mathewhe/aqua_rat huggingface dataset:
Question: Two trains 137 meters and 163 meters in length are running towards each other on parallel lines, one at the rate of 42 kmph and another at 48 kmpb. In what time will they be clear of each other from the moment they meet
(A) 8 sec
(B) 10 sec
(C) 12 sec
(D) 14 sec
(E) 16 sec
Rationale: Explanation:
Relative speed of the trains = (42 + 48) kmph = 90 kmph
= (90×5/18) m / sec = 25 m /sec.
Time taken by the trains to ‘pass each other
= Time taken to cover (137 + 163) m at 25 m /sec = (300/25) sec = 12 sec
Answer: Option C
Answer: (C) 12 sec
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 37% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?
(A) n/6
(B) n/2
(C) 3n/5
(D) 5n/6
(E) 8n/5
Rationale: total V G
1 ounce 0.37 0.6
n ounce 0.37n 0.6n -------------initial expression
lets say g ounces of gin is added to this mixture
n+g 0.37n 0.6n+g --------------final expression
given that after adding g ounces of gin , V should become 25% of the total volume.
=>Volume of V/total volume = 25/100
=> 0.37n /n+g = 1/4
=> 1.48n = n+g
=> g = n/2
Answer is B.
Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:
0.37n=0.25(n+g) --> g=n/2
Answer: B.
Answer: (B) n/2
Question: The ages of Smirthi and Samantha vary by 16 years, Six years ago, Deepika’s age was three times as that of Smirthi’s, find their current ages.
(A) 20
(B) 50
(C) 40
(D) 30
(E) 45
Rationale: D
30
Let Smirthi’s age = A years
So, Deepika’s age = (A + 16) years
Also, 3(A – 6) = A + 16 – 6 or, A = 14
Smirthi’s age = 14 years
and, Deepika’s age = 14 + 16
= 30 years
Answer: (D) 30
Question: What is the sum of two consecutive even numbers, the difference of whose squares is 84?
(A) 34
(B) 38
(C) 42
(D) 46
(E) None
Rationale: EXPLANATION
Let the numbers be x and x + 2.
Then, (x + 2)2 – x2 = 84
4x + 4 = 84
4x = 80
x = 20.
The required sum = x + (x + 2) = 2x + 2 = 42.
Answer C
Answer: (C) 42
Question: Four friends, Patricia, Melyssa, Tania, and Cassandra, are pooling their money to buy a $1100 item. Patricia has three times as much money as Melyssa. Tania has $20 more than Patricia. Cassandra has 25% more than Tania. If they put all their money together and spend the $1100, they will have $19 left. How much money does Patricia have?
(A) $275
(B) $300
(C) $400
(D) $350
(E) $220
Rationale: P= 3M ; T= P+20 ; C= 1.25(T)
P+M+T+C-1100=19
P+(1/3)P+P+20+1.25(P+20) = 1119
P+(1/3)P+P+20+1.25P+25=1119
P+(1/3)P+P+1.25P+45=1119
P+(1/3)P+P+1.25P=1074
3.58P=1074
P=300
Answer:B
Answer: (B) $300
Question: If (1/5)^m * (1/4)^3 = 1/(2*(10)^3), then m =
(A) 4
(B) 3
(C) 1
(D) 6
(E) 8
Rationale: 1/5^m *1/4^3= 2*1/ 2^3*5^3*8
2^3*5^3*8/4^3 =5^m or 5^3 =5^m
m=3
B
Answer: (B) 3
Question: A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 305 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?
(A) 400
(B) 440
(C) 550
(D) 625
(E) 700
Rationale: Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour.
7A+11B=305 ---(1)
8A+22C=600 ---(2)
Dividing (2) by 2
4A+11C=300.....(3)
Adding (1)(3)
11A+11B+11C = 605
A+B+C=55 per hour
So for eight hrs = 55*8 = 440 = Answer = B
Answer: (B) 440
Question: On multiplying a numberZ by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result.
(A) 104345
(B) 107375
(C) 108385
(D) 109395
(E) 105355
Rationale: The only thing you actually know about the correct number Z is that it is divisible by 153 and has 5 as a factor.
You should immediately try to find the factors of 153 and look for them in the options.
153 = 9*17
Divisibility by 9 is easy to check. Only (D) satisfies.
Answer: (D) 109395
Question: 24 lbs of coffee P and 25 lbs of coffee V are mixed to make coffee X and Y. The ratio of P to V in coffee X is 4 to 1, in Y is 1 to 5. How much of P is contained in the mixture X?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Let there be 4x lbs of P in X and x lbs of V in X
Let there be y lbs of P in Y and 5y lbs of V in Y
Now total P is
4x + y = 24
and total Q is
x + 5y = 25
Solving the two equations, we get
x = 5 and y = 4
Mixture X has 4x lbs of P = 4x = 4 * 5 = 20lbs
ANSWER:B
Answer: (B) 20
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 26000, then the share of B is?
(A) 12000
(B) 24000
(C) 24005
(D) 24009
(E) 24002
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 26000
Share of B = 6/13 (26000) = Rs. 12000
Answer: A
Answer: (A) 12000
Question: The average of first five prime numbers greater than 20 is?
(A) 10
(B) 32.2
(C) 30
(D) 40
(E) 50
Rationale: 23 + 29 + 31 + 37 + 41 = 161/5 = 32.2
ANSWER:B
Answer: (B) 32.2
Question: 3550 - (1002 / 20.04) = ?
(A) 2984
(B) 2983
(C) 3500
(D) 2981
(E) None of these
Rationale: 3550-50 = 3500
Answer : C
Answer: (C) 3500
Question: If 5^11 * 4^6 = 2 * 10^n, what is the value of n?
(A) 11
(B) 21
(C) 22
(D) 23
(E) 32
Rationale: My attempt:
5^(11) * 4^(6) = 2*10^p
5^(11) * 2 ^ (12) = 2 * (2*5)^p
5^(11) * 2 ^ (12) = 2 * 2^(p) * 5^(p)
5^(11) * 2 ^ (12) = 2^(p+1) * 5^(p)
=> (p+1) = 12
=> p = 11
Answer: 11 (A)
Answer: (A) 11
Question: The banker's discount on a bill due 4 months hence at 15% is Rs.420. The discount is
(A) Rs. 400
(B) Rs. 360
(C) Rs. 480
(D) Rs.320
(E) None
Rationale: Solution
T.D	= B.D x 100/ 100+(RxT)
= Rs[420x100/100+(15x1/3)]
= Rs.(420x100 / 105)
= Rs.400.
Answer A
Answer: (A) Rs. 400
Question: Which of the following equations represents a line that is perpendicular to the line described by the equation 4x + 3y = 12?
(A) 3x + 4y = 11
(B) 3x – 4y = 12
(C) 5y – 3x = 6
(D) 1.5y + 2x = 8
(E) 8x – 6y = 2
Rationale: Perpendicular lines have slopes which are negative reciprocals of each other.
The line 4x + 3y = 12 in slope-intercept form is y = -(4/3)x + 4
The slope of this line is -4/3.
The slope of a perpendicular line is 3/4.
3x - 4y = 12 in slope-intercept form is y = (3/4)x - 3
The answer is B.
Answer: (B) 3x – 4y = 12
Question: Convert 500 miles into meters?
(A) 784596
(B) 845796
(C) 804670
(D) 784596
(E) 864520
Rationale: 1 mile = 1609.34 meters
500mile = 500*1609.34 = 804670 meters
Answer is C
Answer: (C) 804670
Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
(A) 3
(B) 5
(C) 8
(D) 9
(E) 11
Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Answer: (C) 8
Question: The average height of 50 pupils in a class is 150 cm. Six of them whose height is 146 cm, leave the class and six others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is ?
(A) 287 cm
(B) 151 cm
(C) 276 cm
(D) 151.2 cm
(E) 297 cm
Rationale: Total height = 150 * 50 = 7500 cm.
New average = [7500 - 6 * 146 + 6 * 156 ] / 50
= 151.2 cm.
Answer:D
Answer: (D) 151.2 cm
Question: Square A has an area of 121 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B?
(A) 9/25
(B) 1/5
(C) 16/121
(D) 105/121
(E) 6/25
Rationale: I guess it's mean that square B is placed within square Aentirely.
Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16;
Empty space between the squares is 121-16=105 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=105/121.
Answer: D.
Answer: (D) 105/121
Question: Speed of a boat in standing water is 9kmph and speed of the stream is 1.5kmph. A man can rows to a place at a distance of 105km and comes back to the starting point. The total time taken by him is?
(A) 12hours
(B) 24hours
(C) 36hours
(D) 10hours
(E) 15hours
Rationale: Speed upstream = 7.5kmph
Speed downstream = 10.5kmph
Total time taken = 105/7.5 + 105/10.5 = 24 hours
Answer is B
Answer: (B) 24hours
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined^her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?
(A) Rs. 9423
(B) Rs. 10,250
(C) Rs. 12,500
(D) None of these
(E) Data inadequate
Rationale: Explanation:
Simran : Nanda = (50000 * 36) : (80000 * 30) = 3 : 4.
âˆ´
Simran's share = Rs.
(24500âˆ—3/7)
= Rs. 10500.
ANSWER IS D
Answer: (D) None of these
Question: Look at this series: 80, 10, 70, 15, 60, ... What number should come next?
(A) 20
(B) 23
(C) 25
(D) 30
(E) 35
Rationale: This is an alternating addition and subtraction series. In the first pattern, 10 is subtracted from each number to arrive at the next. In the second, 5 is added to each number to arrive at the next.
ANSWER A
Answer: (A) 20
Question: A thief steals a car at 2.30pm and drives it at 60kmph.the
theft is discovered at 3pm and the owner sets off in another car
at 75kmph when will he overtake the thief
(A) 3.3 pm
(B) 5.5 pm
(C) 4.9 pm
(D) 5 pm
(E) 5.2 pm
Rationale: Let the thief is overtaken x hrs after 2.30pm
distance covered by the thief in x hrs = distance covered by
the owner in x-1/2 hr
60x = 75 ( x- ½)
x= 5/2 hr
thief is overtaken at 2.30 pm + 2 ½ hr = 5 pm
Answer is D.
Answer: (D) 5 pm
Question: Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
(A) 16537.59
(B) 16537.54
(C) 16537.5
(D) 16537.52
(E) 16537.51
Rationale: P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20) = Rs. 16537.50
Answer: C
Answer: (C) 16537.5
Question: A searchlight on top of the watch-tower makes 3 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: 3 revolutions per minute = 1 revolution every 20 seconds
So no matter what anybody appearing at the tower cannot stay in the dark for more than 20 seconds. This will be our total number of possibilities i.e the denominator.
P(man in dark for at least 5 seconds) = 1 - P (man in dark for max of 10 seconds) = 1 - 10/20 = 1 - 1/2 = 1/2
or the other way would be:
P(man in dark for at least 5 seconds) is like saying he can be in dark for 5,6,7...all the way to 20 seconds because that is the max. In this approach it would be 10/20 seconds = 1/2.
Answer is C
Answer: (C) 1/2
Question: A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 29
(B) 33
(C) 37
(D) 43
(E) 45
Rationale: Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of aa by dd be 'x'
Therefore, we can write the relation as a/d = x and the remainder is 24.
i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.
We know that a=dx+24. Therefore, 2a = 2dx + 48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
C)
Answer: (C) 37
Question: A, B and C can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete the work?
(A) 15 days
(B) 65 days
(C) 16 days
(D) 17 days
(E) 19 days
Rationale: One days's work of A, B and C = 1/90 + 1/30 + 1/45
= (1 + 3 + 2)/90 = 1/15
A, B and C together can do the work in 15 days.
Answer:A
Answer: (A) 15 days
Question: The average age of an adult class is 40years. 12new students with an avg age of 32years join the class. Thereforedecreasing the average by 4year. Find what was theoriginal strength of class?
(A) 10
(B) 12
(C) 16
(D) 20
(E) 22
Rationale: Let original strength = y
Then , 40y + 12 x 32 = ( y + 12) x 36
⇒ 40y + 384 = 36y + 432
⇒ 4y = 48
∴ y = 12
B
Answer: (B) 12
Question: How many integers from 0 to 59, inclusive, have a remainder of 1 when divided by 3 ?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 20
Rationale: My ans is also C.17.
Explanation:
1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.
Hence we have an arithmetic progression: 1, 4, 7, 10,..... 58, which are in the form 3n+1.
Now we have to find out number of terms.
tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.
so, 58 = 1+(n-1)3
or, (n-1)3 = 57
or, n-1 = 19
or, n = 20
E
Answer: (E) 20
Question: Ravi can do a piece of work in 25 days while Prakash can do it in 40 days. In how many days will they finish it together?
(A) 15 5/13 days
(B) 16 1/13 days
(C) 17 1/13 days
(D) 17 7/15 days
(E) 18 1/13 days
Rationale: 1/25 + 1/40 = 13/200
200/13
= 15 5/13 days
Answer: A
Answer: (A) 15 5/13 days
Question: Once a week, Susan collects wildflowers around her neighborhood to display in the vase on her family's kitchen table. When her dog Rocko tags along, she gets distracted by his barking, so she collects about 3/4 as many flowers as she usually would when she comes alone. When her father comes along, he collects twice as many as she does. Last week, Susan brought Rocko with her and collected 39 flowers. If Susan and her father go next week without Rocco, how many total flowers will they bring home?
(A) 156
(B) 104
(C) 52
(D) 78
(E) 117
Rationale: X equals Number of Flowers Susan collects while alone
Knowing 39 is 3 equal fourths of X, I can divide 39 by 3 to find the value of each fourth.
1/4 of x = 39 divided by 3
1/4 of x = 13
x = 13 x 4
x = 52
Susan's father collects twice as many flowers as Susan, which would be 52 x 2 = 104
Final calculation is Susan's flowers plus her father's flowers, 52 + 104 = 156 flowers
The correction answer is option A) 156
Answer: (A) 156
Question: The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?
(A) 1:9
(B) 1:4
(C) 1:8
(D) 1:1
(E) 1:2
Rationale: 4πr12 : 4πr22 = 1 : 4
r1 : r2 = 1 : 2
4/3 πr13 : 4/3 πr23
r13 : r23
=1:8
Answer: C
Answer: (C) 1:8
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
(A) 4.5
(B) 5.5
(C) 6.5
(D) 7.5
(E) 8.5
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 180 kilometers?
180 ÷ 40 = 4.5 × 1 gallon = 4.5 gallons
correct answer A
Answer: (A) 4.5
Question: Yesterday's closing prices of 2,860 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
(A)  484
(B)  726
(C)  1,100
(D)  1,320
(E)  1,560
Rationale: Lets consider the below -
The number of stocks that closed at a higher price = H
The number of stocks that closed at a lower price = L
We understand from first statement -> H+L = 2860 ----(1)
We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)
Solve eq (1)(2) to get H = 1560.
E is my answer.
Answer: (E)  1,560
Question: If p is the sum of m and n, then which one of the following must equal m – n ?
(A) p+2n
(B) p/2
(C) p+y
(D) p-y
(E) p-2n
Rationale: Given p= m+n if you subtracts both side with -2n
p-2n = m-n
Answer : E
Answer: (E) p-2n
Question: A man collects cigarette stubs and makes one full cigarette with every 8 stubs. If he gets 64 stubs how many full cigarettes can he smoke
(A) 7
(B) 8
(C) 9
(D) 10
(E) 15
Rationale: From 64, he makes 8. From this 8 he makes one more. Total 9.
ANSWER:C
Answer: (C) 9
Question: A car during its journey travels 1 hour at a speed of 40 kmph, another 30 minutes at a speed of 60 kmph, and 2 hours at a speed of 60 kmph.The average speed of the car is
(A) 63.07 kmph
(B) 54.28 kmph
(C) 62.02 kmph
(D) 64.02 kmph
(E) None of these
Rationale: First car travels 1 hrs at speed of 40 kmph
distance = 40 x 1 = 40 m
Then car travels 30 min at a speed of 60 kmph
distance = 30 min at speed of 60 kmph
distance = 60 x 1/2 = 30 m
at last it travels 2 hours at speed of 60 kmph
distance = 60 x 2 = 120 m
Total distance = 40 + 30 + 120 = 190
Total time= 1+ 1/2 + 2 = 3.50
Average speed of the car = 190/3.25 = 54.28
ANSWER:B
Answer: (B) 54.28 kmph
Question: Find the compound interest on $100000 in 2years at 4% per annum, the interest being compounded half-yearly?
(A) $645.56
(B) $824.32
(C) $954.26
(D) $745.69
(E) $8243.21
Rationale: Principle = $10000
Rate = 2% half yearly = 4 half years
Amount = 100000*(1 + 2/100)^4 = 100000 * 51/50 * 51/50 * 51/50 * 51/50
= $108243.21
C.I. = 108243.21-100000 = $8243.21
Answer is E
Answer: (E) $8243.21
Question: If 12 men do a work in 80 days, in how many days will 16 men do it?
(A) 33 days
(B) 77 days
(C) 99 days
(D) 60 days
(E) 19 days
Rationale: 12 * 80 = 16 * x
x = 60 days
Answer: D
Answer: (D) 60 days
Question: A person purchased a Computer set for Rs. 16000 and a DVD Drive for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 38%
(B) 74%
(C) 40%
(D) 33%
(E) 60%
Rationale: C
40%
The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100 = 40%
Answer: (C) 40%
Question: Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?
(A) Rs. 14.80
(B) Rs. 15.40
(C) Rs. 15.60
(D) Rs. 16.30
(E) Rs. 18.20
Rationale: Explanation:
C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.
S.P. of 50 kg wheat = 130% of Rs. 630 = 130/100 * 630 = Rs. 819.
S.P. per kg = 819/50 = Rs. 16.38 = 16.30.
ANSWER IS D
Answer: (D) Rs. 16.30
Question: The expression (12.86 × 12.86 + 12.86 × p + 0.14 × 0.14) will be a perfect square for p equal to
(A) 0.28
(B) 0.26
(C) 1
(D) 0
(E) 2
Rationale: Explanation :
12.86 × 12.86 + 12.86 × p + 0.14 × 0.14 = (12.86)2 + 12.86 × p + (0.14)2
This can be written as (12.86 + 0.14)2 = 132, if 12.86 × p = 2 × 12.86 × 0.14
i.e., if p = 2 × 0.14 = 0.28
Hence, p = 0.28 . Answer : Option A
Answer: (A) 0.28
Question: 108.	Triangle A’s base is 7% greater than the base of triangle B, and A’s height is 7% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B?
(A)  9 % less
(B)  1 % less
(C)  Equal to each other
(D)  1 % more
(E)  2.1 % more
Rationale: Wish the question specified that we are talking about corresponding height.
Base of A = 8/7 * Base of B
Height of A = 6/7 * Height of B
Area of A = (1/2) * Base of A * Height of A = 8/7 * 6/7 * Area of B = 48/49 * Area of B
Area of A is 2.1% more than the area of B.
Answer (E)
Answer: (E)  2.1 % more
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.
(A) s.4500
(B) s.5200
(C) s.1800
(D) s.Rs.3000
(E) s.5000
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
ANSWER:D
Answer: (D) s.Rs.3000
Question: John opened a shop investing Rs.40000. Joy joined him 4 months later, investing Rs.50000. They earned a profit of Rs.55000 after completion of one year. What will be Joy's share of profit?
(A) 23000
(B) 25000
(C) 24000
(D) 28000
(E) 29000
Rationale: SoL = ~s- So Joy's share = [5/11] x 55000 = 25000
Answer : B
Answer: (B) 25000
Question: Find the largest 4 digit number which isexactly divisible by 88?
(A) 8765
(B) 9543
(C) 9944
(D) 1012
(E) 2465
Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
Answer: (C) 9944
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 336 votes. Find the number of votes casted to the winning candidate?
(A) 288
(B) 744
(C) 788
(D) 868
(E) 177
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 336
62% -------- ? => 868
Answer: D
Answer: (D) 868
Question: It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(A) (216 + 1)
(B) (216 - 1)
(C) (7 x 223)
(D) (296 + 1)
(E) none
Rationale: Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N
ANSWER:D
Answer: (D) (296 + 1)
Question: A school having four classes only have student strength of 10, 40, 30 and 20 respectively. The pass percentages of these classes are 20%, 30%, 60% and 100% respectively. What is the pass percentage for the entire school?
(A) 56%
(B) 76%
(C) 52%
(D) 66%
(E) 46%
Rationale: 20% of 10+30% of 40+60% of 30+100% of 20
=2+12+18+20 =
now 52 of 100
= 52%
ANSWER:C
Answer: (C) 52%
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it exactly once?
(A) 9/100
(B) 1/10
(C) 11/100
(D) 19/100
(E) 1/5
Rationale: Probability = No of balls with exactly one 1 / total number of balls
= {1,10,12 to 19, 21,31,41,51,61,71,81,91,100}/100
= 19/100
Answer is D
Answer: (D) 19/100
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 11 percent, what was the annual interest rate last year?
(A) 1%
(B) 1.1%
(C) 9.1%
(D) 10%
(E) 10.8%
Rationale: Let us suppose the interest rate last year is X, This year the interest rate is increased by 10%. Hence this year interest rate would be 1.1*X.
Setting up the equation -----> 11=1.1*x
X=10%
ANSWER:D
Answer: (D) 10%
Question: A basket contains 4 blue, 4 red and 4 yellow marbles. If 4 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
(A) 2/21
(B) 3/25
(C) 1/6
(D) 9/28
(E) 16/55
Rationale: 12/12*8/11*4/10 = 384/1320 = 16/55
the answer is (E)
Answer: (E) 16/55
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
(A) 360
(B) 960
(C) 329
(D) 391
(E) 310
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is 6P4
= 6 * 5 * 4 * 3
= 360.
Answer: A
Answer: (A) 360
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 9%
(B) 4%
(C) 2%
(D) 1%
(E) 6%
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: B
Answer: (B) 4%
Question: ((-1.9)(0.6) – (2.6)(1.2))/5.0 = ?
(A) -0.71
(B) 1.0
(C) -0.852
(D) 1.71
(E) 2.71
Rationale: Dove straight into calculation
((-1.9)(0.6) – (2.6)(1.2))/7.0 = -0.852
Answer C
Answer: (C) -0.852
Question: Three friends are buying a gift for a friend. Declan contributes 4 dollars more than 1/4 the cost of the gift, Ed contributes 1 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 17 dollars. What is the cost of the gift?
(A) 48
(B) 54
(C) 60
(D) 66
(E) 72
Rationale: Declan = D, Ed = E, Frank = F
t = total
D + E + F = t
(t/4 + 4) + (t/3 - 1) + 17 = t
t = 20 + (7t/12)
12t = 20(12) + 7t
5t = 5*4(12)
t = 48
The correct answer is A.
Answer: (A) 48