mathewhe/aqua_rat huggingface dataset:
Question: A student must answer 7 out of 10 questions on an competitive examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?
(A) 90
(B) 80
(C) 70
(D) 100
(E) 110
Rationale: as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five
choose 2 in first 5 and all 5 from later half..
ways = 5C2 = 10..
total ways = 10C3 = 120
ans = 120-10 = 110
E
Answer: (E) 110
Question: A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.4 per box per month for the record storage, what is the total amount that the company pays each month for record storage?
(A) a. 150
(B) b. 300
(C) c. 600
(D) d. 240
(E) e. 200
Rationale: Volume Per Box: 15x12x10 = 1,800
Total Volume: 1,080,000
Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600
Price Per Month: Number of Boxes * Price Per Box = 600 * 0.4 = 240
Answer: D
Answer: (D) d. 240
Question: In an encryption code 'HOUSE' is written as '1S902' when encoded and 'DASH' is written as '4G01' when encoded. How is ''SHED" written in that encryption code?
(A) S109
(B) 0SG1
(C) 0124
(D) G910
(E) 102G
Rationale: 0 = S
1 = H
2 = E
4 = D
Answer: Option C
Answer: (C) 0124
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 18 sec
(B) 17 sec
(C) 14 sec
(D) 10 sec
(E) 11 sec
Rationale: A
D
RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec
Answer: (D) 10 sec
Question: Kathleen can paint a room in 2 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?
(A) 20/7
(B) 4/3
(C) 15/8
(D) 9/4
(E) 15/4
Rationale: (1/2 + 1/5)t=2
t=20/7
Answer: A
Answer: (A) 20/7
Question: If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 6, what is the units digit of (a+2)^2?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: If the units digit of a^2 is 9, then the units digit of a is either 3 or 7.
If the units digit of (a+1)^2 is 6, then the units digit of a+1 is either 4 or 6.
To satisfy both conditions, the units digit of a must be 3.
Then a+2 has the units digit of 5, thus the units digit of (a+2)^2 will be 5.
The answer is C.
Answer: (C) 5
Question: A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does
the wheel move in one hour?
(A) 6 metre
(B) 12 metre
(C) 120 metre
(D) 1200 metre
(E) 2200 metre
Rationale: Expl : Number of times wheel moves in 1 hour = 10 * 60 = 600
:. Distance moves = (600 *20) cms = 12000 cms
In metres = 120 metre
Answer: C
Answer: (C) 120 metre
Question: Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.153 per kg, the price of the third variety per kg will be
(A) Rs.169.50
(B) Rs.1700
(C) Rs. 175.50
(D) Rs. 180
(E) None
Rationale: Solution
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x-153/22.50 = 1 =› x - 153 = 22.50 =› x=175.50.
Hence, price of the third variety = Rs.175.50 per kg.
Answer C
Answer: (C) Rs. 175.50
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 276 m
(B) 167 m
(C) 245 metrs
(D) 167 m
(E) 178 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time
= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer:C
Answer: (C) 245 metrs
Question: A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among five colors produced enough color codes to identify all but 6 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: 5C2 = 10
The number of test subjects is 10 + 6 = 16
The answer is C.
Answer: (C) 16
Question: n a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
(A) 2 hrs
(B) 3 hrs
(C) 1 hr
(D) 4 hrs
(E) 5 hrs
Rationale: Let the duration of the flight be x hours. Then,
600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr.
ANSWER C
Answer: (C) 1 hr
Question: Shepherd Gopal had a curious aptitude for mathematics and he was known around where he lived as the 'Counting Shepherd.
A man passing throughthe meadow one dat saw Gopal grazing a number of sheep and in the course of a short conversation asked him how many of the grazing sheep were his own. Gopal's reply absolutely baffled him, which was as follows:
If you divide my sheep into two different parts, the difference between yhe two numbers will be the same as the difference between their squares. Now figure it out for yourself the number of sheep I own.'
Can you say just how many sheep Gopal had?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: A
Shepherd Gopal had one sheep only.
Answer: (A) 1
Question: A train 120 meters long completely crosses a 480 meters long bridge in 55 seconds. What is the speed of the train is?
(A) 32
(B) 545
(C) 39
(D) 40
(E) 09
Rationale: S = (120 + 480)/45 = 600/55 * 18/5 = 39
Answer: C
Answer: (C) 39
Question: On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
(A) 2.04%
(B) 6.12%
(C) 8%
(D) 8.25%
(E) 10%
Rationale: Per quarter, interest = 2%
So for a year, interest = 8%
Due to quarter cumulation, effective yield (YTM) would be slight higher than 8%
Answer = 8.25% =ANSWER:D
Answer: (D) 8.25%
Question: What is the ratio between perimeters of two squares one having 2 times the diagonal then the other?
(A) 3: 8
(B) 3: 6
(C) 3: 7
(D) 2: 1
(E) 3: 3
Rationale: d = 2d d = d
a√2 = 2d a√2 = d
a = 2d/√2 a = d/√2 => 2: 1
Answer:D
Answer: (D) 2: 1
Question: A train passes through a telegraph post in 9 seconds moving with a speed of 54 km per hour. The length of the train is
(A) 135 metres
(B) 145 metres
(C) 125 metres
(D) 155 metres
(E) None of these
Rationale: We know from the formula Distance = Speed x time
Thus, Distance = 54 x 5/18 x 9
or, Distance =135 meters.
ANSWER:A
Answer: (A) 135 metres
Question: The total cost of 100 paper plates and 200 paper cups is $4.00 At the same rates what is the total cost of 20 of the plates and 40 of the cups?
(A) $.80
(B) $1.00
(C) $1.20
(D) $1.50
(E) $1.60
Rationale: U dont need to go through all this
What u have with u is
100 P + 200 C = $4.00
Just divide the equation by 5 and you will get what u are looking for
20P + 40 C = $0.80
Therefore OA is A
Answer: (A) $.80
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
(A) 20002
(B) 20000
(C) 20007
(D) 200018
(E) 20012
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer:B
Answer: (B) 20000
Question: A bullet train passes a station platform in 36 seconds and a man standing on the platform in 23 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?
(A) 240 m
(B) 220 m
(C) 195 m
(D) 224 m
(E) 239 m
Rationale: A
195 M
Speed = 54 x 5/18 = 15 m/s
Length of the bullet train = (15 x 23)m = 345 m.
Let the length of the platform be x metres.
Then, (x + 345)/36 = 15
--> x + 345 = 540
x = 195m. C
Answer: (C) 195 m
Question: If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a × b × c < a^3
II. a + b + c > a^3
III. 5b < bc
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
Rationale: Given:
1) a is even prime. The only even prime number known is 2, so a must be equal to 2.
2) a,b,c are consecutive such that a<b<c. So, b must be 3 and c must be 4.
So, we know that a=2, b=3 and c=4.
Substituting the above values in the three equations,
I. abc<a^3
which simplifies to 24<8. False.
II. a+b+c>a^3
which simplifies to 9>8. True.
III. 5b<bc
which simplifies to 15<12. False.
The only option correct is II, so the answer is B.
Answer: (B) II only
Question: If X is to be chosen at random from the integers between 1 to 5, inclusive, and Y is to be chosen at random from the integers between 7 and 10, inclusive, what is the probability that X + Y will be even?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 4/5
(E) 5/6
Rationale: X+Y will be even if X and Y are both even or both odd.
P(X and Y are both even) = 2/5*2/4 = 1/5
P(X and Y are both odd) = 3/5*2/4 = 3/10
P(X+Y is even) = 1/5 + 3/10 = 1/2
The answer is A.
Answer: (A) 1/2
Question: In a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D Scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. How many runs did E score ?
(A) 62
(B) 45
(C) 28
(D) 20
(E) 24
Rationale: a+b+c+d+e=36*5=180
b+c=107
a=x
e=x-8
d=x-3
now 3x-11+107=180
3x=84
x=28
e's score=28-8=20
ANSWER:D
Answer: (D) 20
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.78
(B) 5.28
(C) 5.76
(D) 5.16
(E) 5.19
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer:C
Answer: (C) 5.76
Question: Nicole cycles at a constant rate of 24 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
(A) x/4
(B) x/3
(C) x/2
(D) x
(E) 4x/3
Rationale: In x minutes, Jessica travels (x/60)*30 = x/2 miles
The time it takes Nicole to travel x/2 miles is (x/2) / 24 = x/48 hours = 5x/4 minutes
Jessica needs to wait 5x/4 - x = x/4 minutes.
The answer is A.
Answer: (A) x/4
Question: X can do a piece of work in 40days. He works at it for 8days and then Y finished it in 28 days. How long will Y take to complete the work?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 35
Rationale: Work done by X in 8days = 8*1/40 = 1/5
Remaining work = 1 - 1/5 = 4/5
4/5 work is done by Y in 28 days
Whole work will be done by Y in 28*5/4 = 35 days
Answer is E
Answer: (E) 35
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 277
(B) 237
(C) 245
(D) 376
(E) 368
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 =
25/2
==> 2(130 + X) = 750 ==> X
= 245 m.
Answer:C
Answer: (C) 245
Question: Each factor of 220 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 55?
(A) 1/16
(B) 5/42
(C) 1/8
(D) 3/16
(E) 1/4
Rationale: the # of factors 220 has is 12 ;
so out of 12 factors only three are multiples of 55: 55, 110 and 220, itself;
So, the probability is 3/12=1/4.
Answer: E.
Answer: (E) 1/4
Question: Equal weights of two alloys containing tin, copper and lead in the ratio 3:2:5 and 4:5:3 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?
(A) 41:81:37
(B) 33:91:81
(C) 17:28:27
(D) 38:37:45
(E) 41:86:89
Rationale: Let the weight of the two alloys be w each
Required ratio =
(3w/10 +4w/12): ( 2w/10+5w/12 ): (5w/10+3w/12)
= 38w/60 : 37w/60 : 45w/60
= 38:37:45
ANSWER:D
Answer: (D) 38:37:45
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 76 sec
(B) 16 sec
(C) 48 sec
(D) 17 sec
(E) 54 sec
Rationale: Relative speed
= 60 + 90
= 150 km/hr.
= 150 * 5/18
= 125/3 m/sec.
Distance covered
= 1.10 + 0.9
= 2 km = 2000 m.
Required time = 2000 * 3/125
= 48 sec.
Answer: C
Answer: (C) 48 sec
Question: What is the leastvalue of x.So that 23X57 is divisible by 3?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 7 = 17 + x
Least value of x may be 1
Therefore 17 + 1 = 18 is divisible by 3.
A
Answer: (A) 1
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
(A) 17
(B) 19
(C) 20
(D) 21
(E) 18
Rationale: C
20
Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1.
Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required percentage = (14/70 x 100)% = 20%.
Answer: (C) 20
Question: if the annual rate of simple interest increases from 10% to 12.5% .Then a man’s yearly income from an investment increases by Rs.1250. His principle amount is:
(A) Rs,45000
(B) Rs.50,000
(C) Rs. 60,000
(D) Rs.65,000
(E) Rs.75,000
Rationale: Let the sum be Rs.x Then, (x*25/2*1/100) – (x*10*1/100)= 1250
25x-20x = 250000 ;
x=50000
ANSWER:B
Answer: (B) Rs.50,000
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/7%
(B) 33 1/6%
(C) 33 1/3%
(D) 38 1/3%
(E) 33 2/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: A train 600 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 298 m
(B) 268 m
(C) 700 m
(D) 267 m
(E) 181 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (600 + x)/60 = 65/3
x = 700 m.
Answer: C
Answer: (C) 700 m
Question: If 213 × 16 = 3408, then 0.16 × 2.13 is equal to :
(A) 0.3408
(B) 3.408
(C) 34.08
(D) 340.8
(E) None of these
Rationale: Solution
0.16 × 2.13 = (16/100x 213/100)= (16x 213/10000) = 3408/10000 = 0.3408. Answer A
Answer: (A) 0.3408
Question: Which of the following is a parallelogram:-
(A) 130,50,130,50(angle in deg)
(B) 120,30,130,20(angle in deg)
(C) 90,90,90,90(angle in deg)
(D) a & c
(E) none
Rationale: sum of adjacent angles is 180 degrees.
so, a&c
ANSWER:D
Answer: (D) a & c
Question: Antony, Ben, and Charles each try independently to win a carnival game. If their individual probabilities for success are 2/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
(A) 3/140
(B) 1/280
(C) 3/280
(D) 3/35
(E) 68/280
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 2/5*3/8*5/7 + 2/5*5/8*2/7 + 3/5*3/8*2/7 = 68/280.
Answer: E.
Answer: (E) 68/280
Question: The cost of 8 pens and 4 pencils is Rs.200and the cost of 2pens and 2 pencils is Rs.48. Find the cost of each pen?
(A) Rs.32
(B) Rs.36
(C) Rs.42
(D) Rs.26
(E) Rs.104
Rationale: Let the cost of each pen and pencil be 'p' and 'q' respectively.
8p + 4q = 200 --- (1)
2p + 2q = 48
4p + 4q = 96 --- (2)
(1) - (2) => 4p = 104
=> p = 26
ANSWER:D
Answer: (D) Rs.26
Question: If a function f is defined by f(x)= 1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 3/2 then b= ?
(A) -3
(B) 1/3
(C) -1/3
(D) 3
(E) -12
Rationale: Given that f(x) = 1/x and f(a) = -1/2, then f(a) =1/a=-1/2 ===> a=-2, then backsolve using the answer choices:
f(ab) = f(-2b) = 1/6
A) -3 ===> f(-2*-3) = f(6) = 1/6
B) 1/3 ===> f((-2*1/3) = f(-2/3) = 1/(-2/3) = -3/2
C) -1/3 ===> f(-2*-1/3) = f(2/3) = 1/(2/3) = 3/2 WINS
D) 3 ===> f(-2*3) = f(-6) = -1/6
E) -12 ===> f(-2*-12) = f(24) = 1/-24 = -1/24
Answer: C
Answer: (C) -1/3
Question: If n = (32)^43 + (43)^33 what is the units digit of n?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: First of all, the units digit of (32)^43 is the same as that of 3^43 and the units digit of (43)^33 is the same as that of 3^33. So, we need to find the units digit of 3^43 + 3^33.
Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:
3^1=3 (the units digit is 3)
3^2=9 (the units digit is 9)
3^3=27 (the units digit is 7)
3^4=81 (the units digit is 1)
3^5=243 (the units digit is 3 again!)
...
Thus:
The units digit of 3^43 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).
The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).
Therefore the units digit of (23)^43 + (43)^33 is 5 + 3 = 0.
Answer: E.
Answer: (E) 8
Question: A man took a loan from a bank at the rate of 12% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was :
(A) Rs. 2000
(B) Rs. 10,000
(C) Rs. 15,000
(D) Rs. 20,000
(E) None
Rationale: Solution
Principal = Rs.(100x5400/12x3)= Rs. 15000.
Answer C
Answer: (C) Rs. 15,000
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
(A) 2999
(B) 2788
(C) 4400
(D) 2999
(E) 2989
Rationale: X * (95/100) * (85/100) = 3553
X = 4400
Answer: C
Answer: (C) 4400
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) 5/7
(B) 5/4
(C) 5/1
(D) 5/6
(E) 5/3
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - ⁶C₃/¹⁰C₃
= 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer:D
Answer: (D) 5/6
Question: Photography changed drastically _________ introduced in the market.
(A) when polariod
(B) when polariod
(C) when polariod
(D) as polaroid
(E) 1312
Rationale: Explanation:
There is no adequation information is given about details of subsequent changes. So "when" is the right word. Option a. "As" inditates reason.
Answer:D
Answer: (D) as polaroid
Question: If |e|=−e, which of the following must be true?
(A) x≥0
(B) e≤0
(C) x2>x
(D) x3<0
(E) 2x<x
Rationale: |e| =-e means absolute value of e is equal to negative of e. Since absolute value cannot be negative hence negative of e should result in a non negative number. It means e is a non positive number i.e. e<0. Answer is B
Answer: (B) e≤0
Question: What was the day of the week on, 19th July, 1776?
(A) Friday
(B) Wednesday
(C) Monday
(D) Saturday
(E) SUNDAY
Rationale: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 5 days)
Total number of odd days = (0 + 5) = 5.
Required day was 'Friday'.
Answer:A
Answer: (A) Friday
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
(A) 157.56
(B) 157.51
(C) 157.5
(D) 157.59
(E) 157.52
Rationale: (3500*1.5*3)/100 => 157.50.Answer: OC
Answer: (C) 157.5
Question: 1,000^2 + 1,001^2 +1,002^2 + 1,003^2 =
(A) 6,030,053
(B) 6,030,054
(C) 6,030,055
(D) 6,030,056
(E) 6,012,012
Rationale: Interesting problem.
I think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total.
1000^2 -> 00
1001^1 -> 01
.
.
1005^3 -> 14
Total -> *55
Answer E.
Answer: (E) 6,012,012
Question: If it takes a tub 2 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?
(A) 48 seconds
(B) 1 minute, 12 seconds
(C) 1 minute, 50 seconds
(D) 2 minutes, 14 seconds
(E) 4 minutes, 12 seconds
Rationale: If 5/7 of tub's content is drained 2/7 th of tub still needs to be drained.
If it takes 2 minutes to drain 5/7 th of tub it takes 2*(7/5) minutes to drain the entire tub and 2*(7/5)*(2/7) min to drain 2/7 th of the tub which is 4/5 minutes or 48 minutes
So answer is A
Answer: (A) 48 seconds
Question: the sum of all two digit numbers divisible by 5 is
(A) 945
(B) 3487
(C) 28
(D) 279
(E) 1287
Rationale: Required numbers are 10,15,20,25,...,95
This is an A.P. in which a=10,d=5 and l=95.
Let the number of terms in it be n.Then t=95
So a+(n-1)d=95.
10+(n-1)*5=95,then n=18.
Required sum=n/2(a+l)=18/2(10+95)=945.
Answer: A) 945
Answer: (A) 945
Question: A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?
(A) 11
(B) 21
(C) 88
(D) 77
(E) 61
Rationale: 20 15 5
25 20 8
500 + 300 + 40 = 840/40 = 21
Answer: B
Answer: (B) 21
Question: Two cars cover the same distance at the speed of 50 and 66 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
(A) 212 km
(B) 214 km
(C) 188 km
(D) 216 km
(E) 204 km
Rationale: 50(x + 1) = 66x
X = 3.125
60 * 3.125 = 188 km
ANSWER:C
Answer: (C) 188 km
Question: Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Parvin does not want a bed next to Anju because Anju snores. Then, in how many ways can you allot the beds?
(A) 2388
(B) 2088
(C) 3600
(D) 2028
(E) 1911
Rationale: Let the beds be numbered 1 to 7.Case 1 : Suppose Anju is allotted bed number 1.
Then, Parvin cannot be allotted bed number 2.
So Parvin can be allotted a bed in 5 ways.
After alloting a bed to Parvin, the remaining 5 students can be allotted beds in 5! ways.
So, in this case the beds can be allotted in 5´5!ways = 600 ways.
Case 2 : Anju is allotted bed number 7.
Then, Parvin cannot be allotted bed number 6
As in Case 1, the beds can be allotted in 600 ways.
Case 3 : Anju is allotted one of the beds numbered 2,3,4,5 or 6.
Parvin cannot be allotted the beds on the right hand side and left hand side of Anju’s bed. For example, if Anju is allotted bed number 2, beds numbered 1 or 3 cannot be allotted to Parvin.
Therefore, Parvin can be allotted a bed in 4 ways in all these cases.
After allotting a bed to Parvin, the other 5 can be allotted a bed in 5! ways.
Therefore, in each of these cases, the beds can be allotted in 4´ 5! = 480 ways.
The beds can be allotted in (2x 600 + 5 x 480)ways = (1200 + 2400)ways = 3600 ways
Answer: C
Answer: (C) 3600
Question: Weights of two friends Ram and Shyam are in the ratio 1:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?
(A) 19%
(B) 10%
(C) 21%
(D) 16%
(E) None
Rationale: Solution:
given ratio of Ram and Shayam's weight = 1:5
Hence, (x-15)/(15-10) = 1/5
Or, x = 16%.
Answer: Option D
Answer: (D) 16%
Question: The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.80 per metre.
(A) 2399
(B) 6336
(C) 2999
(D) 5808
(E) 2888
Rationale: Explanation:
Area = (13.86 x 10000) sq.m = 138600 sq.m
Circumference =
Cost of fencing = Rs. (1320 x 4.80) = Rs. 6336.
Answer: B) 6336
Answer: (B) 6336