mathewhe/aqua_rat huggingface dataset:
Question: AB + CD = RRR, where AB and CD are two-digit numbers and RRR is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(A)  1
(B)  3
(C)  7
(D)  9
(E)  Cannot be determined
Rationale: AB and CD are two digit integers, their sum can give us only one three digit integer of a kind of RRR it's 111.
So, A=1. 1B+CD=111
Now, C can not be less than 9, because no to digit integer with first digit 1 (mean that it's<20) can be added to two digit integer less than 90 to have the sum 111 (if CD<90 meaning C<9 CD+1B<111) --> C=9
Answer: D.
Answer: (D)  9
Question: Working together, printer A and printer B would finish the task in 40 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 4 pages a minute more than printer A ?
(A) 250
(B) 375
(C) 450
(D) 480
(E) 500
Rationale: 40*A + 40*B = x pages
in 40 mins printer A will print = 40/60 * x pages = 2/3*x pages
thus in 40 mins printer printer B will print x - 2/3*x = 1/3*x pages
Also it is given that printer B prints 4 more pages per min that printer A. In 40 mins printer B will print 160 more pages than printer A
thus 2/3*x - 1/3*x = 160 => x = 480 pages
Answer: D
Answer: (D) 480
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
(A) 65
(B) 24
(C) 52
(D) 77
(E) 82
Rationale: Explanation:
Let the ten's and unit's digit be x and 8/x respectively.
Then,
(10x + 8/x) + 18 = 10 * 8/x + x
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
So, ten's digit = 2 and unit's digit = 4.
Hence, required number = 24.
Answer: B
Answer: (B) 24
Question: A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 6 ½ sec
(B) 6 ½ sec
(C) 9 ½ sec
(D) 8 ½ sec
(E) 7 ½ sec
Rationale: D
8 ½ sec
D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 ½ sec
Answer: (D) 8 ½ sec
Question: Walking at 8KMPH From Point W to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point W to Railway station?
(A) A)9KM
(B) B)6.66KM
(C) C)7.25KM
(D) D)12.40KM
(E) E)13KM
Rationale: Since time differences given are in minutes so let's convert speed in Km per minute
8 kmph = 8/60 km per minute = (2/15) km per minute
10 kmph = 10/60 km per minute = (1/6) km per minute
Let, Time of train to depart from station = t minutes
Distance between Point W and Railway Station = Speed*Time = (2/15)*(t+5)
Distance between Point W and Railway Station = Speed*Time = (1/6)*(t-5)
i.e. (2/15)*(t+5) = (1/6)*(t-5)
i.e. 12t+60 = 15t - 75
i.e. 3t = 135
i.e. t = 45 minutes
i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km
Answer: Option B
Answer: (B) B)6.66KM
Question: A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 22 inches, how many inches of framing material does the carpenter need to frame the painting?
(A) 12
(B) 22 1/2
(C) 37 1/2
(D) 50
(E) 28
Rationale: (22/2) ( 2+3) * 2 = 28 =E
Answer: (E) 28
Question: The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked the second cow in the second year?
(A) 4730 lt
(B) 4356 lt
(C) 7665 lt
(D) 2314 lt
(E) 6545 lt
Rationale: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15% or 10%
So 8100+15/100⋅x+10/100⋅(8100−x)=9100
Therefore 8100+320x+110(8100−x)=9100
120x=190
x=3800
Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, respectively.
correct answer A
Answer: (A) 4730 lt
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
(A) 7
(B) 6
(C) 3
(D) 4
(E) None of these
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
ANSWER:E
Answer: (E) None of these
Question: The surface of a cube is 96sq cm. Find its volume?
(A) 8cc
(B) 9cc
(C) 2cc
(D) 4cc
(E) 64cc
Rationale: 6a2 = 96 = 6*16
a = 4 => a3 = 64cc
Answer: E
Answer: (E) 64cc
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 3
(B) 8
(C) 2
(D) 1
(E) 9
Rationale: E
9
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x <-> 14 x x = 6 x 21
x = (6 x 21)/14
x = 9
Answer: (E) 9
Question: It takes 3 workers a total of 12 hours to build a giant machine with each worker working at the same rate. If 4 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 3:00 PM, at what time will the machine be complete?
(A) 5:30
(B) 5:45
(C) 6:00
(D) 6:15
(E) 6:30
Rationale: 3 workers build 1/12 of a machine in one hour.
1 worker builds 1/36 of a machine in one hour.
In the first 4 hours, 4 workers build 4*(1/36)*4=16/36 of a machine
From 3:00 to 4:00, 5 workers build another 5/36. The total is 21/36.
From 4:00 to 5:00, 6 workers build another 6/36. The total is 27/36.
From 5:00 to 6:00, 7 workers build another 7/36. The total is 34/36.
To build another 2/36, 8 workers need (2/8)*60 minutes which is 15 minutes.
The machine is complete at 6:15.
The answer is D.
Answer: (D) 6:15
Question: A meal cost $ 35.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
(A) 40-42
(B) 39-41
(C) 38-40
(D) 37-39
(E) 36-37
Rationale: 10%(35.5) = 3.55
15%(35.5) = 5.325
total amount could have been 35.5+3.55 and 35.5+5.325
=> could have been between 39.05 and 40.625
=> approximately between 39 and 41
Answer is B.
Answer: (B) 39-41
Question: Which one of the following is the common factor of (47^43 + 43^43) and (47^47 + 43^47) ?
(A) (2+56)
(B) (47+43)
(C) (3+7)
(D) (4+9)
(E) (12+19)
Rationale: Explanation:
When n is odd, (x^ + a^n) is always divisible by (x + a).
Each one of (47^43 + 43^43) and (47^47 + 43^47) is divisible by (47 + 43).
B
Answer: (B) (47+43)
Question: Eight friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $290. If one of the friends had a coupon for 29% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
(A) $90
(B) $70
(C) $45
(D) $37
(E) $25
Rationale: 290 * 0,29 = 84
290 - 84 = 206
206 / 8 = 25
Answer E
Answer: (E) $25
Question: What is the sum of the prime factors of 3 and the prime factors of 1656?
(A) 35
(B) 45
(C) 55
(D) 25
(E) 65
Rationale: The prime factors of 3 are 3*1
The prime factors of 1656 are 2x2x2x3x3x23
2+2+2+3+3+23 = 35. A is the correct answer
Answer: (A) 35
Question: For any positive x, y and z if x is n% of y and z is m% of y then what percentage E must x be of z?
(A) (n/m)%
(B) (m × n)%
(C) (100 / [m × n]) %
(D) (100 × m/n)%
(E) (100 × n/m)%
Rationale: x is n% of y MEANS x= (n/100 )* y------------------------eq1
z is m% of y MEANS z= (m/100 )* y------------------------eq2
Find equation of xz
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer E is 100n/m %.E
Answer: (E) (100 × n/m)%
Question: If 105 divides into n with no remainder, which of the following must be a factor of n?
(A) 2
(B) 4
(C) 6
(D) 7
(E) 11
Rationale: 105 / n = k (with k an integer)
(7)(5)(3) / n = k
n must have a 7 in his prime factorization to divide 105 without remainder.
answer D
Answer: (D) 7
Question: Two numbers are in the ratio of 5:9. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers?
(A) 150,170
(B) 150,270
(C) 50,270
(D) 180,270
(E) 150,290
Rationale: (5x-25):(9x-25) = 35:59
x = 30 => 150,270
ANSWER:B
Answer: (B) 150,270
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 70% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
(A)  36%
(B)  51%
(C)  66%
(D)  80%
(E)  84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.7*0.7 = 0.49. So, the probability that he will be able to attend is 1 - 0.49 = 0.51.
Answer: B.
Answer: (B)  51%
Question: How many 2 3/4 foot pieces of cable can be cut out of a piece that is 30 feet long?
(A) a.10
(B) b.16
(C) c.17
(D) d.18
(E) e. 20
Rationale: Pretty Simple..the answer is choice (A) 10.
All that one has to do is :
1: Convert 2 3/4 into an improper fraction (11/4) or a decimal (2.75)
2: Divide 30 by 11/4 (or 2.75)
Answer =10 (A)
Answer: (A) a.10
Question: The perimeter of one square is 44 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 13√4
(B) 12.1√2
(C) 23√2
(D) 12√4
(E) 13√9
Rationale: 4a = 44 4a = 20
a = 11 a = 5
a2 = 121 a2 = 25
Combined area = a2 = 146 => a = 12.1
d = 12.1√2
Answer: B
Answer: (B) 12.1√2
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 9 hours. How many hours will take C alone to fill the tank?
(A) 23/2
(B) 41/3
(C) 49/4
(D) 54/5
(E) 63/6
Rationale: The rate of A+B+C is 1/6 of the tank per hour.
After 2 hours, the tank is 1/3 full.
The rate of A+B is 2/3 * 1/9 = 2/27 of a tank per hour.
The rate of C is 1/6 - 2/27 = 5/54
C can fill the tank in 54/5 hours.
The answer is D.
Answer: (D) 54/5
Question: The difference between a number and its three-fifths is 50.What is the number?
(A) 75
(B) 100
(C) 125
(D) Cannot be determined
(E) None of these
Rationale: Suppose the number is N.
Then N - 3⁄5N = 50
⇒ 2N⁄5 = 50
∴ N=50×52=125
Answer.C
Answer: (C) 125
Question: Number N is randomly selected from a set of all primes between 10 and 40, inclusive. Number Z is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that N+Z is odd?
(A)  1/2
(B)  2/3
(C)  3/4
(D)  4/7
(E)  5/8
Rationale: All primes except 2 are odd, thus N must be odd. For N + Z = odd + Z to be odd, Z must be even.
There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd.
Therefore the probability that N + Z is odd is 4/7.
Answer: D.
Answer: (D)  4/7
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
(A) 5,2
(B) 6,9
(C) 2,1
(D) 5,8
(E) 15,10
Rationale: Explanation:
lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer: E
Answer: (E) 15,10
Question: If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer x?
(A) x/3
(B) x^2 - x
(C) 2x - 1
(D) (2x - 1)/(x^2 + x)
(E) (2x - 1)/(x^2 - x)
Rationale: Let two consecutive positive integers be x and x-1 (Greater integer is x)
So,
(1/x) + [1/(x-1)]
= (2x-1)/x(x-1)
=(2x-1)/(x^2- x)
Answer E
Answer: (E) (2x - 1)/(x^2 - x)
Question: A person starting with Rs.64 & making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If eachwager is for half the money remaining at thetime of the bet, then the final result is?
(A) Rs.37
(B) Rs.57
(C) Rs.60
(D) Rs.64
(E) Rs.68
Rationale: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).
The overall resultant will remain same.
So final amount with the person will be (in all cases):
=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727
Hence the final result is:
64−27=3764−27=37:
A loss of Rs.37
A
Answer: (A) Rs.37
Question: The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 22nd of September 1990?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Friday
(E) Saturday
Rationale: 19th September
1987: Saturday
1988: Monday (due to leap year)
1989: Tuesday
1990: Wednesday
Hence 22nd September was a Saturday.
The answer is E.
Answer: (E) Saturday
Question: When 100 is divided by positive integer x, the remainder is 4. What is the remainder when 196 is divided by x?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: f100/x leaves a reminder 4 then (100-4) i.e. 96 is divisible by x
So (100+96)/x leaves a reminder rem(100/x)+rem(96/x)=> 4+0=4
Answer :C
Answer: (C) 4
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq. m ?
(A) Rs. 4082.40
(B) Rs. 1024.21
(C) Rs. 2810.6
(D) Rs. 3214
(E) Rs. 2140
Rationale: Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 x 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
ANSWER IS A
Answer: (A) Rs. 4082.40
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?
(A) 2 days
(B) 3 days
(C) 5 days
(D) 7 days
(E) 9 days
Rationale: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
B)
Answer: (B) 3 days
Question: Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 48 meter head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
(A)  15 seconds
(B)  18 seconds
(C)  24 seconds
(D)  30 seconds
(E)  45 seconds
Rationale: used pluging in method
say t is the time for cristina to catch up with Nicky, the equation will be as under:
for Nicky=N=3*t+48
for Cristina=C=5*t
@t=24, N=120 C=120 right answer
ans:C
Answer: (C)  24 seconds
Question: Submarine P and Submarine Q are equipped with sonar devices that can operate within a 2,000 yard range. Submarine P remains in place while Submarine Q moves 1,700 yards south from Submarine P. Submarine Q then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine Q continue to move and still be within the sonar range of Submarine P? I. North II. South III. West
(A) III only
(B) I,II only
(C) II only
(D) I only
(E) I and III only
Rationale: It's evident if we make a diagram for the Movement of Q respect to P.
From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.
Thus it can only move north or west or anything in that curve.
Answer : E
Answer: (E) I and III only
Question: Number of divisors of 22050 except 1 and itself is.
(A) 22
(B) 52
(C) 87
(D) 26
(E) 19
Rationale: Explanation: 2 22050 3 11025 3 3675 5 1225 5 245 7 49 7 ⇒ 22050 = 21 × 32 × 52 × 72 Using the formula discussed earlier, ∴ Number of divisors = (1+1) (2+1) (2+1) (2+1) = 54 ∴ Number of divisors except 1 and itself = 54 –2 = 52
Answer:B
Answer: (B) 52
Question: Paul completes a piece of work in 80 days, Rose completes the same work in 120 days. If both of them work together, then the number of days required to complete the work is?
(A) 42
(B) 44
(C) 46
(D) 48
(E) 50
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 80 × 120/200 = 48 days
Answer is D
Answer: (D) 48
Question: If log303 = a, log305 = b, then log308 =?
(A) 3(1 - a - b)
(B) (a - b + 1)
(C) (1 - a - b)
(D) (a - b + 1)
(E) none of these
Rationale: a + b = log3015 = log30(30/2) = 1- log302
=> log302 = (1 - a - b)
Therefore, log308 = 3(1 - a - b).
ANSWER:A
Answer: (A) 3(1 - a - b)
Question: If the height of an equilateral triangle QBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔQBC is how many times as long as a leg of the right triangle DEF?
(A) (√2)/(√3)
(B) (√3)/(√2)
(C) √2
(D) (2√2)/(√3)
(E) 2/(√3)
Rationale: Side of the equilateral triangle QBC = 2m ----> height = m * sqtr(2)
Hipotenuse of the right triangle QBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)
Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=D
Answer: (D) (2√2)/(√3)
Question: If a-b= 6 and a^2+b^2=100, find the value of ab
(A) 10
(B) 32
(C) 15
(D) 18
(E) 19
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 100 - 36 = 64
=> ab = 32
ANSWER:B
Answer: (B) 32
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
(A) 384 cm^2
(B) 200 cm^2
(C) 250 cm^2
(D) 350 cm^2
(E) 400 cm^2
Rationale: Area of a parallelogram = base * height = 24 * 16 = 384 cm2
ANSWER A
Answer: (A) 384 cm^2
Question: If Q is an odd number and the median of Q consecutive integers is 110, what is the largest of these integers?
(A) (Q - 1)/2 + 110
(B) Q/2 + 109
(C) Q/2 + 110
(D) (Q + 109)/2
(E) (Q + 110)/2
Rationale: Consider the easiest case, say Q=3, then;
Set = {109, 110, 111};
The largest integer = 111.
Now, plug Q=3 into the answers to see which yields 111.
Answer: A.
Answer: (A) (Q - 1)/2 + 110
Question: The area of one square is x^2 + 10x + 25 and the area of another square is x^2 − 6x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?
(A) 3
(B) 2
(C) 2.5
(D) 4.67
(E) 10
Rationale: spotting the pattern of equations both are in form of (X+C)^2 so
A1= (x+5)^2A2= (x-3)^2
L1= x+5L2= -3
P1 = 4( x+5)P2=4(x-3)
P1+P2=32
4( x+5) +4(x-3)=32.....3
Ans :A
Answer: (A) 3
Question: What is the value of 3x^2 − 2x + 0.3 for x = 0.5?
(A) −0.3
(B) 0
(C) 0.05
(D) 1.08
(E) 2.46
Rationale: 3x^2-2x+0.3 for x=0.6
=3(0.5*0.5)-4*0.5*(0.5)+0.3
=-0.5*0.5+0.3
=-0.25+0.3
=0.05
Correct Option : C
Answer: (C) 0.05
Question: A certain manufacturer of cake, muffin, and bread mixes has 90 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
(A) a. 1/10
(B) b. 3/10
(C) c. 1/3
(D) d. 7/10
(E) e. 9/10
Rationale: C+M+B-CM-MB-CB-2CMB = 90
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-20-2CMB = 90
B-CB-MB-2CMB = 30
hence the probability = 30/90 = 30/90=1/3.
C
Answer: (C) c. 1/3
Question: The avg. age of a group of 32 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
(A) 22 years
(B) 23 years
(C) 24 years
(D) 25 years
(E) 29 years
Rationale: Total age of 32 students=32*20=640
If total age of 4 students=x
Then, (640+x)/(32+4) =(20+1), x=116
So average age of new students=116/4= 29 years
ANSWER:E
Answer: (E) 29 years
Question: Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?
(A) 2776
(B) 2777
(C) 1951
(D) 2966
(E) 1971
Rationale: Explanation:
P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.
Amount = [15625 * (1 + 4/100)3]
= (15625 * 26/25 * 26/25 * 26/25) = Rs. 17576 C.I. = 17576 - 15625 = Rs. 1951.
Answer: C
Answer: (C) 1951
Question: In my core I have 5 But 500 stand in the beginning and the end of mine. I also include the first letter and the first number to make me complete. I am the name of a King.
Who am I?
(A) Johny
(B) Jacky
(C) Ricky
(D) David
(E) Alex
Rationale: D
I am DAVID.
At the core I have 5
If we talk in roman numeric system, 5 = V
Similarly, 500 stands in the beginning and end
500 = D
I also include the first letter i.e. A and the first number i.e. I (in roman numeric system)
All of them combine to form DAVID.
Answer: (D) David
Question: A train 120 m long passed a pole in 20 sec. How long will it take to pass a platform 780 m long?
(A) 150
(B) 170
(C) 160
(D) 100
(E) 120
Rationale: Speed = 120/20 = 6 m/sec.
Required time = (120 + 780)/6 = 150 sec.
Answer: Option A
Answer: (A) 150
Question: Raju age after 9 years will be 5 times his age 3 years back, What is the present age of Raju
(A) 8 years
(B) 7 years
(C) 6 years
(D) 5 years
(E) 4 years
Rationale: Explanation:
Clearly,
x+9 = 5(x-3)
<=> 4x = 24 => x = 6
Option C
Answer: (C) 6 years
Question: The perimeter of a rhombus is 120 feet and one of its diagonal has a length of 40 feet. Find the area of the rhombus.
(A) 100 sqrt(5) ft.sq
(B) 400 sqrt(5) ft.sq
(C) 500 sqrt(5) ft.sq
(D) 200 sqrt(5) ft.sq
(E) 150 sqrt(5) ft.sq
Rationale: A perimeter of 120 when divided by 4 gives the side of the rhombus 30 feet. The length of the side OC of the right triangle is equal to half the diagonal: 20 feet. Let us now consider the right triangle BOC and apply Pythagora's theorem to find the length of side BO.
30^2 = BO^2 + 20^2
BO = 10 sqrt(5) feet
We now calculate the area of the right triangle BOC and multiply it by 4 to obtain the area of the rhombus.
area = 4 ( 1/2) BO * OC = 4 (1/2)10 sqrt (5) * 20
= 400 sqrt(5) ft.sq
Answer is B
Answer: (B) 400 sqrt(5) ft.sq
Question: How many positive integers less than 24 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?
(A) 19
(B) 25
(C) 24
(D) 22
(E) 20
Rationale: 9 prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19, 23}
2 odd multiples of 5: {5, 15}
9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4: {6, 8, 10, 12, 14, 16, 18, 20, 22}
Notice, that 5 is in two sets, thus total # of integers satisfying the given conditions is 9+2+9-1=19.
Answer: A.
Answer: (A) 19
Question: A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 6 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?
(A) 3,150
(B) 4,200
(C) 5,040
(D) 20,520
(E) 84,000
Rationale: For the big album they have to choose 3 out of their 6 photos, and leave out 3:
6! / 3!3! = 20
For the small album they have to choose 19 out of their 21 photos and leave out 2:
21! / 19!2! = 210
All combinations together: 210*20 = 4200, ANS B
Answer: (B) 4,200
Question: Find the average of the series : 235,222,125,135,123
(A) 168
(B) 308
(C) 267
(D) 207
(E) 174
Rationale: Average = (235+222+125+135+123)/5
= 840/5
= 168
Answer: A
Answer: (A) 168