mathewhe/aqua_rat huggingface dataset:
Question: Of the 200 employees at company X, 50 are full-time, and 150 have worked at company X for at least a year. There are 10 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
(A) 20
(B) 30
(C) 10
(D) 80
(E) 100
Rationale: 200 employees
50 are full-time
150have worked at company X for at least a year
10 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.
How many full-time employees of company X have worked at the company for at least a year?
200-50=150 employees not full time
150-10= 140 employees not full time who worked over a year
150 employees have worked at company X for at least a year-140 employees not full time who worked over a year = 10 full-time employees of company X have worked at the company for at least a year
ans C
Answer: (C) 10
Question: How many multiples of 5 are there between 70 and 358?
(A) 54
(B) 55
(C) 56
(D) 57
(E) 58
Rationale: 5 * 14 = 70
5 * 71 = 355
Total no of multiples = (71 - 14) + 1
= 57 + 1
= 58
Answer is E.
Answer: (E) 58
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
(A) 1/5
(B) 2/5
(C) 2/5
(D) 3/5
(E) 3/7
Rationale: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5
C)
Answer: (C) 2/5
Question: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability X that out of the two, one is white and one is blue?
(A) 15/56
(B) 41/56
(C) 13/28
(D) 15/28
(E) 5/14
Rationale: The required probability X= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D is thus the correct answer.
Answer: (D) 15/28
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
(A) 123400 m
(B) 145500 m
(C) 153600 m
(D) 186400 m
(E) 165700 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: (C) 153600 m
Question: If x is a positive even number, then each of the following is even EXCEPT
(A) (x + 3)(x + 5)
(B) x^2 + 5
(C) x^2 + 6x + 9
(D) 3x^2 + 4
(E) 5(x + 3)
Rationale: Since it is given tht x is even number, so any integer multiplied with x will also be even..
so, we should concentrate only on other terms..
lets see the choices..
A. (x + 3)(x + 5)
We have two terms with x and each is added with a odd number..
each bracket becomes odd and Odd*Odd=Odd
B. x^2 + 5
here we are adding an Odd number to even.. so E + O=O
C. x^2 + 6x + 9
here we are again adding an Odd number to even.. so E +E + O=O
D. 3x^2 + 4
here we are adding an Even number to even.. so E + E=E..
so tjis is our answer
E. 5(x + 3)
again O*O=O
E
Answer: (E) 5(x + 3)
Question: In how many ways the letters of the word RAIMBON be arranged?
(A) 2467
(B) 2696
(C) 5040
(D) 5768
(E) 6597
Rationale: Total ways of arranging the letters = 7! = 5040 ways.
C)
Answer: (C) 5040
Question: A house seller can deduct 5 percent from the total sales value. If he has sold 5 houses, and the price of two houses is between $100,000 and $250,000, one of them is $300,000 house, two houses are between $500,000 and 750,000, what is the range of his revenue?
(A) 800
(B) 850
(C) 875
(D) 880
(E) 900
Rationale: (1) 2(100)+300+2(500) = 1500
1500*0.95=1425 (Revenue considering the minimum values with the discount)
(2) 2(250)+300+2(750) = 2300 (Revenue considering the maximum values without the discount)
So, the the revenue range could be = 2300 - 1425 = 875
C
Answer: (C) 875
Question: There is 2/5 chance it will rain today.
There is a probability of 1/2 I will find the love of my life today.
What is the probability that it won't rain and that I will find the love of my life today?
(A) 2/5
(B) 3/5
(C) 3/10
(D) 1/5
(E) 7/10
Rationale: the probability that it won't rain today is 3/5.
therefore the probability that it won't rain and that I will find the love of my life today is 3/5*1/2 = 3/10
Answer:C
Answer: (C) 3/10
Question: The price of a T.V. set worth Rs. 60000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
(A) 22678
(B) 59000
(C) 26788
(D) 19000
(E) 26711
Rationale: Money paid in cash = Rs. 1000
Balance payment = (60000 - 1000) = Rs. 59000
Answer: B
Answer: (B) 59000
Question: The average age of a couple was 24 years. After their 1st and 2nd children (twins) were born, the average age of the family became 13.5 years. The average age of the family just after 3rd child was born was 13.2 years. The average age of the family after 4th child was born was 16 years. The current average age of the family is 19 years. What is the current age of the twin children?
(A) 14 years
(B) 15 years
(C) 11 years
(D) 12 years
(E) 10 years
Rationale: DETAILED SOLUTION
Sum of the ages of the couple = 24 * 2 = 48
After the 1st and 2nd children, sum = 13.5 * 4 = 54
Difference in sum = 54 – 48 = 6 years
Or after 6/ 2 = 3 years, the twin were born to the couple (Ages of children at the time of birth is 0)
After 3rd child, sum = 13.2 * 5 = 66 yrs
Difference = 66 – 54 = 12
Or after 12/4 = 3 yrs, 3rd child was born (Couple + 2 children were already present. So 4)
After 4th child, sum = 16 * 6 = 96 yrs
Difference = 96 – 66 = 30
Or after 30/5 = 6 yrs, 4th child was born
Current sum = 19 * 6 = 114 yrs
Difference 114 – 96 = 18 yrs
Or after 18/6 = 3 yrs
The gap between the children are as follows: 3 yrs, 6 yrs and 3 yrs
Age of eldest ones = 3 + 6 + 3 = 12
Correct Answer: D
Answer: (D) 12 years
Question: A rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14cm. how many times can it go round a cylinder having radius 20 cm?
(A) 49 rounds
(B) 42 rounds
(C) 54 rounds
(D) 52 rounds
(E) 50 rounds
Rationale: Explanation:
Let the required number of rounds be x
More radius, less rounds (Indirect proportion)
Hence we can write as
(radius) 14 : 20 :: x : 70
⇒14×70=20x
⇒14×7=2x
⇒x=7×7=49
Answer: Option A
Answer: (A) 49 rounds
Question: Two persons starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
(A) 17 hrs
(B) 22 hrs
(C) 25 hrs
(D) 12 hrs
(E) 16 hrs
Rationale: The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs
Answer : A
Answer: (A) 17 hrs
Question: In a deck of cards there are 52 cards numbered from 1 to 13. There are 8 cards of each number in the deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it?
(A) 1/4.
(B) 4/17.
(C) 5/29.
(D) 5/16.
(E) 1/3.
Rationale: 8+12 tens/52+12 total cards=20/64=5/16
D
Answer: (D) 5/16.
Question: If a(a + 4) = 21 and b(b + 4) = 21, where a ≠ b, then a + b =
(A)  −4
(B)  −2
(C)  2
(D)  46
(E)  48
Rationale: a(a + 4) = 21
=> we have a = 3 or -7
also b(b + 4) = 21
=> b = 3 or -7
given a ≠ b
1) when a =3, b= -7 and a + b = -4
1) when a = -7, b= 3 and a + b = -4
Answer choice A
Answer: (A)  −4
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) 242 m
(B) 249 m
(C) 245 m
(D) 235 m
(E) 345 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 m
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a customer at the bank. On the last day, when the interest was accumulated into his account, his bank balance doubled to $7540. What is the average monthly balance maintained by John in his account during the year?
(A) 2840
(B) 5680
(C) 6840
(D) 7540
(E) 37700
Rationale: Soln:-
Bank balance is doubled with accumulation of interest to 7540..
this means INTEREST is 7540/2=3770 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 37700..
ANSWER:E
Answer: (E) 37700
Question: At a circular table for nine will sit seven adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the nine people be arranged around the table.
(A) 120
(B) 240
(C) 480
(D) 600
(E) 720
Rationale: Consider the two parents and two children as one unit.
Then there are five adults and one family unit.
The number of ways 6 can form a line is 6!
Around a circular table, there would be 6 rotations so we divide this number by 6.
There are 5! ways for 6 to sit around the circular table.
Then the two children have two options and the two parents have two options.
Then the total number of ways is 5!*2*2= 480
The answer is C.
Answer: (C) 480
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 4 hours, then find the speed of the boat in still water?
(A) A)7
(B) B)2
(C) C)8.73
(D) D)5.77
(E) E)3
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 4
x = 5.77
Answer:D
Answer: (D) D)5.77
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $10. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) 90/(xy)
(B) 90xy
(C) xy/90
(D) xy/10
(E) 10/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 10 / (xy/9) = 90/(xy).
The answer is A.
Answer: (A) 90/(xy)
Question: Carol is three times Alice’s age but only twice as old as Betty. Alice is sixteen years younger than Carol. How old is Betty?
(A) 16
(B) 19
(C) 12
(D) 18
(E) 24
Rationale: Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.
We're told 3 facts about the relative ages of 3 people:
1) Carol's age is 3 times Alice's age
2) Carol's age is 2 times Betty's age
3) Carol is 16 years older than Alice
We're asked for BETTY'S age.
Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST a smaller answer first.
IF....
Betty = 12
Then Carol = 2(12) =24
Then Alice = 24 - 16 = 8 AND 24/3 = 8
All of these values mesh perfectly with the facts and with one another, so Betty MUST be 12
C
Answer: (C) 12
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 20. Which of the following integers is the higher of the remaining two integers?
(A) 32
(B) 86
(C) 44
(D) 82
(E) 55
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 20
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -20 = 144
B = (144 + 20)/2 = 82
Answer:Option D
Answer: (D) 82
Question: Increasing the original price of an article by 8 percent and then increasing the new price by 8 percent is equivalent to increasing the original price by
(A) 16.16%
(B) 16.32%
(C) 16.64%
(D) 17.26%
(E) 18.56%
Rationale: 1.08*1.08*x = 1.1664*x
The answer is C.
Answer: (C) 16.64%
Question: Ravi and Kavi start a business by investing â‚¹ 6000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year.
(A) 2 : 12
(B) 5 : 12
(C) 7 : 12
(D) 1 : 12
(E) 3 : 12
Rationale: Ratio of profit = Ratio of investments
= 6000 : 72000 = 1 : 12
Answer : D
Answer: (D) 1 : 12
Question: Three friends X, Y, Z rented a auto for Rs.520. A used it for 6 hours, B used it for 9 hours and C used it for 11 hours. What is the hire charges paid by Y:
(A) Rs 140
(B) Rs 160
(C) Rs 180
(D) Rs 200
(E) None
Rationale: X : Y : Z = 7 : 8 : 11. Hire charges paid by Y = Rs(520×9/26) = Rs.180.
Answer C
Answer: (C) Rs 180
Question: If n is a positive integer and n^2 is divisible by 18, then what is the largest positive integer that must divide n?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: 18 = 2 * 3^2
If 18 divides n^2, then n must be divisible by 2 * 3 = 6
The answer is C.
Answer: (C) 6
Question: What is the least possible product of 4 different integers, each of which has a value between –6 and 10, inclusive?
(A) –4320
(B) –3600
(C) –720
(D) –600
(E) –120
Rationale: Maximize the total product with a -ve sign
so -6 * 10 * 9 * 8 = 720 * -6 = -4320
Answer is A.
Answer: (A) –4320
Question: A numberais squared and then multiplied by negative 3. The result of this operation Q is equal to three times the sum of three timesaand two. What is one possible value ofa?
(A) -3
(B) -2
(C) 1
(D) 2
(E) 3
Rationale: Q=-3*a^2=3(3a+2)
a= -2 or -1
a=-2=B
Answer: (B) -2
Question: Boy sells a book for Rs. 800 he gets a loss of 20 %, To gain 10%, what should be the SP?
(A) 1100
(B) 450
(C) 550
(D) 590
(E) 600
Rationale: Cost price = 800/80 x 100 = 1000
To gain 10% = 1000 x 10/100 = 100
SP = CP + gain = 1000 + 100 = 1100
Answer :A
Answer: (A) 1100
Question: A right circular cone is exactly fitted inside a cube in such away that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volume of the cube is 343 cc, what approximately is the volume of the cone?
(A) 80 cc
(B) 90 cc
(C) 110 cc
(D) 105 cc
(E) 100 cc
Rationale: Edge of the cube = 3√334= 7 cm
∴ Radius of cone = 3.5 cm
height = 7 cm
volume of cone = 1⁄3πr2h
1⁄3πr2h = 1⁄3 × 22⁄7 × (3.5)2 × 7 = 1⁄3 × 22 × 12.25 ≈ 90 sec
Answer B
Answer: (B) 90 cc
Question: A man is 4 times as old as her daughter. In 3 years she will be 3 times as old as her daughter. How old is the man now?
(A) 3 years
(B) 6 years
(C) 12 years
(D) 24 years
(E) 36 years
Rationale: Let man's present age = w
and daughter's present age = d
w= 4d --- equation 1
w+3 = 3(d+3)
=>w = 3d +6 --- equation 2
From 1 and 2 , we get
d=6
w=24
Answer D
Answer: (D) 24 years
Question: Tom wants to buy items costing $25.35, $50.69, and $85.96. He earns $6.50 an hour doing
odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he
work to earn the money he needs for his purchases? Round your answer to the nearest whole
hour.
(A) 8 hours
(B) 48 hours
(C) 38 hours
(D) 18 hours
(E) 28 hours
Rationale: $6.50 x .10 = $.65 is 10% of his hourly income
$6.50 - .65 = $5.85 hourly amount available to spend
$25.35 + $50.69 + $85.96 = $162 total needed
$162 ÷ $5.85 = 27.69... rounds to 28 hours
correct answer E
Answer: (E) 28 hours
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
(A) 299
(B) 266
(C) 278
(D) 500
(E) 277
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 – 6x/100 = 85
x/100 = 5
=> x = 500
Answer:D
Answer: (D) 500
Question: In a kickball competition of 7 teams, how many possible matches can each team play with each other?
(A)  9
(B)  16
(C)  24
(D)  21
(E)  54
Rationale: 7C2 = 21
Option D
Answer: (D)  21
Question: If n = (33)^40 + (43)^33 what is the units digit of n?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: First of all, the units digit of (33)^40 is the same as that of 3^43 and the units digit of (40)^33 is the same as that of 3^33. So, we need to find the units digit of 3^40 + 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 3^40 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 3^30 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 (33)^40 + (40)^33 is 7 + 4 =1.
Answer: A.
Answer: (A) 1
Question: A car takes 6 hours to cover a distance of 432 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 48 Kmph
(B) 50 Kmph
(C) 52 Kmph
(D) 56 Kmph
(E) 60 Kmph
Rationale: Time = 6
Distence = 432
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 432/9 = 48 Kmph
A
Answer: (A) 48 Kmph
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 12000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 12%
(B) 16%
(C) 20.18%
(D) 82%
(E) 23%
Rationale: Total CP = Rs. 42000 + Rs. 12000 = Rs. 54000 and SP
= Rs. 64900
Profit(%) = (64900 - 54000)/54000 * 100
= 20.18%
Answer:C
Answer: (C) 20.18%
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
(A) 134560 m
(B) 1354760 m
(C) 153600 m
(D) 167800 m
(E) 153600 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: (C) 153600 m
Question: 16 meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?
(A) 2√2
(B) 4
(C) 5
(D) 4√2
(E) none of these
Rationale: Area of Sector, A = x/360*pi*r^2
Circumference of the sector = 16
=> x/360*2*pi*r +2r= 16
=> 2A/r+2r=16
=> A=(r16- 2r^2)/2
= r8-r^2
We will now max using derivations
Max value of A will found at A=0
i.e 8-2r=0
r=4
B
Answer: (B) 4
Question: Jibin went up a certain hill at the rate of one and a half kilometers per hour and came down at the rate of four and a half kilometers per hour, so that it took just four hours to make the double journey. How far was it to the top of the hill ?
(A) 3 km
(B) 6 km
(C) 4.5 km
(D) km
(E) none of the above
Rationale: Assume the distance to the top of the hill (1 way) as: x
Now, speed=distance/time => time=distance/speed
So, for the first half of the journey, he traveled uphill at 1.5km/hr, so the time taken for the first leg of the journey is: x/1.5.
For the second half, he traveled downhill at 4.5km/hr, so the time taken for the second leg of the journey is: x/4.5
Now, the total time for the trip is given as 4 hrs.
Equating, (x/1.5)+(x/4.5)=4 => (3x+x)/4.5=4 => x=4.5 km
So, the distance one side is = 4.5 km.
The OA mentioned is 9km, which is exactly double of this distance, i.e., the total distance traveled during both legs of the journey, but the question only asked for the distance till the top of the hill, i.e., one way, so the answer should be 4.5km
Can someone assist me in understanding where am I wrong here?
Answer: (C) 4.5 km
Question: Indu gave Bindu Rs.1875 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) s.10
(B) s.2
(C) s.5
(D) s.3
(E) s.4
Rationale: 1875 = D(100/4)2
D = 3
ANSWER:D
Answer: (D) s.3
Question: Jonathan, Matthew and Zac are picking strawberries from their yard. Together they have picked a total of 550 strawberries. Jonathan and Matthew have picked 350 strawberries together. Matthew and Zac have picked 250 strawberries together. How many strawberries has Zac picked by himself?
(A) 100
(B) 200
(C) 350
(D) 50
(E) 250
Rationale: Jonathan = Matthew + Zac = 550 strawberries
J + M = 350
M + Z = 250
Use J + M = 350 to plug into the original formula
(J + M) + Z = 550
350 + Z = 550
Subtract 350 from each side
Z = 200
Answer: B
Answer: (B) 200
Question: Ashok secured average of 75 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
(A) 66
(B) 74
(C) 78
(D) 80
(E) None of these
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 75
Therefore total marks in 6 subjects = 75 * 6 = 450
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 450 – 370 = 80
ANSWER D
Answer: (D) 80
Question: Ages of two persons differ by 20 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age
(A) 12,28
(B) 14,30
(C) 16,36
(D) 18,34
(E) 19,34
Rationale: Explanation:
Let the age of younger person is x,
Then elder person age is (x+20)
=> 3(x-6) = (x+20-6) [6 years before]
=> 3x-18 = x+14
=> x = 16
So other person age is x + 20 = 36
Answer: Option C
Answer: (C) 16,36
Question: A train running at the speed of 90 km/hr crosses a pole in 5 seconds. Find the length of the train.
(A) 150 meter
(B) 145 meter
(C) 140 meter
(D) 125 meter
(E) None of these
Rationale: Explanation:
Speed = 90*(5/18) m/sec = 25 m/sec
Length of Train(Distance) = Speed * Time
=25*5=125 meter
Option D
Answer: (D) 125 meter
Question: 45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
(A) 338
(B) 667
(C) 188
(D) 100
(E) 281
Rationale: (45 * 8)/30 = (x * 6)/50 => x =100
100 – 45 = 55
Answer: D
Answer: (D) 100
Question: 108.	Triangle A’s base is 12% greater than the base of triangle B, and A’s height is 12% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B?
(A)  9 % less
(B)  0.7 % less
(C)  Equal to each other
(D)  1 % more
(E)  9 % more
Rationale: Wish the question specified that we are talking about corresponding height.
Base of A = 13/12 * Base of B
Height of A = 11/12 * Height of B
Area of A = (1/2) * Base of A * Height of A = 13/12 * 11/12 * Area of B = 143/144 * Area of B
Area of A is 0.7% less than the area of B.
Answer (B)
Answer: (B)  0.7 % less
Question: a, b, c, and d are positive consecutive integers and a < b < c < d.
If the product of the highest and lowest numbers is three more than the square of the second number, what is the value of the third number?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: ad = bb + 3
We know many squares: 2 squared is 4, 3 squared is 9, 4 squared is 16, 5 squared is 25, 6 squared is 36.
We need to find a sequence where the square is a little smaller than the ad product.
In the sequence 1, 2, 3, 4, the square of b is only 2x2 = 4. The product of the first and last numbers is 1x4 = 4, which is the same. So this can't be our sequence.
In the sequence 3, 4, 5, 6, the square of b is 4x4 = 16. The product of the first and last numbers is 3x6 = 18, which is close, but a little too low.
In the sequence 5, 6, 7, 8, the square of b is 6x6 = 36. The product of the first and last numbers is 5x8 = 40, which is close, but a little too high.
The correct sequence is 4, 5, 6, 7. The square of b is 5x5 = 25, and the product of the first and last numbers is 4x7 = 28, exactly three more than the square.
The answer to the problem is the value of the third number in the sequence, which is 6 (option E).
Answer: (E) 6