2+y^2 = 2y^2-x^2
correct option : D
Question: A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference?
A.10 feet
B.8 feet
C.13 feet
D.15 feet
Answer: B.8 feet
Explanation: total circuit=16/4=4
total feet squirrel travels=4*2=8 feet
ANSWER:B
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
A.11
B.444
C.420
D.287
Answer: C.420
Explanation: 1h ----- 5
? ------ 60
12 h
RS = 14 + 21 = 35
T = 12
D = 35 * 12 = 420
Answer:C
Question: How many of the positive factors of 56 , 96 and how many common factors are there in numbers?
A.2
B.4
C.3
D.5
Answer: C.3
Explanation: factors of 56- 1, 2, 4, 7, 8, 14, 28, 56
factors of 96- 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Comparing both, we have three common factors of 56 and 96- 1,2,4
Answer(C)
Question: Two airplanes take off from one airfield at noon. One flies due east at 204 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?
A.166
B.408
C.400
D.483
Answer: B.408
Explanation: B
In two hours:
the plane flying East will be 408 miles away from airport.
the other plane will be 566 miles away from airport.
566/408 = ~1.4 = ~sqrt(2)
This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 408 miles apart.B