mathewhe/aqua_rat huggingface dataset:
Question: An bus covers a certain distance at aspeed of 240 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
(A) 450 km/hr
(B) 466 km/hr
(C) 559 km/hr
(D) 878 km/hr
(E) 720 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
5
E
Answer: (E) 720 km/hr
Question: The residents of the town A participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town A, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
(A) - 30
(B) - 20
(C) - 6
(D) - 12
(E) - 16
Rationale: (21-6*2)<number of hours that Pat watched television last week <(21-6*1)
=9<W<15
12=C.
Answer: (C) - 6
Question: A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $310,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment?
(A) $1,292
(B) $1,733
(C) $3,466
(D) $12,917
(E) $20,796
Rationale: 0.04x + 0.09y = 310000 [1]
0.04x = 0.80 * 310000 = 248000 [2]
248000 + 0.09y = 310000 --> 0.09y = 62000 [3]
248000 / 12 = 258333.3333 [4]
62000 / 12 = 5166.67 [5]
Adding [4,5] we get: 25833 [6]
Dividing [6] / 2 to get an average we get 1.292,ANS A
Answer: (A) $1,292
Question: a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out the area of square which is not covered by circles?
(A) 0.76
(B) 0.86
(C) 0.96
(D) 1.16
(E) 1.26
Rationale: let the radius of circle is 'r'
area of the circle which is at corner = (22/7*r^2)/4
hence the area of all four circles are = 22/7*r^2
areaof circle which is made on center of suare is = 22/7*r^2
total area of all circles are = 2*22/7*r^2...........................(1)
if we construct the diagram we get the relation
4r = 2sqrt2
r = 1/sqrt2
put the value of r in eqn 1 and we get
2*22/7*1/2 = 22/7 = 3.14
area of suare = 2^2 = 4
area of remaining part = 4-3.14 = 0.86
ANSWER:B
Answer: (B) 0.86
Question: If s and t are positive integers such that s/t = 64.16, which of the following could be the remainder when s is divided by t?
(A) 15
(B) 18
(C) 24
(D) 30
(E) 35
Rationale: 0.16 = 4/25
The remainder must be divisible by 4.
The answer is C.
Answer: (C) 24
Question: The arithmetic mean of 2 numbers is 34 and their geometric mean is 16. One of the numbers will be
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: A.M=x+y2=34
x+y=68
G.M=(x.y)^1/2=16
x.y=256
x^2-68x+256=0
x=4 or 64
ANSWER:D
Answer: (D) 4
Question: What is the sum of mean and median of 17, 45, 59, 113, 76, 95, 59, 35, 12,36 ?
(A) 50.2
(B) 45.8
(C) 54.7
(D) 61.8
(E) 10.5
Rationale: mean = (17+ 45+ 59+ 113+ 76+ 95+ 59+ 35+ 12 + 36)/10 = 547/10 = 54.7
Answer is C
Answer: (C) 54.7
Question: A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 8 salespeople on staff, how many different arrangements of winners are possible?
(A) 1,728
(B) 1,440
(C) 336
(D) 220
(E) 6
Rationale: [quote=Bunuel]A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 8 salespeople on staff, how many different arrangements of winners are possible?
8*7*6
=336
Answer : C
Answer: (C) 336
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 2 (1/2) km/h
(B) 4 km/h
(C) 6 km/h
(D) 3 km/h
(E) 7 km/h
Rationale: Explanation:
100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 ½ kmph
Answer: Option D
Answer: (D) 3 km/h
Question: Two vessels contains equal number of mixtures milk and water in the ratio 5:3 and 6:2. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained?
(A) 11:5
(B) 9:13
(C) 5:11
(D) 11:3
(E) 15:4
Rationale: The ratio of milk and water in the new vessel is = (5/8 + 6/8) : (3/8 + 2/8)
= 11/8 : 5/8 = 11:5
Answer is A
Answer: (A) 11:5
Question: Rita can knit a pair of socks in 3 days. Sita can knit the same in 6 days. If they are knitting together, in how many days will they knit two pairs of socks.
(A) 4
(B) 1
(C) 2
(D) 5
(E) 6
Rationale: 1 /3+ 1/6 = 1 /2 Together they will take, 1/ 1/2 = 2
Answer: C.
Answer: (C) 2
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
(A) 1/37
(B) 1/36
(C) 1/39
(D) 1/34
(E) 1/28
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6
= 216 ways.
Hence the probability is 6/216
=1/36
Answer: B
Answer: (B) 1/36
Question: Running 3/4th of his usual rate, a man is 10min late. Find his usual time in hours ?
(A) 6/4 hrs
(B) 3/4 hrs
(C) 9/4 hrs
(D) 3/4 hrs
(E) 1/2 hrs
Rationale: Explanation:
Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time
so 1/3rd of the usual time = 15min
or usual time = 3 x 10 = 30min = 30/60 hrs = 1/2 hrs.
Answer: E
Answer: (E) 1/2 hrs
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) 482
(B) 725
(C) 992
(D) 837
(E) 923
Rationale: 20000(11/10)4 - 20000(6/5)2 = 482
Answer:A
Answer: (A) 482
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
(A) 188
(B) 270
(C) 288
(D) 266
(E) 128
Rationale: I = (500*9*6)/100 = 270.Answer: B
Answer: (B) 270
Question: A function g(n), where n is an integer, is defined as the product of all integers from 1 to n. How many of the following must be a prime number?
g(11) + 2; g(11) + 3; g(11) + 4; and g(11) + 5
(A) 1
(B) 2
(C) 3
(D) 4
(E) none
Rationale: g(11) is the product of all integers from 1 to 11, so g(11) = 11!
Thus g(11) is a multiple of all the integers from 1 to 11.
Then g(11) is a multiple of 2, 3, 4, and 5.
2 divides g(11)+2
3 divides g(11)+3
4 divides g(11)+4
5 divides g(11)+5
The answer is E.
Answer: (E) none
Question: If (m-8) is a factor of m^2-hm-24, then h=
(A) 3
(B) 5
(C) 6
(D) 11
(E) 16
Rationale: (m-8)(m-a)=m^2-hm-24
A=-3
h=8+a=5=B
Answer: (B) 5
Question: A man can row downstream at the rate of 32 Kmph and upstream at 8 Kmph. Find the man’s rate in still water and rate of current?
(A) 20 Kmph, 10 Kmph
(B) 12 Kmph, 22 Kmph
(C) 22 Kmph, 12 Kmph
(D) 20 Kmph, 12 Kmph
(E) None of these
Rationale: Explanation:
Rate of still water = 1/2 (down stream + upstream)
= 1/2 (32 + 8) = 20 Kmph
Rate of current = 1/2 (down stream - upstream)
= 1/2 (32 - 8)
= 1/2 (24)
= 12 kmph
Answer: Option D
Answer: (D) 20 Kmph, 12 Kmph
Question: Find the odd man out. 1, 5, 11, 17, 23, 29
(A) 29
(B) 11
(C) 17
(D) 1
(E) 23
Rationale: Explanation :
All given numbers except 1 are prime numbers.
One is not a prime number because it does not have two factors. It is divisible by only 1
Answer : Option D
Answer: (D) 1
Question: Excluding stoppages, the speed of a bus is 54 km/hr and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?
(A) 118 min
(B) 10 min
(C) 18 min
(D) 16 min
(E) 15 min
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = 9/54 * 60
= 10 min.
Answer:B
Answer: (B) 10 min
Question: Bradley owns b video game cartridges. If Bradley’s total is one-sixth the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) 23b / 4
(B) 25b / 4
(C) 27b / 4
(D) 29b / 4
(E) 31b / 4
Rationale: b = Bradley’s total
6b = Andrew’s total
b/4 = Charlie’s total
The total number of cartridges is:
b + 6b+ b/4 = (4b + 24b + b) / 4 = 29b / 4
The answer is D.
Answer: (D) 29b / 4
Question: Find large number from below question The difference of two numbers is 750. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1345
(B) 1250
(C) 897
(D) 900
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 750 = 6x + 15
5x = 735
x = 147
Large number = 147+1365 = 897
C
Answer: (C) 897
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3%
(B) 16 2/7%
(C) 16 7/3%
(D) 18 2/3%
(E) 11 2/3%
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Answer: (A) 16 2/3%
Question: A candidate got 35% of the votes polled and he lost to his rival by 2340 votes. How many votes were cast?
(A) 7500
(B) 3388
(C) 2665
(D) 7800
(E) 2661
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2340
100%---------? => 7800
Answer: D
Answer: (D) 7800
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 3 and that the product of the given number and the sum of its digits is equal to 324, then the number is:
(A) 12
(B) 14
(C) 23
(D) 25
(E) 36
Rationale: Let the ten's digit be x. Then, unit's digit = x + 3. Number = 10x + (x + 3) = 11x + 3
Sum of digits = x + (x + 3) = 2x + 3
(11x + 3)(2x + 3) = 324
22(x)(x) + 39x - 315 = 0
(x - 3)(22x + 105) = 0
x = 3
Hence, required number = 11x + 3 = 36.
ANSWER:E
Answer: (E) 36
Question: The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is
(A) 33
(B) 35
(C) 28
(D) 220
(E) 21
Rationale: Explanation:
Excluded number = (27 x 5) - (25 x 4) = 135 - 100 = 35.
Answer: B
Answer: (B) 35
Question: A 9 by 12 rectangle is inscribed in circle. What is the circumference of the circle?
(A) 2.5π
(B) 5π
(C) 10π
(D) 12.5π
(E) 15π
Rationale: The diagonal of the rectangle will be the diameter of the circle.
and perimeter= 2*pi*r
Ans: E
Answer: (E) 15π
Question: Find 18/6*4
(A) 1.25
(B) 4.53
(C) 2.69
(D) 0.89
(E) 0.75
Rationale: Answer=18/6*4
=18/24=0.75
Option E is correct
Answer: (E) 0.75
Question: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1, then what is the value of abc/def ?
(A)  27/4
(B)  27/8
(C)  3/4
(D)  3/2
(E)  1/4
Rationale: Say a = 2. Then:
a/b = 1/3 --> b = 6;
b/c = 2 --> c = 3;
c/d = 1/2 --> d = 6;
d/e = 3 --> e = 2;
e/f = 1 --> f = 2.
abc/def = (2*6*3)/(6*2*2) = 3/2.
Answer: D.
Answer: (D)  3/2
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
(A) 12809
(B) 12800
(C) 12807
(D) 12802
(E) 12801
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
Answer: B
Answer: (B) 12800
Question: A train crosses a platform of 250 m in 20 sec, same train crosses another platform of length 640m in 40 sec. then find the length of the train?
(A) 150m
(B) 180m
(C) 152m
(D) 140m
(E) 160m
Rationale: Length of the train be ‘X’
X + 250/20= X + 640/40
2X + 500 = X + 640
X = 140m
Answer:D
Answer: (D) 140m
Question: A train passes a station platform in 25 seconds and a man standing on the platform in 12 seconds. If the speed of the train is 72 km/hr, what is the length of the platform?
(A) 220
(B) 240
(C) 260
(D) 280
(E) 300
Rationale: The speed of the train is 72 * 5/18 m/s = 20 m/s
The length of the train is 20 x 12 = 240 m
platform + 240 = 20 * 25
platform = 500 - 240 = 260
The answer is C.
Answer: (C) 260
Question: In Gabriel's sheep herd, every sheep has either fleas or lice or both. Half of the sheep have lice, and 84 sheep have both pests. If 94 sheep have lice, how many sheep have only fleas?
(A) 10
(B) 20
(C) 84
(D) 94
(E) 178
Rationale: n(Lice) = n(Only lice) + n(Both lice and fleas)
n(Both lice and fleas) = 84
n(Lice) = 94
n(Only lice) = 94-84 = 10
Since, it is also said that exactly half the sheep have lice, it can be inferred that half the number of sheep is 94.
Therefore, the total number of sheep having only fleas is 10
ANS:(Option A)
Answer: (A) 10
Question: A boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 7.5
(D) 8
(E) 9
Rationale: US = 20
DS = 35
M = (35 - 20)/2 = 7.5
Answer: C
Answer: (C) 7.5
Question: The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 10 percent of the cost of the tomatoes.
(A) $0.94
(B) $0.96
(C) $0.98
(D) $1.00
(E) $1.20
Rationale: Assume the manager bought 100 tomatoes.
Cost Price = 80
Given: 10% are damaged --> Available tomatoes to sell = 90
90 * x - 80 = 0.1 * 80
90x - 80 = 8
90x = 88
x = 88/90 = 44/45 = 0.977
x is slightly under 0.977= 0.98
Answer: C
Answer: (C) $0.98
Question: A can do a piece of work in 14 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
(A) 18
(B) 77
(C) 66
(D) 55
(E) 14
Rationale: 8/14 + 6/x = 1
X = 14 days
Answer:E
Answer: (E) 14
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 6, the dividend is:
(A) 92
(B) 94
(C) 96
(D) 98
(E) 100
Rationale: Divisor = (5 * 6) = 30
= 10 * Quotient = Divisor
=> Quotient = 30/10 = 3
Dividend = (Divisor * Quotient) + Remainder
Dividend = (30 * 3) + 6 = 96.
C
Answer: (C) 96
Question: Two pipes A and B can fill a cistern in 10 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 19 1/7 min
(B) 15 1/7 min
(C) 17 1/7 min
(D) 9.2 min
(E) 7 2/7 min
Rationale: 1/10 + 1/30 - 1/40 = 13/120
120/13 = 9.2
ANSWER:D
Answer: (D) 9.2 min
Question: 20 people went to a hotel for combine dinner party 12 of them spent Rs. 70 each on their dinner and rest spent 4 more than the average expenditure of all the 20. What was the total money spent by them.
(A) 1628.4
(B) 1534
(C) 1453
(D) 1496
(E) None of these
Rationale: Solution: Let average expenditure of 20 people be x.
then,
20x = 12*70+8*(x+4);
Or, 20x = 12*70+8x+32;
Or, x = 72.667;
So, total money spent = 72.67*20 = Rs. 1453.4.
Answer: Option C
Answer: (C) 1453
Question: Calculate the rate on a principal of Rs.1500 which yields a simple interest of Rs. 220.50 in 3 Years?
(A) 6.9%
(B) 2.9%
(C) 9.9%
(D) 5.9%
(E) 4.9%
Rationale: 220.50 = (1500*3*R)/100
R = 4.9%
Answer: E
Answer: (E) 4.9%
Question: A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?
(A) 20 min past 8pm on wednesday
(B) 20 min past 7pm on wednesday
(C) 20 min past 6pm on wednesday
(D) 20 min past 2pm on wednesday
(E) 20 min past 4pm on wednesday
Rationale: This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours.
To show the correct tine, it has to gain 5 min.
So the correct time will be shown on wednesdy at 7:20 PM
Answer: B) 20 min past 7pm on wednesday
Answer: (B) 20 min past 7pm on wednesday
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 28
(B) 68
(C) 92
(D) 66
(E) 21
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer:B
Answer: (B) 68
Question: The compound interest accrued on an amount of Rs.44000 at the end of two years is Rs.1193.60. What would be the simple interest accrued on the same amount at the same rate in the same period?
(A) Rs.10,569
(B) Rs.10,588
(C) Rs.10,560
(D) Rs.10,991
(E) Rs.10,511
Rationale: Let the rate of interest be R% p.a.
4400{[1 + R/100]2 - 1} = 11193.60
[1 + R/100]2 = (44000 + 11193.60)/44000
[1 + R/100]2 = 1 + 2544/1000 = 1 + 159/625
[1 + R/100]2 = 784/625 = (28/25)2
1 + R/100 = 28/25
R/100 = 3/25
Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100
=Rs.10560
Answer:C
Answer: (C) Rs.10,560
Question: How many of the integers between 15 and 55 are even ?
(A) 21
(B) 20
(C) 11
(D) 10
(E) 9
Rationale: Number start between 15 to 55 is 40 numbers
half of them is even..which is 20
ANSWER:B
Answer: (B) 20
Question: The LCM of two numbers is 2310 and HCF is 83. If one of the numbers is 210. Then what is the other number ?
(A) 913
(B) 825
(C) 330
(D) 582
(E) 465
Rationale: First number * Second Number = LCM * HCF
Other number = 2310 * 83 / 210 = 11*83 = 913
ANSWER :A
Answer: (A) 913
Question: A team of 6 cooks is chosen from 8 men and 4 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?
(A) 140
(B) 252
(C) 560
(D) 700
(E) 840
Rationale: Only possible combinations are a team of 2M, 4 W or 3M,3W.
Possible ways to make a team of 2M,4W = 8C2 * 4C4 =28*1 =28
Possible ways to make a team of 3M,3W = 8C3* 4C3 = 56*4 = 224
Total possible ways = 28+224 = 252
Ans B it is.
Answer: (B) 252
Question: Insert the missing number
2, 4, 8, 16, 32, ..., 128, 256
(A) 46
(B) 65
(C) 64
(D) 63
(E) 68
Rationale: series is 2* Previous Number.
ANSWER:C
Answer: (C) 64
Question: Farm Tax is levied on the 50% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
(A) 15%
(B) 25%
(C) 0.125%
(D) 0.2083%
(E) none
Rationale: Only trick n this question is to ignore 50% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/50) = 25% and the answer is not there in the options.
The correct answer is (B).
Answer: (B) 25%
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 9 o'clock in the morning?
(A) 30
(B) 60
(C) 90
(D) 120
(E) 150
Rationale: The hour hand will move 1/12 of a circle.
(1/12)*360 = 30 degrees.
The answer is A.
Answer: (A) 30
Question: A can complete a certain job in 19 days. B is 90% more efficient than A. In how many days can B complete the same job?
(A) 6
(B) 6.25
(C) 7
(D) 7.5
(E) 10
Rationale: Let, Total Work Unit = 190 Units
A can finish in 19 days = 190 unit work
i.e. A can finish in 1 days = 10 unit work
i.e. B can finish in 1 days = 10+(90/100)*10 = 19 unit work
Days in which B will complete the work alone = 190/19 = 10 days
Answer: Option E
Answer: (E) 10
Question: A can do a job in 12 days and B can do it in 20 days. A and B working together will finish twice the amount of work in ------- days?
(A) 15 days
(B) 13 days
(C) 22 days
(D) 11 days
(E) 19 days
Rationale: A
1/12 + 1/20 = 2/15
15/2 *2 = 15 days
Answer: (A) 15 days
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
(A) 26
(B) 39
(C) 42
(D) 56
(E) 82
Rationale: Let the average after 17th inning = x
Then, average after 16th inning = x-3
16(x-3)+87 = 17x
x = 87-48 = 39
Answer is B
Answer: (B) 39
Question: Integer X represents the product of all integers between 1 to 29 (inclusive). The smallest prime factor of (x+1) must be
(A) Between 1 to 10
(B) Between 11 to 15
(C) Between 15 to 20
(D) Between 20 to 29
(E) Greater than 29
Rationale: Answer = E = Greater than 29
This problem is asking smallest prime factor of (25!+1)
29! already have there prime factors 2,3,5,7,11,13.......... so on upto 29 (1 cannot be considered prime factor)
Just adding 1 to 29! will remove all the factors stated above;
so the smallest possible prime factor has to be greater than 29
Answer = E
Answer: (E) Greater than 29
Question: In a theater, the first row has 17 seats and each row has 3 more seats than previous row. If the last row has 44 seats, what is the total number of seats in the theater?
(A) 265
(B) 275
(C) 285
(D) 295
(E) 305
Rationale: The number of seats in the theater is
17 + (17+3) + ...+ (17+27)=
10(17) + 3(1+2+...+9)=
10(17) + 3(9)(10)/2= 170 + 135 = 305
The answer is E.
Answer: (E) 305
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 15 metres?
(A) 5
(B) 10
(C) 3
(D) 12
(E) 6
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 15/5 = 3 seconds.
Answer: C
Answer: (C) 3
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?
(A) 34
(B) 28
(C) 27
(D) 23
(E) 27
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 42
Tu + W + Th = 192 -42 = 150
F = 184 – 150
= 34
Answer: D
Answer: (D) 23
Question: If A = {9, 17, 25, 28, 29, 30}, how much less is the mean of the numbers in A than the median of the numbers in S?
(A) 1.0
(B) 9.6
(C) 3.5
(D) 3.2
(E) 5.1
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (9 + 17 + 25 + 28 + 29 + 30)/6 = 23
Median = (25 + 28)/2 = 26.5
Difference = 3.5
Option C
Answer: (C) 3.5
Question: A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made?
(A) 7
(B) 9
(C) 4
(D) 5
(E) 2
Rationale: Explanation:
The maximum number of bows will be 4 yards (= 4 x 36 inches) divided by 15 inches.
This gives 9.6. But as a fraction of a bow is no use, we can only make 9 bows.
Answer: B) 9
Answer: (B) 9
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 768 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 6
(C) 8
(D) 24
(E) None of these
Rationale: Let rate = R% and time = R years.
Then, (1200 x R x R)/100 = 768
12R2 = 768
R2 = 64
R = 8.
Answer: Option C
Answer: (C) 8
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 13?
(A) 3
(B) 4
(C) 5
(D) 8
(E) 7
Rationale: i'm not sure i got the question right, if it is what i think it is, then 8 should be the right answer
0,1,2,3,4,5, will not have 2 slip sum of 13 add another (either 6,7,8 or 9) and we'll have a pair with sum 13
Ans:D
Answer: (D) 8
Question: Find the average of first 32 natural numbers.
(A) A)12.6
(B) B)16.5
(C) C)15.9
(D) D)17.5
(E) E)20.6
Rationale: Sum of first n natural numbers = n(n+1)/2
sum of first 32 natural numbers = 32*33/2 =528
average = 528/32 = 16.5
Answer is B
Answer: (B) B)16.5