mathewhe/aqua_rat huggingface dataset:
Question: By selling 300 apples a seller gains the selling price of 60 apples. The gain percent of the seller is
(A) 22
(B) 88
(C) 25
(D) 27
(E) 19
Rationale: Explanation:
We know that SP − CP = Profit
⇒300SP - 300CP = 60SP
⇒240SP = 300CP
⇒ SPCP=300240SPCP=300240 = 5454
Let SP = 5, and CP = 4
So profit percentage = 14×100=25%
Answer: C
Answer: (C) 25
Question: There are 4 people of different heights standing in order of increasing height. The difference is 2 inches between the first person and the second person, and also between the second person and the third person. The difference between the third person and the fourth person is 6 inches and the average height is 76. How tall is the fourth person?
(A) 76
(B) 78
(C) 80
(D) 82
(E) 84
Rationale: Let x be the height of the first person.
Then the heights are x, x+2, x+4, and x+10.
4x+16 = 4(76) = 304
x = 72 and the fourth person has a height of 72+10 = 82 inches
The answer is D.
Answer: (D) 82
Question: Tough and Tricky questions: Combinations.
Seven contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 6
(B) 7
(C) 12
(D) 16
(E) 21
Rationale: Number of ways First-place medal can be awarded to four contestants = 7
Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3
Therefore number of possibilities = 7*3 =21
Answer:E
Answer: (E) 21
Question: A man started his journey from Lucknow to Kolkata, which is 200 km, at the speed of 40 kmph then he went to Banglore which is 300 km, at the speed of 20 kmph. Further he went to Ahmedabad which is 500 km, at the speed of 10 kmph. The average speed of the man is :
(A) 14(2/7) kmph
(B) 14(5/7) Kmph
(C) 15.6 kmph
(D) 16.1 kmph
(E) None
Rationale: Solution: Average speed,
= (Total distance /Total time)
= [(200+300+500)/{(200/40)+(300/20)+(500/10)}]
= 1000/70
= 14(2/7) kmph.
Answer: Option A
Answer: (A) 14(2/7) kmph
Question: Sixteen telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of three members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?
(A) 120
(B) 126
(C) 252
(D) 560
(E) 1260
Rationale: My ans is 16C3 = 560
D
Answer: (D) 560
Question: Three medical experts, working together at the same constant rate, can write an anatomy textbook in 32 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 24 days?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Each expert can write 1/96 of the book per day.
To complete the book in 24 days, we need 96/24 = 4 experts, thus 1 more expert is needed.
The answer is A.
Answer: (A) 1
Question: If x and y are different prime numbers, each greater than 10, which of the following must be true? I. x+y is an even integer II. xy is an odd integer III. (x/y) is not an integer
(A) III only
(B) I only
(C) II only
(D) I,II only
(E) I,II and III
Rationale: Given: x and y are different prime numbers, both greater than 10
Statement I: x+y is an even integer
Since x and y are prime numbers greater than 10, they will be odd
Therefore sum will be even.
Correct
Statement II: xy is an odd integer
Since x and y are prime numbers greater than 10, they will be odd
Therefore multiplication will be odd.
Correct
Statement III: (x/y) is not an integer
Since x and y are prime integers, therefore they will not have any common factor apart from 1
Hence (x/y) will not be an integer
Correct
Hence all three statements I, II and III are correct
Answer : E
Answer: (E) I,II and III
Question: [(7/2 ÷ 1/2 × 7/2)]/[(7/2 × 1/2 ÷ 7/2)] = ?
(A) 45
(B) 49
(C) 44
(D) 43
(E) 42
Rationale: Explanation:
[(7/2 ÷ 1/2 × 7/2)]/[(7/2 × 1/2 ÷ 7/2)]
= [7/2 × 2/1 × 7/2]/[7/2 × 1/2 × 2/7]
= 49/2 / 1/2 = 49/2 x 2/1 = 49
Answer: Option B
Answer: (B) 49
Question: How much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a mixture worth Rs.32/3 a litre?
(A) 10 litres
(B) 12 litres
(C) 15 litres
(D) 18 litres
(E) 21 litres
Rationale: C.P. of 1 litre of milk = Rs. 20×2/3 = Rs. 40/3.
C.P. of 1 litre of water =Rs 0.
Mean price = Rs. 32/3.
By the rule of alligation, we have :
C.P of 1 litre C.P of 1 litre
of water of milk
(0) (Rs. 40/3)
\ /
Mean Price
(Rs. 32/3)
/ \
40/3−32/3 32/(3−0)
8/3 32/3
The ratio of water and milk =8/3:32/3.
=8:32=1:4.
Thus, Quantity of water to be added to 60 litres of milk:
=(1/4)×60 litres.
=15 litres. ANSWER : C
Answer: (C) 15 litres
Question: Can you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship?
? : 4623 :: 9 : 647
(A) 17
(B) 18
(C) 13
(D) 10
(E) 20
Rationale: A
17
The relationship holds for below formula :
pow(x,3) - pow(x,2) - 1
=> 9*9*9 - 9*9 - 1
=> 729 - 81 - 1
=> 647
Similarly,
17*17*17 - 17*17 - 1
=> 4913 - 289 - 1
=> 4623
Answer: (A) 17
Question: A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?
(A) 12 km/hr
(B) 15 km/hr
(C) 41 km/hr
(D) 13 km/hr
(E) 18 km/hr
Rationale: Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr
Ans: E
Answer: (E) 18 km/hr
Question: Find the annual dividend received by Nishita from 1200 preferred shares and 3000 common shares both of par value Rs. 50 each if the dividend paid on preferred shares is 10% and semi-annual dividend of 3½ % is declared on common shares.
(A) 16000
(B) 16500
(C) 17000
(D) 17500
(E) 18000
Rationale: Total number of preferred shares = 1200
Face value = Rs.50
dividend paid on preferred shares is 10%
Dividend per share = 50×10/100 = Rs.5
Total Dividend = 1200 × 5 = 6000
Total number of common shares = 3000
Face value = Rs.50
Semi-annual dividend of 3½ % is declared on common shares.
semi-annual dividend per share = 50×7/2×100 = Rs.74
Total semi-annual dividend = 7/4×3000 = Rs.5250
annual dividend = Rs.5250 × 2 = Rs.10500
Total dividend on all all shares(preferred and common) = 6000 + 10500 = Rs.16500
Answer is B.
Answer: (B) 16500
Question: If n is not equal to zero, and n+1/n = 10, then what is the value of n^4 + (1/n)^4?
(A) 9598
(B) 9600
(C) 9602
(D) 9604
(E) 9606
Rationale: n + 1/n=10
we square both sides so we have n^2 + 1/n^2 +2 = 100
or n^2 + 1/n^2= 98
squaring again we have n^4 + 1/n^4 + 2 = 9604
or n^4 + 1/n^4 = 9602
answer =9602 (C)
Answer: (C) 9602
Question: A person saved $10 in buying an item on sale. If he spent $500 for the item, approximately how much percent he saved in the transaction?
(A) 8%
(B) 10%
(C) 2%
(D) 5%
(E) 6%
Rationale: Actual price = 500+10 = $510
Saving = 10/510 * 100 = 100/51 = 2% approximately
Answer is C
Answer: (C) 2%
Question: How many figures are required to number the pages the pages of a book containing 2200 pages?
(A) 7593
(B) 6693
(C) 7693
(D) 7793
(E) 7893
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 999 = 900 * 3 = 2700
1000 to 2200 = 1201 * 4 = 4804
-----------
7693
ANSWER:C
Answer: (C) 7693
Question: If g(x) = ax^5 + bx^3 + 4, and g(5) = 10, then g(–5) =?
(A)  – 10
(B)  – 2
(C)  – 6
(D)  0
(E)  4
Rationale: g(5) = 10
or, 5^5 a + 5^3 b + 4 = 10
or, 5^5 a + 5^3 b = 6
g(-5) = -5^5 a - 5^3 b + 4 = - (5^5 a + 5^3 b) + 4 = - 6 + 4 = - 2 = (B)
Answer: (B)  – 2
Question: A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 750 more than that by the previous schema, his sales were worth?
(A) s. 4,000
(B) s. 6,000
(C) s. 30,000
(D) s. 40,000
(E) s. 50,000
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 750
X = 6000
ANSWER:B
Answer: (B) s. 6,000
Question: How much interest can a person get on Rs. 5000 at 18% p.a. simple interest for a period of three years and six months?
(A) 3150
(B) 3151
(C) 3152
(D) 3153
(E) 3154
Rationale: I = (5000 * 3.5 * 18)/100
= (5000 * 7 * 18)/(100 * 2)
= Rs. 3150
Answer: A
Answer: (A) 3150
Question: The average age of a group of persons going for picnic is years. Fifteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
(A) 5
(B) 10
(C) 15
(D) 40
(E) 50
Rationale: Solution
Let the initial number of persons be x. Then
16x + 15 x 15 = 15.5(x+20)
= 0.5x = 7.5
x = 15.
Answer C
Answer: (C) 15
Question: If a farmer sells 20 of his chickens, his stock of feed will last for 3 more days than planned, but if he buys 15 more chickens, he will run out of feed 4 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
(A) 40
(B) 60
(C) 80
(D) 90
(E) 100
Rationale: Let x = total feed required for the planned period
n= number of chicken
t = total time of the planned feed
x = nt
1) x = (n-15) * (t+4)
2) x = (n+20) * (t-3)
equating 1&2
(n-15) * (t+4) = (n+20) * (t-3)
7n = 35t
n =5t
x= n * n/5
substituting this value in 1
n * n/5 = (n-15) * (n/5+4)
5n = 300
n =60
B
Answer: (B) 60
Question: A boy agrees to work at the rate of one rupee on the first day, two rupees on the second day, and four rupees on third day and so on. How much will the boy get if he started working on the 1st of February and finishes on the 20th of February?
(A) 220
(B) (2)20-1
(C) (2)19-1
(D) (2)19
(E) None of these
Rationale: Solution: 1st term = 1;
Common ratio = 2;
Sum (Sn) = a*(rn-1)/(r-1) = 1*(220-1)/(2-1)
= (2)20-1.
Answer: Option B
Answer: (B) (2)20-1
Question: If BEAT is coded as 4657 and NOT is coded as 328. How is NOTE coded?
(A) 3628
(B) 2386
(C) 3826
(D) 3286
(E) 3268
Rationale: n-3 o-2 t-8 from the code NOT
e - 6 from BEAT
ANSWER:D
Answer: (D) 3286
Question: If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling ten books ?
(A) 23267
(B) 2677
(C) 1800
(D) 2250
(E) 76611
Rationale: Explanation:
Least Cost Price = Rs. (200 * 10) = Rs. 2000.
Greatest Selling Price = Rs. (425 * 10) = Rs. 4250.
Required profit = Rs. (4250 - 2000) = Rs. 2250.
Answer: D) 2250
Answer: (D) 2250
Question: A store’s selling price of $2240 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost?
(A) 	$2800
(B) 	$2464
(C) 	$2650
(D) 	$2732
(E) 	$2400
Rationale: 1.4x = 2240
x=2240/1.4
so, 1.5X = 2240*1.5/1.4= 2400
Answer:- E
Answer: (E) 	$2400
Question: a man spends $2.6 for parking and $34.4 for petrol to travel in car from monday to friday.if he travel by public transport it costs $1.06,find the percentage of savings?
(A) 75.6
(B) 85.6
(C) 85.7
(D) 95.7
(E) 105.7
Rationale: 2.6+34.4=37
for 5 days 1.06*5=5.3
37-5.3=31.7
now the required saving percentage is (31.7/37)*100=85.6
ANSWER:B
Answer: (B) 85.6
Question: A password for a computer uses three digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
(A) 1/32
(B) 1/16
(C) 1/8
(D) 2/5
(E) 1/2
Rationale: To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 = 1,000 possible combinations.
Prime numbers constitute 2, 3 In addition to zero, this is 3 total possibility for each digit. So the number of satisfactory variants is 3× 3 × 3 . So the probability is 1/2 × 1/2 × 1/2 = 1/8.
The right answer is choice (C).
Answer: (C) 1/8
Question: Of the 90 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 35
Rationale: Neither Car nor Garage
= Total - Garage - (Swim - Common)
= 90 - 50 - (40-35) = 90-55 = 35
Answer E
Answer: (E) 35
Question: If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5)+ 2^(a + 6) =
(A) 3^(a + 1)
(B) 2^(a + 1)
(C) 2a
(D) 2a^(a + 1)
(E) 127(2^a)
Rationale: If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5)+ 2^(a + 6) =
2^a(1+2+4+8+16+32+64)
2^a(127)
E. 127(2^a)
Answer: (E) 127(2^a)
Question: According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 20 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
(A) 15
(B) 34
(C) 50
(D) 67
(E) 100
Rationale: Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 20 oz can = 300 oz/20 oz = 15
Answer A, 15 cans
Answer: (A) 15
Question: 40 is subtracted from 60% of a number, the result is 50. Find the number?
(A) 150
(B) 992
(C) 277
(D) 287
(E) 232
Rationale: (60/100) * X – 40 = 50
6X = 900
X = 150
Answer: A
Answer: (A) 150
Question: The average salaryper head of all the workers in a workshop is Rs.850, if the average salary/head of 7technician is Rs.1000 and the average salary/head of the rest is Rs.780, the totalno.of workers in the work-shop is ?
(A) 18
(B) 20
(C) 22
(D) 25
(E) 26
Rationale: Let the total number of workers be y.
So sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y -7 workers.
7 x 1000 + 780(y -7) = 850 y
⇒ 7000 + 780y - 5460 = 850y
⇒ 70y = 1540
∴ y = 22
So total number of workers = 22
C
Answer: (C) 22
Question: It will take 18 days for Cameron to complete a certain task alone. He worked for 9 days before she was joined by Sandra. both of them completed the remaining task in 3 and half days. how many days will it take both of them to complete the entire job?
(A) 6
(B) 7
(C) 5
(D) 8
(E) 9
Rationale: Explanation:
Cameron and Sandra completed half work in 3.5 days
=> they can complete whole work in 7 days
Answer: Option B
Answer: (B) 7
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 4 seconds. What is the length of the fast train?
(A) 23 m
(B) 22 (2/9)m
(C) 27 (7/9)m
(D) 29 m
(E) 28 m
Rationale: Relative speed = (40 - 20) km/hr =	(20 x(5/18))m/sec =	(50/9)m/sec.
Therefore Length of faster train =	((50/9)	x 4) m =	(200/9)m = 22	(2/9)	m.
B
Answer: (B) 22 (2/9)m
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
(A) 329
(B) 2698
(C) 175
(D) 212
(E) 221
Rationale: RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m.Answer: C
Answer: (C) 175
Question: If a/b = 4/5, Then (5a - 3b) / (5a + 3b) = ?
(A) 4
(B) 2/3
(C) 3
(D) 1
(E) 1/7
Rationale: Answer
Dividing numerator as well as denominator by b, we get
Given Exp. = (5a - 3b) / (5a + 3b) = (5a/b - 3) / (5a/b + 3)
Since a/b = 4/5
this implies that
=[(5*4)/5 -3]/[(5*4)/5 +3)]
= (4- 3) / (4 + 3)
= 1/7
Option: E
Answer: (E) 1/7
Question: A man sells an article at a gain 15%. If he had bought it at 10% less and sold it for 4 less, he would have gained 25%. Find the cost price of the article.
(A) 150
(B) 160
(C) 170
(D) 180
(E) None of these
Rationale: Let the C.P. be 100
First S.P. = 115
Second C.P. = 90
Second S.P = 125% of 90 = 112.50
Difference of two selling prices is 115 – 112.50 = 2.50 and C.P. of the article is 100
But actual difference is 4.
∴ C.P. = 100⁄2.50 × 4 = 160.
Answer B
Answer: (B) 160
Question: What percent of 60 is 70?
(A) 133 1⁄3
(B) 75
(C) 60
(D) 33 1⁄3
(E) 116.66
Rationale: % of 60 is 70?
= 70/60 = 7/6 = 116.66%
Thus E is the correct answer.
Answer: (E) 116.66
Question: The dividend is 126, the quotient is 3 and the remainder is 2.
What is the divisor?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: D = d * Q + R
126 = d * 3 + 2
126/3 = d + 2
42 = d + 2
42-2 = d
40 = d
Answer: C
Answer: (C) 40
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, 43, x
(A) 29
(B) 31
(C) 23
(D) 46
(E) 59
Rationale: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 43 + 3 = 46.
Answer: (D) 46
Question: Stacy and Heather are 10 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour fast than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?.
(A) 6.0 mile
(B) 3.0 mile
(C) 4.0 mile
(D) 3.45 mile
(E) 12 mile
Rationale: Ss - Stacy's speed = 6m/hr
Sh - Heather's speed = 5m/hr
In 24 minutes Stacy will cover = (24/60)*6 = 2.4miles
Now since both are walking in opposite directions, add their speeds - 6+5 =11m/hr and distance to cover is 10 -2.4 = 7.6
Time taken = Distance/ Speed = 7.6/11 = 0.69 hrs
Heather will cover = 5*0.69 = 3.45 miles.
Answer D
Answer: (D) 3.45 mile
Question: In a km race, A beats Bby 28 metres or 7 seconds. Find A's timeoverthe course
(A) 4 min
(B) 3 min. 3sec
(C) 4 min.4 sec
(D) 5 min. 3 sec
(E) 4 min. 3 sec
Rationale: Clearly, B covers 28 m in 7 seconds.
:. B's time over the course = (278 x 1000) sec = 250 seconds.
:. A's time over the course = (250 - 7-) sec = 243 sec
= 4 min. 3 sec.
Option E
Answer: (E) 4 min. 3 sec
Question: At a monthly meeting, 1/3 of the attendees were males and 4/5 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?
(A) 1/6
(B) 2/15
(C) 3/20
(D) 7/30
(E) 8/45
Rationale: Males who did not arrive on time are 1/5*1/3 = 1/15 of the attendees.
Females who did not arrive on time are 1/6*2/3 = 1/9 of the attendees.
The fraction of all attendees who did not arrive on time is 1/15 + 1/9 = 8/45
The answer is E.
Answer: (E) 8/45
Question: If Scott has earned 364 dollars by working 4 hrs/day a week at a constant daily rate for 1 weeks, which of the following represents his daily wage?
(A) 15
(B) 14
(C) 13
(D) 12
(E) 11
Rationale: Scott total earning = 364
No days he worked = 4 * 7 = 28
Rate = 1 week
Daily wage = total / (Rate * days)
= 364/(4*7*1)
= 13
C is correct answer...
Answer: (C) 13
Question: Of the people who responded to a market survey, 360 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 9 to 1, how many people responded to the survey?
(A) 80
(B) 160
(C) 240
(D) 360
(E) 400
Rationale: Ratio = 9:1 => 9x respondents preferred Brand X and x preferred Brand Y
Since, no. of respondents who preferred Brand X = 360 => 9x=360 => x=40
Hence Total no. of respondents = 360 + 40 = 400
Hence E is the answer.
Answer: (E) 400
Question: In a group of 5 boys and 3 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 60
(B) 50
(C) 80
(D) 30
(E) 120
Rationale: Required number of ways = 5C1*3C3 + 5C2*3C2 + 5C3*3C1 + 5C4
= 15+30+30+5
= 80
Answer is C
Answer: (C) 80
Question: By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at
(A) 46
(B) 96
(C) 35
(D) 87
(E) 13
Rationale: To earn Rs. 135, investment
= Rs. 1620.
To earn Rs. 8, investment
= Rs. 96.
Market value of Rs. 100 stock
= Rs. 96.
Answer: B
Answer: (B) 96
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150
(B) 277
(C) 272
(D) 278
(E) 121
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: (A) 150
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 289 cm
(B) 800 cm
(C) 829 cm
(D) 288 cm
(E) 289 cm
Rationale: Area of the square = s * s
= 5(125 * 64)
=> s = 25 * 8
= 200 cm
Perimeter of the square
= 4 * 200
= 800 cm.
Answer: B
Answer: (B) 800 cm
Question: A car traveled the first quarter of a certain distance at thrice the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance?
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/7
(E) 1/10
Rationale: These problems can be solved through algebra or sly number picking. Being a big fan of solving problems with numbers, let's pick a total distance divisible by 4 (say 40) so we can break it up into quarters, and a speed that can easily be one-third, say 10. Each quarter is thus 10 kilometers (or miles or feet or angstroms for all it matters), and the runner's speed is 10 km/h for the first quarter and 3 1/3 km/h for the remaining quarters.
He'll take 1 hour to do the first quarter and then 3 hours for the second quarter,3 hours for the third and 3 hours for the fourth. On total he will take 10 hours to complete this race, of which 1 hour was spent on the first quarter. So 1/10. Answer E.
Answer: (E) 1/10
Question: In how many ways can 7 identical beads be stung into a ring?
(A) 7!
(B) 5!
(C) 6!
(D) 6!/2
(E) 3!
Rationale: since the arrangement is either clockwise or anticlockwise, we have 6!/2 ways. Ans:( D )
Answer: (D) 6!/2
Question: On Teacher's Day, sweets were to be equally distributed among 190 children in a school. Actually, on the Teacher's day, 70 children were absent and therefore each child got 14 sweets extra. How many sweets did each child get on that day?
(A) 18
(B) 22
(C) 28
(D) 32
(E) 38
Rationale: Total Children = 190.
Let each student gets x chocolates if all were present.
So, Total chocolates = 190x.
70 students were absent. So, no of extra chocolates distributed among 120 students,
= 14 *70 = 980.
Now,
Total chocolates = 190x
120 * (x +14) = 190
120x + 1680 = 190x
70x = 1680
x = 24.
Total no of chocolates = 24 * 190 = 4560.
No of chocolates each student gets on that day = 4560/120 = 38.
ANSWER : OPTION E
Answer: (E) 38
Question: The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
(A) 1/2
(B) 3/4
(C) 3/7
(D) 4/5
(E) 5/7
Rationale: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
Answer: (B) 3/4
Question: In a department store prize box, 40% of the notes give the winner a dreamy vacation; the other notes are blank. What is the approximate probability that 3 out of 5 people that draw the notes one after the other, and immediately return their note into the box get a dreamy vacation?
(A) 0.12
(B) 0.23
(C) 0.35
(D) 0.45
(E) 0.65
Rationale: The probability of winning is 40% = 40/100 = 2/5.
The probability of NOT winning is 60% = 3/5.
P(WWWNN)=5!3!2!∗(25)3∗(35)2=144625≈23P(WWWNN)=5!3!2!∗(25)3∗(35)2=144625≈23 (we multiply by 5!3!2!5!3!2!, because WWWNN scenario can occur in several ways: WWWNN, WWNWN, WNWWN, NWWWN, ... the # of such cases basically equals to the # of permutations of 5 letters WWWNN, which is 5!3!2!5!3!2!).
Answer: B.
Answer: (B) 0.23
Question: A is 7/2 times as fast as B. If A gives B a start of 80 m, how long should the race course be so that both of them reach at the same time?
(A) 140 metre
(B) 180 metre
(C) 190 metre
(D) 240 metre
(E) 12 metre
Rationale: Speed of A : Speed of B = 7⁄3 : 1 = 7 : 3
It means, in a race of 7 m, A gains (7-3)=4 metre
If A needs to gain 80 metre, race should be of 7/4×80 = 140 metre
Answer is A
Answer: (A) 140 metre
Question: If x represents the sum of the interior angles of a triangle and y represents the sum of the interior angles of a regular pentagon, then the addition x and y is equal to the sum of the interior angles of what geometric shape?
(A) Hexagon
(B) Square
(C) Rhombus
(D) Trapezoid
(E) Pentagon
Rationale: Sum of angles of Triangle= 180*(3-2) = 180 => using formula sum of angles of polygon = 180*(n-2) where n is the number of sides in a polygon
Sum of angles in Pentagon = 180*(5-2) =540
Difference = 180 +540 = 720 => Hexagon
hence (A).
Answer: (A) Hexagon