mathewhe/aqua_rat huggingface dataset:
Question: In August,a cricket team that played 120 matches won 30% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?
(A) 40
(B) 55
(C) 68
(D) 80
(E) 98
Rationale: let the no of matches played more=x
so,
(120+x)*52/100=36+x
by solving we get x=55
ANSWER:B
Answer: (B) 55
Question: If 3 boys can do 3 times of a particular work in 3 days, then, 7 boys can do 7 times of that work in
(A) 2 days
(B) 3 days
(C) 4 days
(D) 5 days
(E) 6 days
Rationale: That is, 1 boy can do one time of the work in 3 days.
Therefore, 7 boys can do 7 times work in the same 3 days itself.
B
Answer: (B) 3 days
Question: In how many ways can the letters of the word OCARINA be arranged if the O, R, and N remain in their original positions?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 48
Rationale: The word OCARINA has 7 letters and if the O, R, and N remain in their original positions
then we have 4 positions to arrange the remaining letters - C , 2A , I
Number of ways = 4!/2!
= 12
Answer B
Answer: (B) 12
Question: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/10
II. 1/9
III. 1/8
(A) None
(B) I only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us B as the only possible answer.
Answer: (B) I only
Question: A sum of Rs. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is ?
(A) 23
(B) 87
(C) 84
(D) 26
(E) 19
Rationale: Given total sum = Rs. 427
And given that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal.
=> 3A = 4B = 7C
But given
=> A + B + C = 427
Now express A and B in terms of C i.e
=> (7C/3) + (7C/4) + C = 427
=> C = 84
Answer: C
Answer: (C) 84
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 45 km/hr
(B) 50 km/hr
(C) 54 km/hr
(D) 55 km/hr
(E) 56 km/hr
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
ANSWER:B
Answer: (B) 50 km/hr
Question: What percent of 10 is 10 percent of 1?
(A) 0.1%
(B) 1%
(C) 10%
(D) 90%
(E) 100%
Rationale: 10 percent of 1 is equal to 0.1
So we have to compute what percent of 10 is 0.1. so this means we have to compute what percent of 100 is 1....so 1%
Answer B.
Answer: (B) 1%
Question: Running at the same constant rate, 6 identical machines can produce a total of 330 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
(A) 648
(B) 1800
(C) 2200
(D) 10800
(E) 10900
Rationale: Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines	6	:	10	:: 330 : x
Time (in minutes)	1	:	4
6 x 1 x x = 10 x 4 x 330
x =	(10 x 4 x 330)/(6)
x = 2200.
ANSWER:C
Answer: (C) 2200
Question: If p and r are integers, and p^2 = 18r, then r must be divisible by which of the following?
(A) 2
(B) 4
(C) 5
(D) 7
(E) 9
Rationale: Ans: D
Solution: for p to be an int 18 r must be whole square of a number.
18r= 9*2*r
to make it whole square we need 9
so r can must be divisible by 9y where y is itself a whole square.
so E is the ans
Answer: (E) 9
Question: 2+2+2^2+2^3+2^4+2^5=？
(A) (2^3-1)(2^3+1)
(B) 2^6
(C) 2^5-1
(D) 2^5+1
(E) 2^5-2
Rationale: From 2+2+2^2+2^3+2^4+2^5=64,
2^6=64
the correct answer is B.
Answer: (B) 2^6
Question: Machines A and B produce bottles at their respective constant rates. Machine A produces k bottles in 2 hours and machine B produces k bottles in 4 hours. How many hours does it take machines A and B, working simultaneously, to produce 15k bottles?
(A) 10
(B) 15
(C) 12
(D) 20
(E) 18
Rationale: A's rate = k/2
B's rate = k/4
k/2 + k/4 = 3k/4
15k / (3k/4) = 20 hours
The answer is D.
Answer: (D) 20
Question: There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?
(A) 1/13
(B) 2/13
(C) 3/17
(D) 4/17
(E) 8/21
Rationale: Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: (E) 8/21
Question: The relationship between quantities m and n is expressed by the equation 11m = 5(n - 52). If the difference between the two chosen values of n is 40, what is the difference in the corresponding values of m?
(A) 200/11
(B) 42/11
(C) 60/11
(D) 150/11
(E) 14
Rationale: Another Simple way
11m=5(n-52)
Assume n = 52 to make one side equal to 0
then 11m=0
and m = 0
Repeat it by assuming n as 52+40 i.e 92
11m= 5(92-52)
11m=200
m=200/11
diff = 200/11 - 0 = 200/11
Answer : A
Answer: (A) 200/11
Question: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 33 pints of Perfect Pink paint?
(A) 9
(B) 16
(C) 17
(D) 25 1/3
(E) 28 1/2
Rationale: 3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
33 pints will require 9/17 * 33= 17 pints..
C
Answer: (C) 17
Question: ramu sells gud for 27 per kg. but he has two plates for wighting one plate is 10% shorter then other.. he put 1 kg weight on shorter plat and apple on other plat.. at the end their is no profit no loss..what is cost price of apple
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: ramu is making profit of 10% on weight because he puts 1 kg on shorter site.
to balance this profit if there is decrease of 1/10 in weight then there should be increse of 1/9 in price so 1/9 of 27=3
cost price=27+3=30
ans=30
ANSWER:A
Answer: (A) 30
Question: Working alone, machine X can manufacture 1,000 nails in 16 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?
(A) 3 9/17
(B) 5 1/3
(C) 7
(D) 7 3/11
(E) 8 4/7
Rationale: rate of machine x = 1000/16
(1000/16 + y)5=1000
y=200-125/2=275/2
275/2 * t = 1000
t=7 3/11
D. 7 3/11
Answer: (D) 7 3/11
Question: A car covers a distance of 624 km in 6 ½ hours. Find its speed?
(A) 104 kmph
(B) 176 kmph
(C) 298 kmph
(D) 186 kmph
(E) 268 kmph
Rationale: 624/6
= 104 kmph
Answer:A
Answer: (A) 104 kmph
Question: At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:40 a.m., how long A will the conference last if there are a total of 6 seminars that day?
(A) 5 hours and 15 minutes
(B) 5 hours and 20 minutes
(C) 5 hours and 25 minutes
(D) 5 hours and 30 minutes
(E) 5 hours and 35 minutes
Rationale: Shouldnt the answer be 5 hours 20 mins?
Break = b
Seminar= 10b
9am to 11:40am= 160mins
3s+b=160
30b+b=160
b=160/31
6 seminar will take
6s+2b
=60b+2b
=62b
=62*160/31
=320
A=5 hours 20 mins.B
Answer: (B) 5 hours and 20 minutes
Question: A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss?
(A) 9
(B) 8
(C) 7
(D) 5
(E) 3
Rationale: (30*30)/100 = 9%loss
Answer: A
Answer: (A) 9
Question: Of the goose eggs laid at a certain pond, 1/3 hatched and 4/5 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
(A) 1025
(B) 1075
(C) 1125
(D) 1175
(E) 1225
Rationale: Let x be the number of eggs that were laid.
(2/5)(4/5)(1/3)x = 120
(8/75)x = 120
x = 1125
The answer is C.
Answer: (C) 1125
Question: The average expenditure of a man for the first five months is Rs.300 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :
(A) Rs.140
(B) Rs.150
(C) Rs.190
(D) Rs.225
(E) none
Rationale: Explanation:
Total income = Rs.(300Ã—5+130Ã—7+290)=Rs.2700
Average monthly income
= Rs. (2700/12)=Rs.225
Correct Option: D
Answer: (D) Rs.225
Question: 225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: 26 trees have 25 gaps between them,
Required distance (225/25) = 10
A
Answer: (A) 10
Question: The length of box 12 Cm long, 8 Cm breadth and 9Cm height. Find the length of pencil in that box?
(A) 19
(B) 14
(C) 17
(D) 16
(E) 13
Rationale: Diagonal (d) = √l(power2)+b(power2)+h(power2)
= √12(power2)+8(power2)+9(power2)
= √144+64+81
= √289 => 17 Cm
Answer is C.
Answer: (C) 17
Question: The average of 20 results is 65 and the average of other 65 results is 20 . what is the average of all the results?
(A) 30
(B) 25
(C) 48
(D) 50
(E) None
Rationale: Answer
Sum of 85 result = sum of 20 result + sum of 65 result.
= 20 x 65 + 65 x 20
= 2600
Correct Option: A
Answer: (A) 30
Question: The average of 10 numbers was calculated as 20. It is discovered later on that while calculating the average, one number, namely 86, was incorrectly read as 26. What is the correct average?
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: 10*20 - 26 + 86 = 260
260 / 10 = 26
The answer is E.
Answer: (E) 26
Question: In one hour, a boat goes 11km along the stream and 5 km against it. Find the speed of the boat in still water
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Explanation:
We know we can calculate it by 1/2(a+b)
=> 1/2(11+5) = 1/2(16) = 8 km/hr
ANSWER IS C
Answer: (C) 8
Question: If the function Q is defined by the formula Q = 5w/(4vf(z^2)), by what factor will Q be multiplied if w is quadrupled, f is doubled, and z is tripled?
(A) 1/9
(B) 2/9
(C) 4/9
(D) 3/9
(E) 2/27
Rationale: We just need to find the factor thats all,
w -> quadrupled -> 4w
f-> doubled -> 2f
z-> tripled -> 3Z
Hence, Z^2 = 9Z^2
W is in numerator, and f*z in denominator.
Hence,
Additional factor being introduced = 4/2*9
=4/18 = 2/9 = B
Answer: (B) 2/9
Question: A Train requires 12 seconds to pass a pole while it requires 27 seconds to cross a stationary train which is 300 mtrs long. Find the speed of the train.
(A) 60 kmph
(B) 75 kmph
(C) 80 kmph
(D) 85 kmph
(E) 72 kmph
Rationale: In 12s the train crosses the pole and in 27 sec the train crosses one more stationary train
In 15 sec the train travels a distance of 300 mtrs
Speed = 300/15 = 20 m/s = 20 (3600/1000) = 20 * 18/5 = 72 kmph
Answer: E
Answer: (E) 72 kmph
Question: 5/[(1/0.03) + (1/0.37)] = ?
(A) 0.004
(B) 0.1388
(C) 2.775
(D) 3.6036
(E) 36.036
Rationale: Approximate.
1/.03 = 100/3 = 33
1/.37 = 100/37 = 3
Denominator becomes 33 + 3 = 36
5/36 = .1388
Answer (B)
Answer: (B) 0.1388
Question: Machine A and machine B are each used to manufacture 220 sprockets. It takes machine A 10 hours longer to produce 220 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Machine B: Takes x hours to produce 220 sprockets
Machine A: Takes (x+10) hours to produce 220 sprockets
Machine B: In 1 hour, B makes 220/x sprockets
Machine A: In 1 hour, A makes 220/(x+10) sprockets
Equating:
1.1(220/(x+10)) = 220/x
242/(x+10) = 220/x
242x = 220x+2200
22x = 2200
x = 100
A makes 220/(110) = 2 sprockets per hour
Answer : A
Answer: (A) 2
Question: There was a cycle race going on. 1/5th of the those in front of a person and 5/6th of those behind him
gives the total number of participants. How many people took part in the race?
(A) 31
(B) 39
(C) 30
(D) 33
(E) 34
Rationale: Explanation :
Let total participants be (x+1)
Then
=> (1 / 5) * x + (5/6) * x = x+1
=> 31x/30=x+1
=> x=30
So total participants (x+1)=31
Hence (A) is the correct answer.
Answer : A
Answer: (A) 31
Question: The rate of a certain chemical reaction is directly proportional to the concentration of chemical B present and inversely proportional to the concentration of chemical A present. If the concentration of chemical B present is increased by 100 percent, which of the following is closest to the percent change in the the concentration of chemical B required to keep the reaction rate unchanged.
(A) 10 % decrease
(B) 50% decrease
(C) 40% decrease
(D) 30% increase
(E) 100% increase
Rationale: Let's say here is the formula of how B and A affects the reaction speed:
rate = B/A
After the concentration A is increased by 100%, the percentage of A
become 2A, to keep 'rate' the same, need to have 2B being doubled.
Which means A increased by 100%.
Answer : E
Answer: (E) 100% increase
Question: Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:
(A) 334
(B) 500
(C) 265
(D) 197
(E) 121
Rationale: Let the investment in 9% stock be Rs. x.
Then, investment in 10% stock = Rs. (9800 - x).
9	x x =	10	x (9800 - x)
75	80
3x	=	9800 - x
25	8
24x = 9800 x 25 - 25x
49x = 9800 x 25
x = 500
Answer:B
Answer: (B) 500
Question: Mr. Mike sold two books at $2.20 each. Based on the cost, his profit one was 20% and his loss on the other was 30%. On the sale of the books. Find the amount of his profit or loss?
(A) lost 10 cents
(B) lost 4 cents
(C) broke even
(D) lost amount 0.22 cents.
(E) gained 10 cents
Rationale: 20 % profit on $ 2.20
= $ 20/100 × 2.20
= $ 0.20 × 2.20
= $ 0.44
Similarly, 30 % loss on $ 2.20
= $ 30/100 × 2.20
= $ 0.30 ×2.20
= $ 0.66
Therefore, in one book his profit is $ 0.44 and in the other book his loss is $ 0.66.
loss amount 0.22 cents.
Answer is D.
Answer: (D) lost amount 0.22 cents.
Question: The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers
(A) 28,22
(B) 28,17
(C) 27,17
(D) 26,17
(E) 28,19
Rationale: If two numbers are x, y
x-y=11 --(i) & (x+y)/5=9 --(ii)
Solving (i) & (ii), x=28, y=17
ANSWER:B
Answer: (B) 28,17
Question: The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?
(A) 10 and 30
(B) 12 and 18
(C) 24 and 64
(D) 21 and 63
(E) 22 and 44
Rationale: 64 has only the prime 2 (64=2^6) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.
The answer is C.
Answer: (C) 24 and 64
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 3, and 5, if the digits are allowed to repeat within a number?
(A) 4551
(B) 5661
(C) 6771
(D) 7881
(E) 8991
Rationale: The number of these 3-digit numbers is 3*3*3 = 27
Each digit 1, 3, and 5 will appear in the ones, tens, and hundreds place 9 times each.
The sum equals 9(111) + 9(333) + 9(555) = 9(999) = 8991
The answer is E.
Answer: (E) 8991
Question: A straight fence is to be constructed from posts 8 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot)
(A) 17
(B) 28
(C) 35
(D) 39
(E) 50
Rationale: The fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}
The minimum length is with 2 posts = 0.5 + 5 + 0.5 = 6 feet. To increase the fence, each time we should add{post = 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:
6 feet;
8 + 5.5 = 13.5 feet;
11.5 + 5.5 = 19 feet;
17 + 5.5 = 24.5 feet;
22.5 + 5.5 = 30 feet;
28 + 5.5 = 35.5 feet;
33.5 + 5.5 = 41 feet.
...
We skipped 39 feet.
Answer: D.
Answer: (D) 39
Question: A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of q square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)
(A) (5,280 mt) / 12 q
(B) (5,280 pt) / 12m
(C) (5,280 pmt) /12
(D) (5,280)(12m) / pt
(E) (5,280)(12p) / mt
Rationale: Given that: 1 gallon of paint covers an area ofqsquare feet. Question:how many gallonsof paint will be needed ...
In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/q, so q must be in the denominator: eliminate all but A and D.
Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.
Answer: A.
Answer: (A) (5,280 mt) / 12 q
Question: Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite direction for 4 miles and then turn to left and run for another 3 miles.
what is the distance between the the two twins when they stop ?
(A) 11 miles
(B) 10 miles
(C) 9 miles
(D) 12 miles
(E) 13 miles
Rationale: B
10 miles
Answer: (B) 10 miles
Question: In the biology lab of "Jefferson" High School there are 0.037*10^5 germs, equally divided among 148000*10^(-3) Petri dishes. How many germs live happily in a single dish?
(A) 10
(B) 25
(C) 35
(D) 40
(E) 55
Rationale: 0.037*10^5 can be written as 3700
148000*10^(-3) can be written as 148
Required= 3700/148= 25
ANSWER:B
Answer: (B) 25
Question: The bankerâ€™s gain on a sum due 3 years hence at 12% per annum is Rs. 180. The bankerâ€™s discount is
(A) Rs.960
(B) Rs.840
(C) Rs.1020
(D) Rs.680
(E) None
Rationale: Solution
T.D	=(B.G x 100 / R x T)
= Rs.(180x100/12 x 3)
= Rs.500.
B.D
=Rs(500+ 180)
= Rs.680.
Answer D
Answer: (D) Rs.680
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 39
(B) 27
(C) 30
(D) 288
(E) 291
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer: C
Answer: (C) 30
Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 9 businessmen, how many possible team submissions are possible?
(A) 76
(B) 100
(C) 162
(D) 198
(E) 202
Rationale: P(at least one Tech)= p(total) - P( no tech)
=13c3 - 9c3
=198 (Ans :D )
Answer: (D) 198
Question: If the cost price of 65 chocolates is equal to the selling price of 50 chocolates, the gain percent is :
(A) 35%
(B) 10%
(C) 20%
(D) 30%
(E) 33%
Rationale: Explanation :
Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 50 chocolates = Rs. 50;
S.P. of 50 chocolates =Rs. 65.
.'. Gain% = 15*100/50 = 30%
Answer : D
Answer: (D) 30%
Question: A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
(A) 2:6
(B) 2:9
(C) 2:3
(D) 2:2
(E) 2:1
Rationale: Let the principal be P and rate of interest be R%.
Required ratio = [(P * R * 6)/100] / [(P * R * 9)/100] = 6PR/9PR = 6/9 = 2:3
Answer: C
Answer: (C) 2:3
Question: If 0 < Z < Y, Z is an odd number and Y is a prime number, which of the following can be the value of Z + Y ?
(A) 11.
(B) 13.
(C) 17.
(D) 10.
(E) 15.
Rationale: If Z is odd ,implies Z(odd)+y(odd/even prime)=(Even/Odd)
If Y is even, the 2 is the even prime , therefore y=2z=1 since 0<Z<Y therefore Z+Y =3. But 3 is not an option
which implies y is odd,
Now Z(odd)+Y(odd)=Even
10 is the only option that is even=D
Answer: (D) 10.
Question: on dividing a N by 9,remainder is 8. the quotient obtained when divided by 11,leaves remainder 9. now the quotient when divided by 13,leaves remainder 8. find the remainder when when the N is divided by 1287
(A) 871
(B) 881
(C) 891
(D) 904
(E) 987
Rationale: take from the last step division
suppose no. is n which is divided by 13 and remainder 8 = 13n+8
now 13n+8 will be the no. which is divided by 11 and remainder is 9
= [11*(13n+8)]+9
now this no. is used for the very first step which is divider is 9 and remainder is 8
={9*[11*(13n+8)]+9}+8 solve and ans is 881
ANSWER:B
Answer: (B) 881
Question: If the current in a circuit equals 0 A, it is likely that the
(A) 22
(B) 37
(C) 36
(D) 28
(E) 22
Rationale: Answer: Option D
Answer: (D) 28
Question: I have a basket of 500 apples.
I want to divide them equally into 20 places.
How long will it take to divide if for each 25 apples counted i spent 5 minutes ?
(A) 199
(B) 100
(C) 60
(D) 5
(E) 20
Rationale: 500 apples divided by 20 is 25. If it takes 5 minutes to sort out 25 apples then it would take 100 minutes to perform the same task 20 times
Answer is B
Answer: (B) 100
Question: The number of permutations of the letters of the word 'MESMERISE' ?
(A) 9!/(2!)2 3!
(B) 9!/(2!)2 8!
(C) 9!/(2!)2 6!
(D) 9!/(9!)2 3!
(E) 9!/(2!)3 3!
Rationale: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = 9!/(2!)2 3!
Answer: A
Answer: (A) 9!/(2!)2 3!
Question: A carton contains 25 bulbs, 8 of which are defective. What is the probability that if a sample of 4 bulbs is chosen, exactly 2 of them will be defective ?
(A) (8/25) x (7/24) x (17/23) x (16/22)
(B) (4C2) x (8/25) x (7/24) x (17/23) x (16/22)
(C) (8/26) x (8/24) x (17/33) x (16/22)
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
The probability that exactly two bulbs are defective and exactly two are not defective will be given by
(4C2) x (8/25) x (7/24) x (17/23) x (16/22)
Answer : B
Answer: (B) (4C2) x (8/25) x (7/24) x (17/23) x (16/22)
Question: How many times in a day, the hands of a clock are shows opposite directions ?
(A) 12
(B) 20
(C) 21
(D) 23
(E) 22
Rationale: Sol.
In 12 hours, the hands coincide or are in opposite direction 11 times.
âˆ´ In 24 hours, the hands coincide or are in opposite direction 22 times a day.
( between 5 and 7 they point in opposite directions at 6 o'clock only)
Answer E
Answer: (E) 22
Question: If 2994 Ã· 14.5 = 171, then 29.94 Ã· 1.45 = ?
(A) 17.1
(B) 17.3
(C) 17.5
(D) 17.7
(E) 17.2
Rationale: 29.94/ 1.45 = 299.4/14.5
= (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ]
= 171/10
= 17.1
Answer is A.
Answer: (A) 17.1
Question: Solve(0.76 × 0.76 × 0.76 − 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04)
(A) 0.56
(B) 0.71
(C) 0.45
(D) 0.67
(E) 0.71
Rationale: Option 'A'
Answer: (A) 0.56
Question: The perimeter of a rectangular yard is completely surrounded by a fence that measures 36 meters. What is the length of the yard if the area of the yard is 40 meters squared?
(A) 12
(B) 10
(C) 8
(D) 14
(E) 16
Rationale: Perimeter of rectangular yard = 2(l + b) = 36 --> l + b = 18
Area = l * b = 40
b = 18 - l
l(18 - l) = 40
18l - l^2 = 40
l^2 - 18l + 40 = 0
Upon simplifying we get l = 5 or 8. Only 8 is there in the answer choice.
Answer: C
Answer: (C) 8
Question: A train 110 m long is running with a speed of 56 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 5
(B) 6.4
(C) 7
(D) 8
(E) 9
Rationale: Speed of train relative to man = 56 + 6 = 62 km/hr.
= 62 * 5/18 = 155/9 m/sec.
Time taken to pass the men = 110 * 9/155 = 6.4 sec.
Answer: Option B
Answer: (B) 6.4
Question: If A : B= 1 : 4 and B : C = 2 : 3, then A : B : C is:
(A) 4:14:24
(B) 8:6:9
(C) 2:5:7
(D) 6:4:7
(E) 2:8:12
Rationale: A:B=1:4, B:C=2:3, A:B:C=1Ã—2:2Ã—4:4Ã—3
â‡’ 2:8:12
Answer: E.
Answer: (E) 2:8:12