mathewhe/aqua_rat huggingface dataset:
Question: In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height?
(A) 10
(B) 20
(C) 40
(D) 50
(E) 80
Rationale: His height was = 5 feet 5 inch = 5 + 60 = 65 inch. Required % correction =65*(1.25-1)* 100 = 20
B
Answer: (B) 20
Question: In how many ways can you seat 8 people on a bench if one of them does not want to sit at either end?
(A) 26,360
(B) 27,480
(C) 28,120
(D) 29,860
(E) 30,240
Rationale: One person can choose 6 possible chairs to sit. The remaining 7 people can sit in 7! ways.
The number of arrangements is 6*7! = 30,240.
The answer is E.
Answer: (E) 30,240
Question: A car takes 6 hours to cover a distance of 288 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 50 Kmph
(B) 60 Kmph
(C) 32 Kmph
(D) 70 Kmph
(E) None
Rationale: Time = 6
Distence = 288
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 288/9 = 32 Kmph
C)
Answer: (C) 32 Kmph
Question: The compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is:
(A) 400
(B) 500
(C) 600
(D) 800
(E) 1000
Rationale: Let the sum be $. P.
(P(1+10/100)^2-P)=525
P((11/10)^2-1)=2500
SUM = 2500
So SI = 500
ANSWER B
Answer: (B) 500
Question: [1/4(2/5) + 1/2(4/9)] = ?
(A) 7/11
(B) 5/11
(C) 2/11
(D) 1/11
(E) 2/11
Rationale: Explanation:
[1/4(2/5) + 1/2(4/9)] = 1/(22/5) + 1/(22/9)
= 5/22 + 9/22 = 14/22 = 7/11
Answer: Option A
Answer: (A) 7/11
Question: Two trains of length 90 m and 95 m are 250 m apart. They start moving towards each other on parallel tracks, at speeds 64 kmph and 92 kmph. After how much time will the trains meet?
(A) 53/10
(B) 55/10
(C) 56/10
(D) 57/10
(E) 58/10
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (64 + 92)*5/18 = 43.3 mps.
The time required = d/s = 250/43.3 = 58/10sec.
Answer:E
Answer: (E) 58/10
Question: A store reported total sales of $416 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?
(A) 2%
(B) 17%
(C) 30%
(D) 65%
(E) 83%
Rationale: New Value – Old Value)/Old Value x 100
We are given:
February sales this year = 416 million
February sales last year = 320 million
We need to determine the percent increase between sales from last year to sales this year.
Thus, the new value = 416 million and the old value = 320 million. Let’s plug them into our percent change formula.
(New Value – Old Value)/Old Value x 100
[(416 – 320)/320] x 100 =30%
The answer is C.
Answer: (C) 30%
Question: The average speed of a car decreased by 3 miles per hour every successive 8-minutes interval. If the car traveled 3.6 miles in the fifth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8 minute interval?
(A) 31
(B) 35
(C) 39
(D) 43
(E) 47
Rationale: (3.6 miles / 8 minutes)*60 minutes/hour = 27 mph
Let x be the original speed.
x - 4(3) = 27
x = 39 mph
The answer is C.
Answer: (C) 39
Question: A bus travel 5/7 of its speed covers 42 km in 1 hr 40 min48 sec. What is theactual speed of the bus ?
(A) 20 km/hr
(B) 35 km/hr
(C) 42 km/hr
(D) 45 km/hr
(E) 50 km/hr
Rationale: Time = 1 hr 40 min 48 sec = 1hr +4060hr+483600hr=1+23+175=12675hrdistance = 42 kmspeed=distancetime=42(12675)=42×75126⇒57 of the actual speed = 42×75126⇒actual speed = 42×75126×75=42×1518=7×153=7×5=35 km/hr
B
Answer: (B) 35 km/hr
Question: What is the perimeter of a triangle with sides 5 and 3 that has the maximum possible area?
(A) 8 + √34
(B) 7 + √26
(C) 12
(D) 8 + 3√5
(E) 8 + 3√6
Rationale: We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(25+9) = √34
The perimeter is 8 + √34
The answer is A.
Answer: (A) 8 + √34
Question: A man buy a book in Rs50 & sale it Rs60. What is the rate of profit ???
(A) 10%
(B) 20%
(C) 30%
(D) 25%
(E) 28%
Rationale: cp=50
sp=60
profit=60-50=10
%=10/50*100=20%
ANSWER:B
Answer: (B) 20%
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 75 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) 15 sec
(B) 16 sec
(C) 14 sec
(D) 67 sec
(E) 13 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 75
D = 75 * 100/18 = 1250/3
RS = 60 + 50 = 100 * 5/18
T = 1250/3 * 18/500 = 15 sec
Answer: A
Answer: (A) 15 sec
Question: If daily wages of a man is four times to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
(A) 12
(B) 4
(C) 6
(D) 8
(E) 20
Rationale: Explanation :
Wages of 1 woman for 1 day = 21600/40Ã—30
Wages of 1 man for 1 day = 21600Ã—4/40Ã—30
Wages of 1 man for 25 days = 21600Ã—4Ã—25/40Ã—30
Number of men = 14400/(21600Ã—4Ã—25/40Ã—30)=144/(216Ã—100/40Ã—30)= 8
Answer : Option D
Answer: (D) 8
Question: Arrange the following in descending order :
A) 111(4),
B) 110 x 109 x 108 x 107,
C)109 x 110 x 112 x 113
(A) all are equal
(B) B,A.C
(C) A,B,C
(D) A,C,B
(E) None
Rationale: Explanation :
if you see option B...you can easily say it is the lowest value. Now about A and C you can see the sum of the values on both side is equal on this type of cases the side which as more number of values closer than other side and to the maximum value among given numbers will be the biggest value..If you couldn't understand the explanation take two sample and compare
Answer : D
Answer: (D) A,C,B
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 10
(B) 15
(C) 20
(D) 30
(E) None
Rationale: Sol.
Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = [9/54 * 60] min = 10 min.
Answer A
Answer: (A) 10
Question: Find the next number in the sequence ?
2 11 25 44 68 ?
(A) 65
(B) 78
(C) 99
(D) 97
(E) 91
Rationale: D
97
Explanation:
Difference between number sequence is below:
9,14,19,24,29
Now the difference between above sequence is 5.
So next number is 68 + 29 =>97
Answer: (D) 97
Question: Two trains 140 m and 160 m long run at the speed fo 60 k/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
(A) 7
(B) 8.6
(C) 10.8
(D) 11
(E) 12
Rationale: Sol.
Relative speed = (60 + 40) km/hr = [100 * 5/18] m/sec = [250/9] m/sec.
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = [300 * 9/250] sec = 54/5 sec = 10.8 ec.
Answer C
Answer: (C) 10.8
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 140
(B) 150
(C) 160
(D) 170
(E) 180
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: Option B
Answer: (B) 150
Question: John was thrice as old as Tom 6 years ago. John will be 7/5 times as old as Tom in 6 years. How old is Tom today?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: J-6 = 3(T-6), so J = 3T-12
J+6 = 7/5 * (T+6)
5J + 30 = 7T + 42
5(3T-12) + 30 = 7T + 42
8T = 72
T = 9
The answer is B.
Answer: (B) 9
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 6 seconds. What is the length of the fast train?
(A) 23 m
(B) 33 (1/3)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 6) m =	(300/9)m = 33	(1/3)	m.
B
Answer: (B) 33 (1/3)m
Question: Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 each. How much money was left?
(A) $5.85
(B) $2.85
(C) $4.85
(D) $8.85
(E) $7.85
Rationale: John spent and gave to his two friends a total of
1.25 + 1.20 + 1.20 = $3.65
Money left
8.50 - 3.65 = $4.85 correct answer C
Answer: (C) $4.85
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is -.
(A) 1/36
(B) 1/216
(C) 1/48
(D) 1/55
(E) 1/90
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 A
Answer: (A) 1/36
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
(A) 10.5
(B) 10.8
(C) 10.9
(D) 10.4
(E) 10.2
Rationale: Total distance traveled = 10 + 12 = 22 km /hr.
Total time taken = 10/12 + 12/10 = 61/30 hrs.
Average speed = 22 * 30/61 = 10.8 km/hr.
Answer: B
Answer: (B) 10.8
Question: In a kilometer race, A beats B by 40 meters or 10 seconds. What time does A take to complete the race?
(A) 199 sec
(B) 190 sec
(C) 240 sec
(D) 127 sec
(E) 128 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/40 = 250 sec.
Time taken by A = 250 - 10
= 240 sec.
Answer: C
Answer: (C) 240 sec
Question: The average age of a class of 20 students is 19 years. The average increased by 2 when the teacher's age also included. What is the age of the teacher?
(A) 40 years
(B) 41 years
(C) 42 years
(D) 43 years
(E) 44 years
Rationale: If age of the teacher was 19, average would not have changed.
Since average increased by 2,
Age of the teacher=19+22×1=41
ANSWER:B
Answer: (B) 41 years
Question: The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 142. What is the number of frogs in the pond ?
(A) 148
(B) 152
(C) 156
(D) 145
(E) None
Rationale: Solution:
Ratio of Ducks and Frogs in Pond,
= 37 : 39.
Average of Ducks and Frogs in Pond,
= 142.
So, total number of Ducks and Frogs in the Pond,
= 2* 142 = 284.
Therefore,
Number of Frogs, = (284 *39)/76 = 145.
Answer: Option D
Answer: (D) 145
Question: The probability that A speaks truth is 2/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 17/35
(B) 18/35
(C) 18/36
(D) 18/33
(E) 18/32
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 2/5 * 4/7 + 3/5 * 3/7
= 8/35 + 9/35 = 17/35
Answer: A
Answer: (A) 17/35
Question: If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)Q of x, x^2, x^3, x^4 and x^5 is equal to which of the following?
(A) 12x
(B) 13x
(C) 14x
(D) 16x
(E) 20x
Rationale: 1 + x^4 + x^3 + x^2 + x = 81
i.e. 1 +x+ x^2+ x^3+ x^4 = 81
x+ x^2+ x^3+ x^4 = 80
x(1 +x+ x^2+ x^3) = 80
x(81-x^4) = 80
81x - x^5 = 80
x^5 = 81x -80
Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x
Average of Q{x, x^2, x^3, x^4, x^5} = 81x/5 ~ 16x
AnswerD
Answer: (D) 16x
Question: Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 3, she will stop rolling the cube. What is the probability that Molly will roll the die less than 4 times before stopping?
(A) 11/180
(B) 125/216
(C) 11/36
(D) 91/216
(E) 27/128
Rationale: The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:
The probability that Molly will roll the die once: P=1/6 (she gets 3 on the first roll);
The probability that Molly will roll the die twice: P=5/6*1/6 (not 3, 3);
P = 1/6 + 5/6*1/6 = 11/36
Answer: C
Answer: (C) 11/36
Question: The average monthly income of P and Q is Dollar 5050. The average monthly income of Q and R is Dollar 6250 and the average monthly income of P and R is Dollar 5200. The monthly income of P is:
(A) $ 4000
(B) $ 3000
(C) $ 7000
(D) $ 8000
(E) $ 2000
Rationale: A
$ 4000
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)
Subtracting (ii) from (iv), we get P = 4000. P's monthly income = $ 4000.
Answer: (A) $ 4000
Question: If √10 = 3.16, find the value of If √5/2
(A) 1.3
(B) 1.58
(C) 2.03
(D) 2.15
(E) 3.15
Rationale: Explanation:
√(5/2) =√(5×2/2×2)= √(10)/2 =3.16/2 = 1.58
ANSWER: B
Answer: (B) 1.58
Question: One-third of a two digit number exceeds its one fourth by 6. What is the sum of the digits of the number?
(A) seven
(B) eight
(C) nine
(D) ten
(E) eleven
Rationale: Explanation:
x/3 – x/4 = 6 => x =72
7 + 2 = 9
C
Answer: (C) nine
Question: Which of the following numbers is between 2⁄3 and 3⁄4?
(A) .45
(B) .35
(C) .70
(D) .22
(E) .20
Rationale: Isn't it C?
2/3 = .66
3/4 = .75
The only answer between that is C, .70.
Answer: (C) .70
Question: At what rate percent on simple interest will Rs.800 amount to Rs.950 in 5 years?
(A) 3.75%
(B) 5.93%
(C) 4.75%
(D) 5.33%
(E) 6.33%
Rationale: 150 = (800*5*R)/100
R = 3.75%
ANSWER:A
Answer: (A) 3.75%
Question: Evaluate 64 / .08
(A) 800
(B) 500
(C) 505
(D) None of these
(E) 506
Rationale: Explanation:
64/.08 = 6400/8 = 800
Option A
Answer: (A) 800
Question: A collection of books went on sale, and 2/3 of them were sold for $3.50 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?
(A) $252
(B) $135
(C) $90
(D) $60
(E) $54
Rationale: Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($3.50) or $252. The best answer is therefore A.
Answer: A.
Answer: (A) $252
Question: 6x − 12 = 6y
y + x = 15
Which of the following is the number of solutions to the system of equations shown above?
(A) More than three
(B) Exactly three
(C) Exactly two
(D) Exactly one
(E) None
Rationale: 6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1
y + x = 15
=>x + y =15 -- 2
From equation 1 and 2 , we get
2x = 17
=> x=8.5
y=6.5
Therefore , the given system will have Exactly one solution
D
Answer: (D) Exactly one
Question: John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 3, 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet?
(A) 1/5
(B) 2/5
(C) 3/10
(D) 3/20
(E) 7/20
Rationale: John will run farther if he runs at 5 mph and Amanda runs at 4 mph or 3 mph.
In this case, P(John runs farther) = 1/4 * 2/5 = 2/20
John will run farther if he runs at 4 mph and Amanda runs at 3 mph.
In this case, P(John runs farther) = 1/4 * 1/5 = 1/20
P(John runs farther) = 2/20 + 1/20 = 3/20
The answer is D.
Answer: (D) 3/20
Question: A 30% alcohol mixture is added to a 50% alcohol mixture to form a 10 litre mixture of 45% alcohol. How much of the 30% mixture was used?
(A) 1.5 liters
(B) 2.5 liters
(C) 3.5 liters
(D) 4.5 liters
(E) 5.5 liters
Rationale: solution A=50% solution solution b=30% solution
30%-45% =15% solution B
50%-45%=5% solution A
so the ratio is 3:1 for 30%:50% solutions
3/4 *10 liter=7.5 for 30% solution and 2.5 for 50% solution..
ANSWER:B
Answer: (B) 2.5 liters
Question: The number of permutations of the letters of the word 'MESMERISE' is?
(A) 9!/(2!)2 3!
(B) 6!/(2!)2 3!
(C) 9!/(7!)2 3!
(D) 7!/(2!)2 9!
(E) 9!/(2!)4 3!
Rationale: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = 9!/(2!)2 3!
Answer: A
Answer: (A) 9!/(2!)2 3!
Question: Alka bought 15 books for Rs.2580 from one shop and 20 books for Rs.920 from another. What is the average price he paid per book ?
(A) 104
(B) 181
(C) 100
(D) 35
(E) 20
Rationale: Average price per book
= (2580 + 920) / (15 + 20)
= 3500 / 35
= Rs.100
Answer:C
Answer: (C) 100
Question: There was a grandmother in a village who had a grandchild. Upon asking her grandchild's age she told dat she is as older as many days old as her daughter's age in weeks and as many days as her own age in years. The sum of the three is 130. then how old is the child?
(A) .3 year
(B) .4 year
(C) .5 year
(D) .7 year
(E) .9 year
Rationale: There was a grandmother in a village who had two grandchild. Upon asking her younger grandchild's age she told that she is as older as many days old as her elder grandchild's age in weeks and as many days as her own age in years. The sum of the three is 130. then how old is the younger child?
answer:
grandmother age - 127 year.
elder grand child - 127 weeks ~ 2.5 year
younger child - 127 days ~ .5 year
ANSWER:C
Answer: (C) .5 year
Question: How many keystrokes are needed to type the numbers from 1 to 200?
(A) 195
(B) 280
(C) 364
(D) 492
(E) 512
Rationale: There are 9 one-digit numbers from 1 to 9.
There are 90 two-digit numbers from 10 to 99.
There are 101 three-digit numbers from 100 to 200.
9 + 90(2) + 101(3) = 492
The answer is D.
Answer: (D) 492
Question: In what time will a train 100 m long cross an electric pole, it its speed be 216 km/hr?
(A) 2.5 sec
(B) 1.6 sec
(C) 8.5 sec
(D) 2.2 sec
(E) 4.5 sec
Rationale: Speed = 216 * 5/18
= 60 m/sec
Time taken = 100/60
= 1.6 sec.
Answer:B
Answer: (B) 1.6 sec
Question: A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in meters) is:
(A) 600
(B) 750
(C) 1000
(D) 1250
(E) None of these
Rationale: Speed=(5*5/18)m/sec=25/18 m/sec.
Distance covered in 15 minutes = (25/18*15*60)m=1250m.
Correct Option: D
Answer: (D) 1250
Question: If a certain computer is capable of printing 4700 monthly credit card bills per hour, while a new model is capable of printing at a rate of 6800 per hour, the old model will take approximately how much longer than the new model to print 10000 bills?
(A) 19 mins
(B) 29 mins
(C) 39 mins
(D) 38 mins
(E) 37 mins
Rationale: old model's 1 hr work = 4700
new model's 1 hr work = 6800
old model' time taken to print 10000 cards
for 1 hr -- 4700 cards
x -- 10000
x= 10000/4700 = 100/47
new model' time taken to print 10000 cards
for 1 hr -- 6800 cards
y -- 10000
y= 10000/6800 = 100/68
x= 10000/4700 = 100/47 = 2 6/47 hr
Difference is
100/47 - 100/68 = 6800 - 4700 /(47*68)
2100/3196 = 0.66 hrs => 39minutes
Old model ll take 39 minutes longer to print 10000 cards than new model
Ans : 39 mins
ANSWER:C
Answer: (C) 39 mins
Question: What was the day of the week on 28th May, 2006?
(A) Thursday
(B) Friday
(C) Saturday
(D) Sunday
(E) Monday
Rationale: 28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days
Jan. Feb. March April May
(31 + 28 + 31 + 30 + 28 ) = 148 days
148 days = (21 weeks + 1 day) 1 odd day.
Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day.
Given day is Sunday.
Answer: Option D
Answer: (D) Sunday
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 60 sq.units
(B) 158 sq.units
(C) 187 sq.units
(D) 607 sq.units
(E) 815 sq.units
Rationale: Given that the area of the square = 225 sq.units
=> Side of square = √225 = 15 units
The radius of the circle = side of the square = 15 units
Length of the rectangle = 2/5 * 15 = 6 units
Given that breadth = 10 units
Area of the rectangle = lb = 6 * 10 = 60 sq.units
Answer: A
Answer: (A) 60 sq.units
Question: A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is
(A) 1:3
(B) 4:3
(C) 2:3
(D) 2:1
(E) 2:4
Rationale: Work done by 20 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16×20)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×16)
Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20
= 1/3 :1/4 = 4:3
Option B
Answer: (B) 4:3
Question: Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
(A) 8
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
Answer: (B) 12
Question: The department received a bonus of $2075 to be split amongst the 25 employees in the department. The senior team members received $100 each while the junior team members received only $75 each. How many junior team members are in the department?
(A) 2
(B) 4
(C) 5
(D) 8
(E) 10
Rationale: s = senior team members
j = junior team members
s + j = 25
j = 25 - s
100s +75j = 2075
100s + 75(25 - s) = 2075
100s + 1875 - 75s = 2075
25s = 200
s = 8
Answer: D
Answer: (D) 8
Question: For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?
(A) 23
(B) 19
(C) 17
(D) 13
(E) 11
Rationale: f(24) = 2*4*6*8*10*12*14*16*18*20*22*24 = 2^12*(1*2*3*4*5*6*7*8*9*10*11) --> the greatest prime factor is 11.
Answer: E.
Answer: (E) 11
Question: The maximum number of students among them 890 pens and 630 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
(A) 10
(B) 910
(C) 1001
(D) 1911
(E) None of these
Rationale: Explanation:
Required number of students = H.C.F of 890 and 630 = 10. Answer: A
Answer: (A) 10
Question: Factor: 3x4y3 – 48y3
(A)  3y3(x2 + 4)(x + 2)(x -2)
(B)  2y3(x2 + 4)(x + 2)(x -2)
(C)  3y3(x2 + 4)(x + 2)(x -3)
(D)  3y3(x2 + 4)(x + 3)(x -2)
(E)  3y3(x2 + 4)(x + 2)(x -4)
Rationale: 3x4y3– 48y3.
= 3y3(x4 – 16).
= 3y3[(x2)2 - 42].
= 3y3(x2 + 4)(x2 - 4).
= 3y3(x2 + 4)(x2 - 22).
= 3y3(x2 + 4)(x + 2)(x -2).
Answer: (A) 3y3(x2 + 4)(x + 2)(x -2)
Answer: (A)  3y3(x2 + 4)(x + 2)(x -2)
Question: From a number of mangoes, a man sells half the number of existing mangoes plus 1 to the first customer, then sells 1/3rd of the remaining number of mangoes plus 1 to the second customer, then 1/4th of the remaining number of mangoes plus 1 to the third customer and 1/5th of the remaining number of mangoes plus 1 to the fourth customer. He then finds that he does not have any mangoes left. How many mangoes did he have originally?
(A) 12
(B) 14
(C) 15
(D) 13
(E) 16
Rationale: Let the No. of mangoes that the man had originally = X
No. of mangoes sold balance
1st customer = (X/2) + 1 (X - 2)/2
2nd customer = (X - 2)/6 + 1 (X - 5)/3
3rd customer = (X - 5)/12 + 1 (X - 9)/4
4th customer = (X - 9)/20 + 1 0
(X - 9)/20 + 1= (X - 9)/4 => X = 14
ANSWER:B
Answer: (B) 14
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) 78
(C) 268
(D) 268
(E) 298
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 first five numbers in a regular sequence are 1, 4, 10, 22 and 46. What is the next number in the sequence?
(A) 142
(B) 154
(C) 94
(D) 182
(E) 190
Rationale: it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals..
when we see the sequence 1, 4, 10, 22 and 46 we see that each succeeding number is some value more than twice the previous number..
10=2*4+2..
22=2*10+2..
and so on..
so next number= 2*46+2=94..
C
Answer: (C) 94