mathewhe/aqua_rat huggingface dataset:
Question: A pupil's marks were wrongly entered as 67 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
(A) 30
(B) 80
(C) 44
(D) 25
(E) 26
Rationale: Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (67 - 45)
=> X/2 = 22
=> X = 44.
ANSWER:C
Answer: (C) 44
Question: The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at
75 km/hr. At what time will they meet?
(A) 11 am.
(B) 12 a.m
(C) 10 a.m
(D) 9 a.m
(E) 8 a.m
Rationale: x hrs after 8 am
train 1 starting from A travel x hours till the trains meet
dist travelled by train 1 in x hrs = 60x km
train 2 starting from B, travels (x-1) hrs
distance travelled by train 2 in(x-1) hrs = 75(x-1) km
total dist travelled = dist travelled by train 1 + dist travelled by train 2
=>330 = 60x+75(x-1)
12x+15(x-1) = 66
12x+15x-15 =66
27x=66+15=81
3x=9=>x=3
hence 3 hrs after 8 am =>11 am
ANSWER A
Answer: (A) 11 am.
Question: The average of 13 numbers is 60. Average of the first 6 of them is 57 and that of the last 8 is 61. Find the 8th number?
(A) 46
(B) 48
(C) 50
(D) 52
(E) 54
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 6 of them = 6 * 57 = 342
Sum of the last 8 of them = 8 * 61 = 488
So, the 8th number = 342 + 488 - 780 = 50.
ANSWER:C
Answer: (C) 50
Question: A bag marked at Rs. 80 is sold for Rs. 68. The rate of discount is :
(A) 12 %
(B) 13 %
(C) 15 %
(D) 18 %
(E) 19 %
Rationale: Sol.
Rate of discount = [12/80 * 100] % = 15%.
Answer C
Answer: (C) 15 %
Question: A corporation triples its annual bonus to 50 of its employees. What percent Q of the employees’ new bonus is the increase?
(A) 50%
(B) 662⁄3%
(C) 100%
(D) 200%
(E) 300%
Rationale: Q of the employees’ new bonus is the increase Hence B.
Answer: (B) 662⁄3%
Question: One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 200 of the attendees are neither female nor students, what is the total number of attendees at the convention?
(A) 600
(B) 300
(C) 1200
(D) 900
(E) 1000
Rationale: Let no. of Attendee are A.
Now As per the condition of the problem stated above .
We have following population in the convention as Attendee.
Total no. of females = [2/3]*A
Total no. of females as student : [1/6]*A
Total no. of students = [1/3]*A
Total no. of male as student = [1/6]*A
Total no. of males = A - [2/3]*A = [1/3]A
No. of males which are not student = [1/3]A - [1/6]*A = 200
Hence A = 1200
Total no of males who are not student will be the answer as it states it should be neither female nor student
So Answer is C
Answer: (C) 1200
Question: if price of t.v set is reduced by 22%, then its sale increases by 86%, find net effect on sale value
(A) 44
(B) 45
(C) 46
(D) 47
(E) 48
Rationale: - a + b + ((-a)(b)/100)
= -22+86+(-22*86)/100
= -22+86-19
=45
ANSWER:B
Answer: (B) 45
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 55 km
(B) 20 km
(C) 77 km
(D) 34 km
(E) 22 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
Answer: B
Answer: (B) 20 km
Question: How many three letter words are formed using the letters of the word TIME?
(A) 16
(B) 86
(C) 12
(D) 24
(E) 27
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 4P3
= 4 * 3 * 2 = 24.
Answer:D
Answer: (D) 24
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 17
(B) 20
(C) 26
(D) 31
(E) NONE OF THESE
Rationale: Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
B's weight = 31 kg.
ANSWER: D
Answer: (D) 31
Question: The dimensions of a rectangular solid are 6 inches, 5 inches, and 8 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?
(A)  10:17
(B)  2:5
(C)  5:16
(D)  10:19
(E)  32:25
Rationale: Answer: D.
Answer: (D)  10:19
Question: The average of 6 no.'s is 3.95. The average of 2of them is 4.2, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
(A) 4.2
(B) 4.4
(C) 4.6
(D) 3.8
(E) 5.7
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(4.2 * 2) + (3.85 * 2)]
=7.60.
Required average = (7.6 / 2) = 3.8.
D
Answer: (D) 3.8
Question: A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number W of tickets sold by the male members of the association
(A) 50
(B) 56
(C) 58
(D) 62
(E) 66
Rationale: Given that, Total average W sold is 66, Male/Female = 1/2 and Female average is 70. Average of Male members isX.
(70*F+X*M)/(M+F) = 66 -> Solving this equation after substituting 2M=F, X = 58. ANS C.
Answer: (C) 58
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
(A) 8 cm
(B) 5 cm
(C) 4 cm
(D) 2 cm
(E) 9 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h
= (4/3)π (12)3
=> h = 9 cm
Answer:E
Answer: (E) 9 cm
Question: In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 6%.what is population of after 2 year.
(A) 140
(B) 141
(C) 142
(D) 143
(E) 145
Rationale: next year total population=[150^2+90^2]^.5=174.92=175
man decreased by 6% so total man =150*.94=141
women will be= 175-141=34
so population after two years= [135^2+34^2]^.5=145.04=145
so population after two year= 145
ANSWER:E
Answer: (E) 145
Question: If the price of 23 toys is 276, then what will the price of 12 toys ?
(A) 144
(B) 361
(C) 117
(D) 287
(E) 112
Rationale: Explanation:
Less toys, Less Price (Direct Proportion)
So, let the price be Rs. x
then,
23:12::276:x => x=(276*12)/23
=> x=144
So price of 12 toys will be Rs. 144
Answer: A
Answer: (A) 144
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
(A) 228
(B) 144
(C) 268
(D) 277
(E) 299
Rationale: Given that SP = Rs. 102 and loss
= 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6
= Rs. 120.
To get 20% profit, New SP
= [(100 + p%)CP]/100
= (120 * 120)/100
= Rs. 144
Answer:B
Answer: (B) 144
Question: A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?
(A) 20 days
(B) 10 days
(C) 30 days
(D) 60 days
(E) 50 days
Rationale: Work done by A in 10 days=10/80=1/8
Remaining work=(1-(1/8))=7/8
Now, work will be done by B in 42 days.
Whole work will be done by B in (42*8/7)=48 days
Therefore, A's one day's work=1/80
B’s one day's work=1/48
(A+B)'s one day's work=1/80+1/48=8/240=1/30
Hence, both will finish the work in 30 days.
Answer : C.
Answer: (C) 30 days
Question: In a car wheel, twenty spokes cover 120 degrees. Then for the entire car,how many spokes are there?
(A) 240
(B) 340
(C) 440
(D) 540
(E) 640
Rationale: given, 20 spokes cover 120degrees,
so for 360 degrees.---->360*20/120=60..
so, for entire car, 4*60=240
ANSWER:A
Answer: (A) 240
Question: What is the sum of the greatest common factor and the lowest common multiple of 24 and 36?
(A) 92
(B) 84
(C) 24
(D) 60
(E) 184
Rationale: Prime factorization of 24 = 2 x 2 x 2 x 3
Prime factorization of 36 = 2 x 2 x 3 x 3
GCF = 12
LCM = 72
Sum = 84
Answer B.
Answer: (B) 84
Question: A question paper has two parts X and Y, each containing 10 questions. If a student wants to choose 8 from part X and 4 from part Y, in how many ways can he do that?
(A) 9450
(B) 1200
(C) 1500
(D) 8500
(E) 9500
Rationale: No of ways => 8 ques from X = 10C8
No of ways => 4 ques from part Y = 10C4
Total no of ways => 10c8*10c4==> 45 * 210
= 9450
ANSWER A
Answer: (A) 9450
Question: If a radio is purchased for Rs 490 and sold for Rs 465.50 Find the loss%?
(A) 3%
(B) 4%
(C) 5 percent
(D) 6%
(E) None of these
Rationale: Explanation :
Loss = 490 – 465.5 = 24.5 loss in % = 24.5/ 490 x 100 = 5%.
Answer : C
Answer: (C) 5 percent
Question: Analyze the number square carefully and find out what number fits in place of question mark.
2	4	6
3	6	9
4	8	?
(A) 2
(B) 8
(C) 4
(D) 14
(E) 20
Rationale: 20 fits in place of question mark.
This is because (number in first column) / (number in second column) * 8 = number in third column.
Here (left number / middle number) * 8 = right number
(4 / 8) * 8 = (1 / 2) * 8 = 1 x 4= 4
C
Answer: (C) 4
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 18, how many more dollars, in terms of x, will it cost per person?
(A)  x/6
(B)  x/16
(C)  x/40
(D)  3x/40
(E)  3x/80
Rationale: Choose x as a multiple of 16, I chose 64:
So for 10 people, that's 6.4 each and for 18 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is B.
Answer: (B)  x/16
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
What is the average amount of interest per year which the company had to pay during this period?
(A) Rs. 35 lakhs
(B) Rs. 36.66 lakhs
(C) Rs. 45.66 lakhs
(D) Rs. 47 lakhs
(E) Rs. 47.45 lakhs
Rationale: Average amount of interest paid by the Company during the given period
= Rs.	[	23.4 + 32.5 + 41.6 + 36.4 + 49.4	]	lakhs
5
= Rs.	[	183.3	]	lakhs
5
= Rs. 36.66 lakhs.
B)
Answer: (B) Rs. 36.66 lakhs
Question: 8.008/2.002
(A) 0.004
(B) 0.04
(C) 4
(D) 40
(E) 400
Rationale: Answer is 4, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 8008/2002= 4
Answer C
Answer: (C) 4
Question: A man goes downstream at 10 kmph, and upstream8 kmph. The speed of the stream is
(A) 0kmph
(B) 4kmph
(C) 1kmph
(D) 2.5kmph
(E) 26kmph
Rationale: Speed of the stream = 1/2(10-8)kmph
=1kmph.
correct option :C
Answer: (C) 1kmph
Question: The average marks of a class of 35 students is 40 and that of another class of 45 students is 60. Find the average marks of all the students?
(A) 52.6
(B) 52.4
(C) 52.1
(D) 51.2
(E) 52.9
Rationale: Sum of the marks for the class of 35 students = 35 * 40 = 1400
Sum of the marks for the class of 45 students = 45 * 60 = 2700
Sum of the marks for the class of 80 students =
1400 + 2700 = 4100
Average marks of all the students = 4100/80 = 51.2.Answer: D
Answer: (D) 51.2
Question: A sum of money is to be distributed among A, B, C, D in the proportion of
5 : 2 : 4 : 3. If C gets Rs. 2000 more than D, what is B's share?
(A) Rs. 500
(B) Rs. 1000
(C) Rs. 4000
(D) Rs. 2000
(E) NOne
Rationale: Sol.
Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 2000 ⇔ x = 2000.
∴ B's share = Rs. 2x= Rs. (2x2000) = Rs. 4000.
Answer C
Answer: (C) Rs. 4000
Question: 375 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) 15
Rationale: 26 trees have 25 gaps between them,
Required distance (375/25) = 15
E
Answer: (E) 15
Question: If a(a - 8) = 9 and b(b -8) = 9, where a ≠ b, then a + b =
(A) −48
(B) −2
(C) 8
(D) 9
(E) 48
Rationale: i.e. if a = -1 then b = 9
or if a =9 then b = -1
But in each case a+b = -1+9= 8
Answer: option C
Answer: (C) 8
Question: Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were FOUR times the amount she spent per month, what should be the fraction of her salary that she spent each month?
(A) 1/4
(B) 3/4
(C) 1/2
(D) 1
(E) 5/4
Rationale: Saving = S, Expenditure = E, Income = I
At the end of 12months; 12S=4E=4(I-S)
=> 16S = 4I => Savings = 1/4 I
Hence Expenditure = 1-(1/4) = 3/4 I
Answer (B)
Answer: (B) 3/4
Question: A tourist purchased a total of $2,000 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
(A) $1,430
(B) $1,310
(C) $1,290
(D) $1,770
(E) $1,150
Rationale: Let the number of $10 checks cashed beT
Let the number of $50 checks cashed beF
7 checks cashed;
T+F=7
Now; T can be F+1 OR T can be F-1
Let's check both conditions;
T=F+1
T+F=7
F+1+F=7
2F=6
F=3
T=4
Value cashed = 3*50+4*10=150+40=$190
Let's check the other condition as well;
T=F-1
T+F=7
F-1+F=7
2F=8
F=4
T=3
Value cashed = 4*50+3*10=200+30=$230
The more money he cashes, the less loss he incurs. Thus, we must consider the latter case.
Value cashed = $230
Value lost = 2000-230 = $1770
Ans:D
Answer: (D) $1,770
Question: If x, y, and z are three different prime numbers, which of the following is the smallest possible value of x + y + z?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: The sum of the three small smallest primes numbers is 2+3+5=10.
The answer is A.
Answer: (A) 10
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 8 owned exactly two of the three types of pet, how many people owned all three?
(A) 2
(B) 4
(C) 6
(D) 12
(E) 32
Rationale: You are considering a case when cat dogs and rabbit are not exactly equal to 12 .
The solution shall be 60=30+40+10-8-2x
and hence x shall be 6
Answer C
Answer: (C) 6
Question: A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance?
(A) 35.3km/hr
(B) 42km/hr
(C) 48.9km/hr
(D) 52.6km/hr
(E) 27.6km/hr
Rationale: Total distance traveled = 100+200+300+100 = 700km
Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs
Average speed = 700/16.67 = 42km/hr approximately ;
Answer is B
Answer: (B) 42km/hr
Question: It is being given that (5^32+1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(A) 5^16+1
(B) 5^16-1
(C) 7*5^33
(D) 5^96+1
(E) None
Rationale: Solution: Let 5^32=x.
Then (5^32+1)=(x+1). Let (x+1) be completely divisible by the whole number Y.
then (5^96+1)=[(5^32)^3+1]=>(x^3+1)=(x+1)(x^2-x+1) which is completely divisible by Y.
since (x+1) is divisible by Y.
Answer D
Answer: (D) 5^96+1
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?
(A) 10,100
(B) 20,200
(C) 22,650
(D) 40,200
(E) 45,150
Rationale: Firstly calculate the number of even integers between 99 and 301:
No of even integers = (300 - 100)/2 + 1 = 101
Avg of the even integers is (100+300)/2 = 200.
The sum would be = no of even integers * Avg.
==> 101*202 = 20,200
Answer B.
Answer: (B) 20,200
Question: A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 13% below the cost price of the claimed weight.
(A) 19.63%
(B) 20%
(C) 37.5%
(D) 25%
(E) 37.5%
Rationale: There is a one step calculation method too. It requires more thought but is faster.
The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer $110. Hence, in effect, there is a 10% mark up.
While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only $80 for it. So this is again a mark up of $20 on $80 which is 25%.
But he also sells at 13% less
(1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)
11/10 * 5/4 * 87/100 = (1 + p%)
profit % = 19.63%
A
Answer: (A) 19.63%
Question: How many numbers from 32 to 97 are exactly divisible by 9?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 12
Rationale: Option 'B'
32/9 = 3 and 97/9 = 10 ==> 10 - 3 = 7 Numbers
Answer: (B) 7
Question: On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5 ?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 2
Rationale: Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
x=5k+3
x^2=(5k+3)^2=(25k^2+30k+9)
=5(5k^2+6k+1)+4
on dividing x^2 by 5,we get 4 as remainder.
Answer is D
Answer: (D) 4
Question: A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 3.5 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
(A) 3
(B) 4.2
(C) 3.4
(D) 5.5
(E) 5.7
Rationale: 72 km/hr = 1.2 km/min
The total distance is 3.6 km.
3.6 / 1.2 = 3 minutes
The answer is A.
Answer: (A) 3
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?
(A) 4/18
(B) 4/12
(C) 4/15
(D) 4/13
(E) 4/16
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13
Answer: D
Answer: (D) 4/13
Question: An article is bought for Rs.475 and sold for Rs.525, find the gain percent?
(A) 33 1/7%
(B) 33 1/6%
(C) 33 1/3%
(D) 10.53%
(E) 33 2/3%
Rationale: 475 ---- 50
100 ---- ? => 10.53%
Answer: D
Answer: (D) 10.53%
Question: In an animal behavior experiment, 40 tagged white pigeons and 200 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory?
(A) 80.5
(B) 82
(C) 81.75
(D) 85
(E) 86.5
Rationale: Weighted mix method is best here....
Ratio is 1:5 for 88:80.5...
So the answer required = 80.5+ (88-80.5)*1/6=80.5+7.5*1/5
80.5+1.25=81.75
C
Answer: (C) 81.75
Question: What annual installment will discharge a debt of $1092 due in 3 years at 12% simple interest?
(A) $210
(B) $115
(C) $295
(D) $325
(E) $415
Rationale: Let each installment be x
[x + (x*12*1/100)] + [x + (x*12*2/100)] + x = 1092
28x/25 + 31x/25 + x = 1092
x = 325
Answer is D
Answer: (D) $325
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 769m
(B) 678m
(C) 350m
(D) 168m
(E) 198m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer: C
Answer: (C) 350m
Question: A batsman in his 18th innings makes a score of 150 runs and there by increasing his Average by 6.
Find his average after 18th innings.
(A) 150
(B) 18
(C) 6
(D) 17
(E) 42
Rationale: Let the average for 17 innings is x runs
Total runs in 17 innings = 17x
Total runs in 18 innings = 17x + 150
Average of 18 innings = 17x + 150/18
: . 17x + 150/18 = x + 6 -- > x = 42
Thus, average after 18 innings = 42
Answer is E.
Answer: (E) 42
Question: Two trains leave a station traveling in the same direction. Train A leaves traveling at a constant speed of 50 mph, while train B leaves traveling at a constant speed of 80 mph. If train B left the station 30 minutes after train A left, in how many minutes will train B overtake train A?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: We can use a form of the equation D=RT [distance=rate*time]
Train A will have traveled for 30 minutes longer when train B overtakes it so
time of train A: T + 30 minutes = T + 1/2 hours (switch to hours since the rates are in hours)
time of train B: T
rate of train A: 50 mph
rate of train B: 80 mph
the distance traveled by each will be the same when B overtakes A so set the right side of D=RT equal to each other for the two trains
50*(T+1/2)=80*T
50T+25=80T
25=30T
25/30=T
5/6 hours = T which is 5/6*60 = 50 minutes
C
Answer: (C) 50
Question: 3: 5 = 4/3: x. The value of x is?
(A) 1
(B) 20/9
(C) 3
(D) 4
(E) 5
Rationale: x * 3 = 5 * 4/3
x *3= 20/3
x=20/9
ANSWER:B
Answer: (B) 20/9
Question: How many natural numbers between 23 and 137 are divisible by 7?
(A) 12
(B) 17
(C) 16
(D) 13
(E) 15
Rationale: Solution : These numbers are 28, 35, 42,…., 133.
This is in A.P. in which a= 28, d=(35-28)=7 and L=133.
Let the number of there terms be n. then, Tn=133
a+(n-1)d=133 by solving this we will get n=16.
Answer C
Answer: (C) 16
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
(A) 40
(B) 45
(C) 125
(D) Data inadequate
(E) None of these
Rationale: Explanation:
Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300/26.50m = 200 m
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m.
Answer: E
Answer: (E) None of these
Question: In a group of cows and hens, the number of legs are 20 more than twice the number of heads. The number of cows is :
(A) 5
(B) 6
(C) 7
(D) 10
(E) 12
Rationale: Let no of cows be x, no of hens be y.
So heads=x+y
Legs=4x+2y
Now, 4x+2y = 2(x+y)+ 20
2x = 20
x = 10.
ANSWER:D
Answer: (D) 10
Question: A train 300 m long passed a pole in 30 sec. How long will it take to pass a platform 1000 m long?
(A) 90 sec
(B) 100 sec
(C) 110 sec
(D) 120 sec
(E) 130 sec
Rationale: Speed = 300/30 = 10 m/sec.
Required time = (300 + 1000)/10 = 130 sec
Answer:E
Answer: (E) 130 sec
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?
(A) 12,0000
(B) 130000
(C) 261000
(D) 627000
(E) 12690
Rationale: Explanation:
X * (105/100) * (105/100) * (105/100) = 138915
X = 138915/1.157625
X = 120000
Answer: Option A
Answer: (A) 12,0000
Question: One water pump can fill half of a certain empty tank in 3 hours. Another pump can fill half of the same tank in 312312 hours. Working together, how long will it take these two pumps to fill the entire tank?
(A) 1 7/13
(B) 1 5/8
(C) 3 1/4
(D) 3 3/13
(E) 3 1/2
Rationale: One pump can fill a tank in 3 hours and another in 3.5 hours
so the rate at which both can half fill the tank is (1/3+1/3.5) => 13/21
Thus half of the tank can be filled in 21/13
so for filling the complete tank => 21/13*2 = 42/13
ANSWER:D
Answer: (D) 3 3/13
Question: Cost is expressed by the formula tb^4. If b is doubled, the new cost Q is what percent of the original cost?
(A) Q=200
(B) Q=600
(C) Q=800
(D) Q=1600
(E) Q=50
Rationale: Original Cost C1=t1*b1^4
New Cost C2=t2*b2^4....only b is doubled so t2=t1 and b2=2b1
C2=t2*(2b1)^4
=16(t1*b1^4)
=16C1
16 times C1=>1600% of C1
Ans D =1600
Answer: (D) Q=1600
Question: What is the smallest possible common multiple of three integers, all larger than 26?
(A) 27
(B) 54.
(C) 846.
(D) 19,656
(E) 21,924
Rationale: The Least common positive multiple would be for the immediate least number(s) after 26 i.e 27.
Since nowhere is it stated that the three integers must be different, the integers could be 27,27 and 27...
leading to least possible positive common multiple to be 27.
Answer A.
Answer: (A) 27