RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The function f(Y) represents the number of ways that prime numbers can be uniquely summed to form a certain number Y such that Y = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?
A.4
B.5
C.6
D.7
Answer: D.7
Explanation: It is so better to start with 2 and check whether sum of two primes is primes is even.
1) 2(6 times)
2) 2(3 times) + 3(2 times)
3) 2(2 times) + 3 + 5
4) 2 + 3 + 7
5) 2 + 5 + 5
6) 3(4 times)
7) 5 + 7
Answer: D
Question: In what time will Rs.4400 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
A.7 4/3
B.7 4/6
C.7 4/7
D.7 1/2
Answer: C.7 4/7
Explanation: (4400*3*R)/100 = (5000*5*4)/100
R = 7 4/7
Answer: C
Question: In Josephs convent school,80% are boys at the same time 75% are girls students.If 88% are boys students then, what is percentage of the girls students in the particular school?
A.54
B.41
C.50
D.39
Answer: B.41
Explanation: Percentage of boys students = 80%; Percentage of girls students = 70% (ie) 0.75; Total = 0.7*100; Percentage of boys students = 88-80 = 8; Percentage of girls students =100-70 =30; So total Percentage of girls students =0.70*30=21;
Total Percentage of girls students = 30+21=41 Answer: B
Question: A can have a piece of work done in 10 days, B can work two times faster than the A, C can work three times faster than A. How many days will they take to do the work together ?
A.3/5 days
B.5/2 days
C.4/3 days
D.can't say
Answer: B.5/2 days
Explanation: A's 1 day work is 1/15
B's 1 day work is 2/15
C's 1 day work is 3/15
(A+B+C)'s 1 day work(1/15+2/15+3/15) is 2/5
so, they can finish the work in 5/2 days
ANSWER:B
Question: A card player is dealt a poker hand of 5 cards. Considering that there are 12 face cards and 40 other cards in a deck of cards, how many hands are there in which the player will be dealt 2 face cards and 3 other cards?
A.410,860
B.580,420
C.652,080
D.712,600
Answer: C.652,080
Explanation: (12c2)*(40c3)
i.e.
[12!/(2!*10!)]*[40!/(3!*37!)]
66*9,880
652,080
C
Question: The ratio of flour to water to sugar in a recipe is 10:6:3. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 2 cups of water, how much sugar is required?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: The ratio of flour to water is 10:3.
The ratio of flour to sugar is 5:3=10:6.
The new ratio of flour to water to sugar is 10:3:6
If we need 2 cups of water, then we need 4 cups of sugar.
The answer is B.
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 20 years now, the son's age five years back was:
A.9 years.
B.8 years.
C.7 years.
D.5 years.
Answer: D.5 years.
Explanation: Let the son's present age be x years. Then, (20- x) = x
2x = 20
x = 10.
Son's age 5 years back (10 - 5) = 5 years.
Answer: Option D
Question: A rectangular lawn of dimensions 100 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
A.A)3820
B.B)930
C.C)9309
D.D)4500
Answer: D.D)4500
Explanation: Explanation:
Area = (l + b – d) d
(100 + 60 – 10)10 => 1500 m2
1500 * 3 = Rs.4500
Answer: Option D
Question: Find the compound ratio of (4:3), (1:3) and (2:3) is
A.16:27
B.12:13
C.13:14
D.14:15
Answer: A.16:27
Explanation: Required ratio = 4/3 * 1/3 * 2/3 = 16/27 = 16:27
Answer is A
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
A.77
B.88
C.72
D.66
Answer: C.72
Explanation: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph.Answer:C
Question: In a game of billiards, A can give B 40 points in 80 and he can give C 70 points in 80. How many points can B give C in a game of 100?
A.18
B.27
C.25
D.75
Answer: D.75
Explanation: A scores 80 while B score 40 and C scores 10.
The number of points that C scores when B scores 100 = (100 * 10)/40 = 25
In a game of 100 points, B gives (100 - 25) = 75 points to C.
Answer: D
Question: There are 4 children and 3 chairs. In how many ways children can occupy the chairs?
A.76
B.84
C.56
D.24
Answer: D.24
Explanation: total children = 4
total chairs = 3
1st chair can be occupy in 4ways
2nd chair can be occupy in 3ways
3rd chair can be occupy in 2ways
total number of ways = 4*3*2 = 24 ways
correct option is D
Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
A.4:5:6
B.3:4:5
C.1:2:3
D.2:3:4
Answer: D.2:3:4
Explanation: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
= (140/100 x 5x), (150/100 x 7x) and (175/100 x 8x)
= 7x, 21x/2 and 14x.
Therefore, The required ratio = 7x : 21x/2 : 14x
= 14x : 21x : 28x
= 2 : 3 : 4.
Answer is D.
Question: What is the least value of x. So that 24x57 is divisible by 3.
A.2
B.0
C.1
D.3
Answer: B.0
Explanation: Explanation:
The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 4 + x + 5 + 7 = 18 + x
Least value of x may be 0
Therefore 18 + 0 = 18 is divisible by 3.
Answer: Option B
Question: At what rate percent on simple interest will Rs.850 amount to Rs.950 in 5 years?
A.2.35%
B.5.95%
C.4.35%
D.5.33%
Answer: A.2.35%
Explanation: 100 = (850*5*R)/100
R = 2.35%
ANSWER:A
Question: The work done by a man, a woman and a child is in the ratio of 3:2:1. There are 20 men, 30 women & 48 children in a factory. Their weekly wages amount to Rs.840, which is divided in the ratio of work done by the men, women and children. What will be the wages of 15 men, 21 women & 30 children for 2 weeks?
A.Rs.1000
B.Rs.1100
C.Rs.1170
D.Rs.1190
Answer: C.Rs.1170
Explanation: sax Ratio of wages of 20 men, 30 women
and 45 chﬂdren perweek
: (3 x 2o):(2 x 30) (1 x 43) 5
Total wages or 20 men per week
= R5 300
Therefore, wages of a man per week : Rs 15,
sirmlarly, wages of woman per week
: Rs 10 and wages ofchwld perweek Rs 5
Total wages of (15 men, 21 women and 30
chﬂdrenj perweek
= 15x15 + 21x10 + 30x5 = 585
Total wages for 2 weeks = Rs.1170
C
Question: When x divided by 288, the remainder is 47. Find the remainder when the same x is divided by 24?
A.20
B.21
C.23
D.25
Answer: C.23
Explanation: 23
Option C
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
A.76 kg
B.76.5 kg
C.85 kg
D.None of these
Answer: C.85 kg
Explanation: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Answer: Option C
Question: 34.95 + 240.016 + 23.98 = ?
A.298.946
B.289.946
C.298.964
D.298.496
Answer: A.298.946
Explanation: 34.95
240.016
+ 23.98
--------
298.946
Answer is A.
Question: What is the difference between the CI on Rs. 5000 for 1 years at 4% per annum CI yearly and half yearly?
A.Rs. 2.04
B.Rs. 2.12
C.Rs. 2.23
D.Rs. 3
Answer: A.Rs. 2.04
Explanation: C.I. when interest
compounded yearly
= Rs. 5000 x 1 +	4 x 1 + x 4
100	100
= Rs. 5000 x	26	x	51
25	50
= Rs. 5304.
C.I. when interest is
compounded half-yearly
= Rs. 5000 x 1 +	2 3
100
= Rs. 5000 x	51	x	51	x	51
50	50	50
= Rs. 5306.04
Difference = Rs. (5306.04 - 5304) = Rs. 2.04
A
Question: Which of the following describes all values of x for which 1–x^2 < 0?
A. x > 1
B. x < –1
C. 0 <= x <= 1
D. x < –1 or x > 1
Answer: D. x < –1 or x > 1
Explanation: Which of the following describes all values of x for which 1–x^2 >= 0?
(A) x > 1
Plugged in 2. 1–(2)^2 >= 0 -3>=0? yes. But are these all the values? No. Wrong
(B) x < –1
Plugged in -2. 1–(-2)^2 >= 0 -3>=0? yes. But are these all the values? No. Wrong.
(C) 0 <= x <= 1
Start with 0. 1-0 = 1. Wrong. All the other values wrong as well.
(D) x <= –1 or x >= 1
This is the Correct Answer as it captures both A and B. Answer is D.
(E) –1 <= x <= 1
Plug in 0. Value is greater than 0. Wrong.
Which of the following describes all values of x for which 1–x^2 >= 0?
(A) x >= 1
Plugged in 2. 1–(2)^2 >= 0 -3>=0? yes. But are these all the values? No. Wrong
(B) x <= –1
Plugged in -2. 1–(-2)^2 >= 0 -3>=0? yes. But are these all the values? No. Wrong.
(C) 0 <= x <= 1
Start with 0. 1-0 = 1. Wrong. All the other values wrong as well.
(D) x <= –1 or x >= 1
This is the Correct Answer as it captures both A and B. Answer is C.
(E) –1 <= x <= 1
Plug in 0. Value is greater than 0. Wrong.
Which of the following describes all values of x for which 1–x^2 >= 0?
(A) x >= 1
Plugged in 2. 1–(2)^2 >= 0 -3>=0? yes. But are these all the values? No. Wrong
(B) x <= –1
Plugged in -2. 1–(-2)^2 >= 0 -3>=0? yes. But are these all the values? No. Wrong.
(C) 0 <= x <= 1
Start with 0. 1-0 = 1. Wrong. All the other values wrong as well.
(D) x <= –1 or x >= 1
This is the Correct Answer as it captures both A and B. Answer is C.
(E) –1 <= x <= 1
Plug in 0. Value is greater than 0. Wrong.
Correct Answer is D.
Question: AV + CD = AAA, where AV and CD are two-digit numbers and AAA is a three digit number; A, V, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
A. 1
B. 3
C. 7
D. 9
Answer: D. 9
Explanation: Since AV and CD are two-digit integers, their sum can give us only one three digit integer of a kind of AAA: 111.
So, A=1 and we have 1V+CD=111
Now, C can not be less than 9, because no two-digit integer with first digit 1 (1V<20) can be added to two-digit integer less than 90, so that to have the sum 111 (if CD<90, so if C<9, CD+1V<111).
Hence C=9.
Answer: D.
Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 45. What is the difference between the two digits of that number?
A.4
B.5
C.6
D.8
Answer: B.5
Explanation: Sol.
Let the ten’s digit be x and unit’s digit be y,
Then, (10x + y) - (10y + x) = 45 ⇔ 9 (x - y) = 45
⇔ x - y = 5
Answer B
Question: How many 4's are there in the following series which are preceded by 7, but are not preceded by 8?
3 4 5 7 4 3 7 4 8 5 4 3 7 4 9 8 4 7 2 7 4 1 3 6
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: count 1 - - - - - - 7 4 3
count 2------------748
count 3------------749
count 4------------741
ANSWER:D
Question: Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3850. What is the difference between Rohan’s and Sudhir’s share in the profit?
A.s.345
B.s.350
C.s.352
D.s.362
Answer: B.s.350
Explanation: Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 3850 × 1/11 = Rs.350.
B
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
A.128
B.150
C.882
D.272
Answer: B.150
Explanation: 1/2 * 20(9 + 6) = 150 cm2
Answer: B
Question: A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was :
A.665
B.376
C.998
D.1277
Answer: A.665
Explanation: Explanation:
Let the total score be x.
(x + 92 - 85) / 8 = 84.
So, x + 7 = 672 => x = 665.
Answer: A) 665
Question: If e≠f and e·f≠0, which of the following may be true?
A.e=f
B.e.f=0
C.(e+f)(e-f)=0
D.e^2 = f^2
Answer: C.(e+f)(e-f)=0
Explanation: except c all conditions are not as per question
C
Question: A vendor sells 50 percent of the apples he had and throws away 20 percent of the remainder. The next day, the vendor sells 50 percent of the remaining apples and throws away the rest. In total, what percent of his apples does the vendor throw away?
A.30
B.35
C.40
D.45
Answer: A.30
Explanation: Let x be the original number of apples.
On day one, the vendor throws away (0.2)(0.5)x=0.1x.
The remaining apples are (0.8)(0.5)x = 0.4x.
On day two, the vendor throws away (0.5)(0.4)x=0.2x.
The vendor throws away a total of 0.1x + 0.2x = 0.3x.
The vendor throws away 30 percent of the apples.
The answer is A.
Question: In what time will a railway train 64 m long moving at the rate of 46 kmph pass a telegraph post on its way?
A.3
B.5
C.4
D.6
Answer: B.5
Explanation: T = 64/46 * 18/5 = 5 sec
Answer:B
Question: If it takes two teams of factory workers 6 days to complete a task. How many days will it take each team working separately, to complete the same task if it will take one of the teams 3 days earlier to complete the task.
A.10 and 15
B.5 and 8
C.4 and 7
D.9 and 12
Answer: A.10 and 15
Explanation: Work = (A)(B)/(A+B) where A and B are the individual times of each entity.
Here, we're told that (working together) the two teams would complete a job in 6 days. This means that (individually) each team would take MORE than 6 days to do the job.
Answers E, B and C are illogical, since the individual times must both be greater than 6 days.
so we can TEST the values for Answers D and E.
Using the values for Answers D and A, we have...
Answer D: (9)(12)/(9+12) = 108/21 = 5.14 This is NOT a match
Answer A: (10)(15)/(10+115) = 150/25 = 6 This IS a match
Final Answer:
A
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 60% goods during theft. His loss percent is:
A.72%
B.42%
C.56%
D.12%
Answer: C.56%
Explanation: Explanation:
Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 40.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 40 = Rs. 44
Hence, loss % = 56/100 * 100 = 56%
Answer:C
Question: If green means red, red means yellow, yellow means blue, blue means orange and orange means green, what is the colour of blood ?
A.Blue
B.Red
C.Yellow
D.Green
Answer: D.Green
Explanation: Explanation:
The colour of blood is 'red' and as given 'green' means 'red'.
so, the colour of blood is 'green'.
Answer: D
Question: For which of the following functions f is f(z) = f(1-z) for all z?
A.f (x) = 1 - x
B.f (z) = 1 - z^2
C.f (z) = z^2 - (1 - z)^2
D.f (z) = z^2*(1 - z)^2
Answer: D.f (z) = z^2*(1 - z)^2
Explanation: I remember seeing this problem in a GMATprep test. I think choice D should be F(z)=(z^2) (1-z)^2. If that is true then substituting (1-z) for will give us the same function back and the answer choice is D, where the function is multiplicative
Question: Which is a better investment 8% stock at 212 or 6 2/3 stock at 350?
A.8% stock at 212
B.6 2/3 stock at 350
C.None
D.Both are equally good
Answer: B.6 2/3 stock at 350
Explanation: Let investment in each case be Rs. (212 x 350).
Income in 1st case = Rs. 8 x 212 x 212/350= Rs. 1027.29.
Income in 2nd case = Rs.20 x 212 x 350/(3*350)= Rs. 1413.3
Clearly, 6 2/3 stock at 350 is better.
ANSWER:B
Question: If 24 men working for 12 hrs a day can do a work in 16 days, in how many days can 8 men working 6 hrs a day do it?
A.12 days
B.24 days
C.36 days
D.96 days
Answer: D.96 days
Explanation: Explanation :
24 men 12 hrs 16 days
8 men 6 hrs ? days (n)
n =16 X (12 / 6) X (24 / 8) ( since no of hrs reduced no of days has to increase and no of men reduced also increases no of days i.e., inverse proportional)
=> n = 96 days.
Answer : D
Question: A train running at the speed of 80 km/hr crosses a pole in 10 seconds. What is the length of the train?
A.450 m
B.350 m
C.150 m
D.250 m
Answer: D.250 m
Explanation: Speed=(90* 5/18) m/sec =25 m/sec Length of the train = (Speed x Time) = (25* 10) m = 250 m. Answer: D
Question: A truck carrying cans of paint contains P stacks. Each stack contains P/4 cases, and each case contains 2P cans. How many cans of paint are contained in 8 trucks?
A.4P
B.4P^3
C.P^2/8
D.P^3/4
Answer: B.4P^3
Explanation: There are 2P cans in each case.
There are P^2/2 cans in each stack.
There are P^3/2 cans in each truck.
There are 4P^3 cans in 8 trucks.
The answer is B.
Question: If on an item a company gives 25% discount, they earn 25% profit.If they now give 10% discount then what is the profit?
A.30
B.40
C.50
D.60
Answer: A.30
Explanation: let market price =100
then sp=75
but they earn 25% so= (100/125)*75
= 60
so cp=60
now again 10% discount on 100=90
so profit is =90-60
=30
ANSWER:A
Question: An amount of Rs.40,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
A.2378
B.2697
C.10000
D.5000
Answer: C.10000
Explanation: Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 40,000
Thus we get, 2Q + Q + Q + 4Q = 40,000
8Q = 40,000 or Q = Rs. 5000
Thus, R = Rs. 2500, P = 10000 & S = Rs. 20000
Hence, the required difference = (S – P) = (20000 – 10000) = Rs. 10000
ANSWER:C
Question: If $1088 are divided between worker A and worker B in the ratio 5:11,what is the share that worker B will get?
A.62.45%
B.64.55%
C.66.65%
D.68.75%
Answer: D.68.75%
Explanation: Worker B will get 11/16 = 68.75%
The answer is D.
Question: Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did?
A.
A.2 minute and 12 seconds.
B.two minutes.
C.44 seconds.
D.20 seconds.
Answer: D.20 seconds.
Explanation: om is running alone for 20 seconds.
So he will cover a distance of 20*2.5 = 50 m in 20 seconds.
Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side :)
D is the answer
Question: On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?
A.0
B.3
C.5
D.11
Answer: C.5
Explanation: Let x be the number and y be the quotient. Then,
x = 357 x y + 39
= (17 x 21 x y) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
Required remainder = 5.
Answer :C
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
A.9
B.4
C.7
D.3
Answer: B.4
Explanation: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Question: Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
A.6
B.6.25
C.7.25
D.7.5
Answer: B.6.25
Explanation: Required run rate = 282 - (3.2 x 10) =	250 = 6.25
40	40
B
Question: Albert is 2 times Mary’s age and 4 times as old as Betty. Mary is 10 years younger than Albert. How old is Betty?
A.5
B.8
C.10
D.12
Answer: A.5
Explanation: A = 2M = M+10
M = 10
A = 20
A = 4B, and so B = 5
The answer is A.
Question: On a certain transatlantic crossing, 40 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 20 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
A.20%
B.40%
C.50%
D.60%
Answer: C.50%
Explanation: Let T be the total number of passengers.
Let x be the number of people with round trip tickets.
0.4T had round trip tickets and took their cars.
0.8x had round trip tickets and took their cars.
0.8x = 0.4T
x = 0.5T
The answer is C.
Question: If MEDICAL is written as EFNJDBM and VERSION is written as SFWTJPI then PROBLEM is written as
A.CPSQMFN
B.NQOCMFN
C.PSQCMFN
D.PSQCMFM
Answer: C.PSQCMFN
Explanation: M E D I C A L
13 4
E F N J D B M
5 14
1st and 3rd letters sum is same i.e.,13=5=18 and d+n=18
and the remaining letters are increased by 1 ((e,f),(i,j),(c,d),....
for version also sequence is same....
follow the same sequence for problem :
answer is : PSQCMFN
ANSWER:C
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
A.1
B.2
C.7
D.4
Answer: B.2
Explanation: 1250 = D(100/4)2
D = 2
Answer:B
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
A.6 days
B.4 days
C.8 days
D.5 days
Answer: B.4 days
Explanation: 1/7 + 1/14 + 1/28 = 7/28 = 1/4
=> 4 days
Answer: B
Question: Look at this series: 8, 22, 8, 28, 8, ... What number should come next?
A.36
B.28
C.44
D.34
Answer: D.34
Explanation: D
34
This is a simple addition series with a random number, 8, interpolated as every other number. In the series, 6 is added to each number except 8, to arrive at the next number.
Question: Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
A.1 ≤ n ≤23
B.3 ≤ n ≤21
C.5 ≤ n ≤19
D.6 ≤ n ≤18
Answer: B.3 ≤ n ≤21
Explanation: ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer
Question: An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 30 cm, find the sum of the perimeters of all the triangles.
A.180 cm
B.220 cm
C.240 cm
D.270 cm
Answer: A.180 cm
Explanation: We have 30 for first triangle, when we join mid-points of first triangle we get the second equilateral triangle then the length of second one is 15 and continues.
So we have 30,15,7.5,...
We have ratio = 1/2, and it is GP type.
Sum of infinite triangle is a/1-r = 30/1-(1/2) = 60
Equilateral triangle perimeter is 3a = 3*60 = 180.
So option A.
Question: What is the decimal equivalent of (1/6)^2?
A.0.0016
B.0.0625
C.0.16
D.0.278
Answer: D.0.278
Explanation: (1/6)² = (1/6)(1/6)= 1/36
APPROACH #1: use long division to divide 36 into 1 to get 1/36 = 0.0278
D
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
A.2500 m^2
B.2510 m^2
C.2520 m^2
D.2540 m^2
Answer: C.2520 m^2
Explanation: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Question: A father is twice as old as his son. 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is
A.33
B.44
C.45
D.46
Answer: B.44
Explanation: Let son’s age = x. Then father’s age = 2x
12 (x - 20) = (2x - 20)
10x = 220
x = 22
Father’s present age = 44 years.
ANSWER:B
Question: A swimmer can swim in still water at 4 km/h. If the speed of the water current is 2 km/h, how many hours will the swimmer take to swim against the current for 7 km?
A.3.0
B.3.25
C.3.5
D.3.75
Answer: C.3.5
Explanation: The swimmer can swim against the current at a speed of 4-2 = 2 km/h.
The time it will take is 7/2 = 3.5 hours.
The answer is C.
Question: Suresh borrowed some money at the rate of 6% p.a. for the first two years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?
A.s.8500
B.s.6000
C.s.8500
D.s.9000
Answer: C.s.8500
Explanation: using the formula S.I=P*T*R/100
(x*6*2/100)+(x*9*5/100)+(x*13*3/100)=8160
x=8500
i.e money borrowed is Rs.8500
ANSWER:C