mathewhe/aqua_rat huggingface dataset:
Question: Beth got a job painting dorm rooms at her
college. At top speed, she could paint 5
identical rooms during one 6-hour shift.
How long did she take to paint each room?
(A) 50 minutes
(B) 1 hour and 10 minutes
(C) 1 hour and 12 minutes
(D) 1 hour and 15 minutes
(E) 1 hour and 20 minutes
Rationale: Six hours equals 360 minutes, so Beth paints 5 rooms in 360 minutes. She paints 1 room
in 360 ÷ 5 = 72 minutes, which equals 1 hour and 12 minutes
correct answer C)1 hour and 12 minutes
Answer: (C) 1 hour and 12 minutes
Question: If 5 + 7/X = 6 - 5/X, then X =
(A) 7
(B) 14
(C) 12
(D) 6/7
(E) 5
Rationale: We're given the equation 5 + 7/X = 6 - 5/X. We're asked for the value of X.
The common-denominator of these 4 numbers is X, so we need to multiply both sides of the equation by X, giving us...
5X + 7X/X = 6X - 5X/X
We can then eliminate that denominator, which gives us....
5X + 7 = 6X - 5
12 = X
C
Answer: (C) 12
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.86. How much was lent at 5%?
(A) 388
(B) 2998
(C) 277
(D) 500
(E) 400
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 86
5x/100 + 90 – 6x/100 = 86
x/100 = 4
=> x = 400.Answer: E
Answer: (E) 400
Question: In how many ways can 7 boys and 2 girls be arranged a ta table if 2 girls are never together?
(A) 30240
(B) 31240
(C) 32410
(D) 32540
(E) 36540
Rationale: Total ways of arranging 9 person in a circle = 8! = 40320 ways
If we consider two women as one, then we have 7+1=8 persons. Arranging these eight persons in circle will take = 7! = 5040 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 7!*2! = 10080 ways
Total ways in which two women doesn’t sit together in circle = 8! - 7!*2! = 40320 - 10080 = 30240 ways
A
Answer: (A) 30240
Question: Look at this series: 7.2, 7, 6.8, 6.6, ... What number should come next?
(A) 6.4
(B) 6
(C) 5.8
(D) 6.3
(E) 5.6
Rationale: A
6.4
In this simple subtraction series, each number decreases by 0.2.
Answer: (A) 6.4
Question: In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 4 kmph
(B) 5 kmph
(C) 6 kmph
(D) 7 kmph
(E) 8 kmph
Rationale: Speed in still water = ½ (11+5) kmph = 8 kmph
answer : E
Answer: (E) 8 kmph
Question: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
(A) 144
(B) 152
(C) 160
(D) 168
(E) 65
Rationale: The first digit can be filled in 5 ways
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 7 values
number of codes = 5 * 1 * 7 = 35
Case 2 -
If second digit is 0,Third digit can take 6 values ( Third digit can't be zero)
number of codes = 5 * 1 * 6= 30
Total number of codes = 65
Answer E
Answer: (E) 65
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 288
(C) 276
(D) 299
(E) 211
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer: A
Answer: (A) 270
Question: Difficulty:
There are five sales agents in a certain real estate office. One month Andy sold thrice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold thrice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?
(A) Andy
(B) Bob
(C) Cary
(D) Dora
(E) Ellen
Rationale: a= 3e
b =3 +e
c = 3b = 9+ 3e (highest of all)
d = b + e = 3+ e +e = 3 + 2e
Ans. C
Answer: (C) Cary
Question: In how many ways Chief Minister and Minister be elected from a team of 14 members?
(A) 182
(B) 131
(C) 132
(D) 143
(E) 145
Rationale: To do this, if captain is elected first, then we have 14 ways of doing this.
For election of vice-captain, we have only 13 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 14*13 = 182 ways.
Answer : A
Answer: (A) 182
Question: Insert the missing number.
8, 7, 16, 5, 24, 3, 32, 1, 40,-1, (....)
(A) 48
(B) 40
(C) 35
(D) -3
(E) -4
Rationale: Explanation:
There are two series, beginning respectively with 8 and 7. In one 8 is added and in another 2 is subtracted.
The next number is 40 + 8 = 48.
Answer: A) 48
Answer: (A) 48
Question: The sum of 99 consecutive integers is 9999. What is the greatest integer in the set?
(A) 100
(B) 120
(C) 149
(D) 150
(E) 151
Rationale: sum of n numbers = (n(2a+(n-1)d))/2 where n = no of terms a = 1st term , d - difference between two terms (ie d= a2-a1)
here sum = 9999 , n= 99 d = 1 (since consecutive numbers)
9999= (99/2) * (2a+(99-1)1)
from this 'a' (ie the 1st term) = 52
nth term in a sequence : nth term = a + (n-1) d
here a = 52 , n = 99 , d = 1
So nth term = 52 + (99-1)*1
therefore Nth term = 150
ANSWER:D
Answer: (D) 150
Question: Roses can be purchased individually for $4.50, one dozen for $36, or two dozen for $50. What is the greatest number of roses that can be purchased for $680?
(A)  156
(B)  162
(C)  318
(D)  324
(E)  325
Rationale: Buy as many $50 deals as possible. We can by 650/50=13 two dozen roses, thus total of 13*24 = 312 roses.
We are left with 680 - 650 = $30. We can buy 30/4.5 = ~6 roses for that amount.
Total = 312 + 6 = 318.
Answer: C.
Answer: (C)  318
Question: If a 19-cup mixture of powder and water contained 1 cup of powder. How many cups of powder must be added to get a mixture having powder and water in the ratio of 1:2?
(A) 6
(B) 8
(C) 17
(D) 19
(E) 24
Rationale: Concentration of powder in Mix 1 = 1/19
Concentration of powder in Mix 2 = 1 ( i.e. 100% since it is all powder)
Concentration of powder in final mixture = 1/3
w1/w2 = (1 - 1/3)/(1/3 - 1/19) = 19/8
So for every 19 cups of mix1, you need to put 8 cups of powder to make the required mix with ratio 1:2.
ANSWER:D
Answer: (D) 19
Question: Pipe B that can fill a tank in an hour and pipe A that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe A is shut 15 minutes before the tank overflows. When will the tank overflow?
(A) 32 mins
(B) 35 mins
(C) 40 mins
(D) 30 mins
(E) 36 mins
Rationale: The last 15 minutes only pipe B was open. Since it needs 1 hour to fill the tank, then in 15 minutes it fills 1/4th of the tank, thus 3/4 of the tank is filled with both pipes open.
The combined rate of two pipes is 1 + 2 = 3 tanks/hour, therefore to fill 3/4th of the tank they need (time) = (work)/(rate) = (3/4)/3 = 1/4 hours = 15 minutes.
Total time = 15 + 15 = 30 minutes.
Answer: D
Answer: (D) 30 mins
Question: A vessel of capacity 2 litre has 20% of alcohol and another vessel of capacity 6 litre had 55% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
(A) 37%.
(B) 71%.
(C) 49%.
(D) 29%.
(E) 51%.
Rationale: 20% of 2 litres = 0.4 litres
55% of 6 litres = 3.3 litres
Therefore, total quantity of alcohol is 3.7 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 37%
A
Answer: (A) 37%.
Question: In a barrel of juice there is 20 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
(A) 3:2.
(B) 2:1.
(C) 3:1.
(D) 4:3.
(E) 3:4.
Rationale: Juice barrel : beer Barrel = 20:80 i.e. 3:8
price of Juice : Price of Beer = 3 : 4
so for 2/8 costs 3/4, ie 2J / 8B = 3/4.
Solving for J/B, we get 3:1
Answer C.
Answer: (C) 3:1.
Question: By selling a bat for Rs.720/- a man loses 10% what is that bat cost price
(A) Rs.600/-
(B) Rs.630/-
(C) Rs.700/-
(D) Rs.780/-
(E) Rs.800/-
Rationale: 90 % ------> 720 (90 * 8 = 720)
100 % ------>800 (100 * 8 = 800)
Cost price = Rs.800/-
E)
Answer: (E) Rs.800/-
Question: If a/x = 1/2 and a/y =1/ 4, then (x + y) =
(A) A)2a
(B) B)a/2
(C) C)6a
(D) D)7a
(E) E)9a
Rationale: Ratio 1:
2a = x
Ratio 2:
4a = y
x+y = 6a
Answer is C
Answer: (C) C)6a
Question: Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 96% water by weight. What is the new weight of the cucumbers, in pounds?
(A) 2
(B) 25
(C) 92
(D) 96
(E) 98
Rationale: Out of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After somewaterevaporates the cucumbers become 96% water and 4% of non-water, so now 1 pound of non-water composes 4% of cucucmbers, which means that the new weight of cucumbers is 1/0.04=25 pounds.
Answer: B.
Answer: (B) 25
Question: If the annual increase in the population of a town is 10% and the present number of people is 10000, what will the population be in 2 years?
(A) 12100
(B) 15240
(C) 12456
(D) 11452
(E) 10002
Rationale: The required population is = 10000 (1 + 10/100)^2
= 10000 * 11/10 * 11/10
= 12100
Answer is A
Answer: (A) 12100
Question: In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2?
(A) 20 liters
(B) 30 liters
(C) 60 liters
(D) 38 liters
(E) 40 liters
Rationale: 2:1 --- 60
1:2
2:4
---------------
3
3 ----------- 60
3 ----------- ? => 60 liters
Answer: C
Answer: (C) 60 liters
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?
(A) 20%
(B) 10%
(C) 60%
(D) 70%
(E) 30%
Rationale: 2420 --- 242
100 --- ? => 10%
Answer: B
Answer: (B) 10%
Question: In a fuel station the service costs $1.50 per car, every liter of fuel costs 0.35$. Assuming that you own 3 limos and 2 fleet vans and all fuel tanks are empty. How much will it cost to fuel all cars together if a limo tank is 32 liters and an fleet van tank is 75% bigger?
(A) $78.80
(B) $79.80
(C) $78.90
(D) $79.90
(E) $77.80
Rationale: Lots of calculations.
1.50*4 + 3*.35*32+ 2*(7/4)*32 *.35
Answer=$78.80
The correct option is A
Answer: (A) $78.80
Question: 4 letters have to be put into their 4 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the letters go into their respective envelopes?
(A) 1/30
(B) 1/64
(C) 1/120
(D) 1/240
(E) 3/5
Rationale: A-B-C-D-E (envelopes)
a-b-c-d-e (letters)
4 letters (a, b, c, d, and e) can be assigned to 4 envelopes (arranged) in 4! ways, out of which only one will be correct, thus the probability is 1/4! = 1/64.
Answer: B.
Answer: (B) 1/64
Question: Two trains 200 m and 800 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.6
(B) 10.9
(C) 36
(D) 10.8
(E) 10.1
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 200 + 800 = 1000 m.
Required time = 1000 * 9/250 = 36 sec.
Answer: C
Answer: (C) 36
Question: Three different containers contain 50 litres, 100 litres and 150 litres of mixture of milk and water respectively. What is the biggest measure can measure all the different quantities exactly ?
(A) 120 litres
(B) 57 litres
(C) 60 litres
(D) 50 litres
(E) 100 litres
Rationale: M1 = 50 litres
M2 = 100 litres
M3 = 150 litres
Required measurement = H.C.F. of M1,M2,M3 = 50 litres
Answer is D
Answer: (D) 50 litres
Question: Amber works 30 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?
(A) m/(20d)
(B) 20d
(C) 10md/6
(D) 20d/m
(E) 30d
Rationale: ANSWER: E The passage states that she works 30 days a month at d dollars per day, so 30 d is her monthly pay
Answer: (E) 30d
Question: Insert the missing number
5, -15, 45, -135, (....)
(A) 350
(B) -405
(C) 405
(D) -350
(E) 0
Rationale: 5*-3=-15
-15*-3=45
45*-3=-135
-135*-3=405
ANSWER:C
Answer: (C) 405
Question: A fellow borrowed a certain sum of money at 8% per annum at simple interest and in 8 years the interest amounted to Rs.900 less than the sum lent. What was the sum lent?
(A) 1050
(B) 1220
(C) 2500
(D) 1060
(E) 1110
Rationale: P - 900 = (P*8*8)/100
P = 2500
Answer: C
Answer: (C) 2500
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What isthe probability that first is white and second is black?
(A) 31/111
(B) 36/145
(C) 21/115
(D) 11/154
(E) None of these
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
(A) 1/3
(B) 2/3
(C) 2/5
(D) 2/7
(E) 2/9
Rationale: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C
Answer: (C) 2/5
Question: A math teacher has 26 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: a square is a special kind of rhombus (sides are perpendicular)
a square is a special kind of rectangles (sides with same length)
Among the 26 cards with have:
15 rectangles
10 rhombus
8 squares
Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.
Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.
We have 8 squares.
So the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17
Which means that the maximum number of circles that you could have is 26 - 17 = 9
Answer (A)
Answer: (A) 9
Question: Sunanth is 22 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
(A) 20 years
(B) 23 years
(C) 21 years
(D) 22 years
(E) 24 years
Rationale: Let present age of the son =c years
Then, present age of the sunanth =(c+22) years
Given that, in 2 years, sunanth's age will be twice the age of his son
=>(c+22)+2=2(c+2)
=>x=20
ANSWER:A
Answer: (A) 20 years
Question: A constructor estimates that 3 people can paint Mr. Gokhle's house in 10 days. If he uses 5 people instead of 3,how long will they take to complete the job?
(A) 6
(B) 5
(C) 10
(D) 5
(E) 4
Rationale: Explanation:
Use formula For a work Members Ã— days = constant
3 Ã— 10 = 5Ã— a
a = 6
so answer is 6days
Answer:A
Answer: (A) 6
Question: Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 6.24
(B) B) 4.1
(C) C) 10
(D) D) 15
(E) E) 24
Rationale: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9
New time in minutes to cross 10 miles stretch = 10*60/40 = 10*3/2 = 15
Time difference = 4.1
Ans:B
Answer: (B) B) 4.1
Question: Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in mph?
(A) 37.5 mph
(B) 40 mph
(C) 50 mph
(D) 44 mph
(E) None of these
Rationale: Explanation :
Average speed=Total Distance/Time.
Total distance travelled by Jim = Distance covered in the first 3 hours + Distance covered in the next 5 hours.
Distance covered in the first 3 hours = 3×60=180 miles
Distance covered in the next 5 hours= 5×24=120 miles
Therefore, total distance travelled = 180+120=300 miles.
The total time taken = 3+5=8 hours.
Hence, the average speed = 300/8= 37.5 mph.
Answer : A
Answer: (A) 37.5 mph
Question: Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It continues in such a way that by adding 5 to the nth term, one obtains the (n + 2)th term. What is the sum of the first 18 members of this sequence?
(A) 878
(B) 900
(C) 788
(D) 810
(E) 1022
Rationale: I would split them up like this.
23 28 33 and so on (9 terms)....the 10th term = 23+8*5 = 63
27 32 37 and so on (9 terms)......the 9th term = 27+8*5 = 67
Since the distance between any two numbers is the same we can use arithmetics
first+last/2 times no of numbers = the sum
(23+63)/2 * 9= 387
(27+67)/2 * 9 = 423
= 810
D
Answer: (D) 810
Question: If A = 2B+1 where A is an Integer then which of the following is true?
(A) A is always Odd
(B) A is always Even
(C) A is a non multiple of 2
(D) A is even if B is a non integer and a multiple of 0.5
(E) A=1
Rationale: D
Answer: (D) A is even if B is a non integer and a multiple of 0.5
Question: Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
(A) Rs.81.60
(B) Rs.160
(C) Rs.172
(D) Rs.727
(E) Rs.728
Rationale: SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6
Answer:A
Answer: (A) Rs.81.60
Question: . A man pays off 3/20 of his debt every month.At the end of 6 months, his remaining debt is $A.How much amount has he cleared off every month?
(A) 3A/20
(B) 9A/10
(C) A/10
(D) 3A/10
(E) 3A/2
Rationale: Let his total debt be T
Every month he pays off 3/20 of his debt = 3/20∗T3/20∗T
After 6 months he would have paid = 3/20∗6∗T3/20∗6∗T
His remaining debt after 6 months is A.
Hence Total debt = Remaining debt + Paid debt
T=A+3/20∗6∗TT=A+3/20∗6∗T
T−18/20∗T=AT−18/20∗T=A
T∗2/20=AT∗2/20=A
T=10AT=10A
Every month he pays off 3/20 of his debt = 3/20∗T=3/20∗10A=3A/2
Answer : E
Answer: (E) 3A/2
Question: Which of the options is a multiple of 3!+6
(A) 4!-12
(B) 4!+2
(C) 4!-2
(D) 3!+20
(E) 4!+20
Rationale: When expanded 3!+6 equal (3*2) +6
Therefore (3*2) +6=6+6=12
Looking at the options the only one that gives a multiple of 12 is option A)
Answer: (A) 4!-12
Question: The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?
(A) 50
(B) 60
(C) None of these
(D) 70
(E) 100
Rationale: C
100
2C + 3T = 1300 --- (1)
3C + 3T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 100 => T - C = 100
Answer: (C) None of these
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
(A) 24007
(B) 24000
(C) 24028
(D) 240011
(E) 240121
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs. 24000
Answer:B
Answer: (B) 24000
Question: The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ?
(A) 4.5
(B) 4.2
(C) 4.7
(D) 4.8
(E) None of these
Rationale: solution:
Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)]
=23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4.
∴ Required average =8.4/2 = 4.2 Answer B
Answer: (B) 4.2
Question: If x/2 years ago Roger was 18 years old and x/2 years from now he will be 4x years old, how old will he be 5x years from now?
(A) 32
(B) 35
(C) 30
(D) 51
(E) 28
Rationale: Assume the current age = a
a - x/2 = 18 (i)
a + x/2 = 4x
Or a = 7x/2 (ii)
Putting the value of a from (ii) in (i)
7x/2 - x/2 = 18
Or 6x/2 = 18 Therefore x = 6 and a = 21
5x years from now, age will be 21 + 5*6 = 51
Option D
Answer: (D) 51
Question: A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
(A) 224km
(B) 233km
(C) 277km
(D) 256km
(E) 297km
Rationale: distance = speed x time
Let time taken to travel the first half = x hr
then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x
Distance covered in the the second half = 24(10 - x)
But distance covered in the the first half = Distance covered in the the second half
=> 21x = 24(10 - x)
=> 21x = 240 - 24x
=> 45x = 240
=> 9x = 48
=> 3x = 16
⇒x=163Hence Distance covered in the the first half = 21x=21×163=7×16=112 kmTotal distance = 2×112=224 km
Answer :A
Answer: (A) 224km
Question: For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What is the value of <3>*<4>?
(A)  60
(B)  116
(C)  710
(D)  756
(E)  478
Rationale: Since <x>=2x+(2x-1)+(2x-2)+......2+1=1+2+..+(2x-2)+(2x-1)+2x then<x> is basically the sum of all integers from 1 to 2x, inclusive.
Hence <3> is the sum of all integers from 1 to 2*3=6 and <4> is the sum of all integers from 1 to 2*4=8--> <3>=21 and <4>=36 --> <3>*<4>=21*36=756.
Answer: D
Answer: (D)  756
Question: The average age of an adult class is 40years. 12new students with an avg age of 32years join the class. Therefore decreasing theaverage by 4year. Find what was theoriginal strength of class?
(A) 11
(B) 12
(C) 17
(D) 19
(E) 21
Rationale: Let original strength = y
Then , 40y + 12 x 32 = ( y + 12) x 36
⇒ 40y + 384 = 36y + 432
⇒ 4y = 48
∴ y = 12
B
Answer: (B) 12
Question: A company has $329,864 in its account. What is the least amount of money (in whole number of dollars) that it must add to the account if the money is paid evenly among 9 of its vendors?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $6
Rationale: To find the least amount that must be added to the Account to split the money evenly among 9 of its vendors,
the total divisible by 9
Simply add the individual digits of the total = 3+2+9+8+6+4 = 32
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Answer: (D) $4
Question: A beekeeper has 600,000 bees living in four beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have?
(A) 20,000
(B) 176470
(C) 10000
(D) 13000
(E) 56600
Rationale: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+3*(0.8)*x = 600,000 => 3.4x = 600,000 => x = 176470.
B is the answer.
Answer: (B) 176470
Question: The cross section of a canal is a trapezium in shape. If the canal is 7 metres wide at the top and 9 metres at the bottom and the area of cross-section is 1280 square metres, find the length of the canal.
(A) 160 metres
(B) 172 metres
(C) 154 metres
(D) 165 metres
(E) None of these
Rationale: None of these
Let the length of canal = h m.
Then,area of canal = 1⁄2 × h(9 + 7)
or 1280 = 1⁄2h(16)
∴ h = 1280×2/16=160m
Answer A
Answer: (A) 160 metres
Question: If n is a positive integer, which one of the following numbers must have a remainder of 1 when
divided by any of the numbers 4, 5, and 6?
(A) 125n + 1
(B) 240n + 1
(C) 275n + 1
(D) 290n + 1
(E) 320n + 1
Rationale: The numbers 4, 5, and 6 all divide 240 so they all divide 240n.
When we divide (240n + 1) by 4, 5, or 6, the remainder must be 1.
The answer is B.
Answer: (B) 240n + 1
Question: Find the average of all the numbers between 6 and 34 which are divisible by 5?
(A) 10
(B) 20
(C) 34
(D) 54
(E) 28
Rationale: Average = (10 + 15 + 20 + 25 + 30)/5
= 100/5 = 20.
Answer:B
Answer: (B) 20
Question: A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:
(A) 90
(B) 106
(C) 110
(D) 120
(E) 130
Rationale: sax Letlheo g alnumberofworkers hex
x workers can do the wor - 100 days
(x — 10) workers can do the work in 110 days
4 100x 1u1x— 10)
1100 Q x 110
C
Answer: (C) 110