mathewhe/aqua_rat huggingface dataset:
Question: Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
(A) 10.30
(B) 10
(C) 8.45
(D) 9.3
(E) 11
Rationale: Explanation:
Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 110
=> 20x + 25(x-1) = 110
=> 45x = 135
=> x= 3
Means, they meet after 3 hours after 7 am, ie, they meet at 10 am. Answer: B
Answer: (B) 10
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 3x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)
(A) 100
(B) 90
(C) 82
(D) 78
(E) 75
Rationale: The question say:A welder received an order to make a 1 million liter cube-shaped tank. (1 cubic meter = 1,000 liters)
In other words, the tank is going to have a volume of 1000 cubic meters. That would equal 1 million liters.
A cube with a volume of 1000 cubic meters must be (10 meters) x (10 meters) x (10 meters).
The question doesn't specify whether this tank should have a closed top or an open top. (The real GMAT is good about specifying things like that.) Here, we are going to assume a closed top, only because if the top is open, we don't use enough metal --- we get an answer smaller than any of the answer choices. A closed-top cube, a full cube, has 6 sides, each of which is (10 meters) x (10 meters). That's a total surface area of 600 sq m.
The question tells us:he has only 3x2 meter sheets of metal that can be cut.
Each sheet has an area of 6 sq m. How many of these need to fill up 600 sq m? 600/6 = 100. He needs 100 sheets.
Answer =A
Answer: (A) 100
Question: The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
(A) W = 15 and L = 20
(B) W = 25 and L = 30
(C) W = 35 and L = 40
(D) W = 45 and L = 50
(E) W =55 and L = 60
Rationale: L * W = 300 : area , L is the length and W is the width.
2 L + 2 W = 70 : perimeter
L = 35 - w : solve for L
(35 - W) * W = 300 : substitute in the area equation
W = 15 and L = 20 : solve for W and find L using L = 35 - w.
correct answer A
Answer: (A) W = 15 and L = 20
Question: In how many different number of ways 7 men and 2 women can sit on a shopa which can accommodate persons?
(A) 17000
(B) 18000
(C) 15120
(D) 21000
(E) 23000
Rationale: 9p5 =9 x 8 x 7 Ã— 6 Ã— 5 = 15120
Answer : C
Answer: (C) 15120
Question: Following an increase in prices, the price of a candy box was 15 pounds and the price of a can of soda was 6 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised?
(A) 11.
(B) 12.
(C) 13.
(D) 14.
(E) 16
Rationale: Price of candy before price increase= 15/1.25= 12
Price of soda before price increase= 6/1.5= 4
Total price = 12+4= 16
E is the answer
Answer: (E) 16
Question: If 183 is divisible by 11, find the value of the smallest natural no. N?
(A) 5
(B) 7
(C) 9
(D) 10
(E) 12
Rationale: In aptitude tests , we get questions on divisibility by 11.
A number is divisible by 11, when the difference between the sum of digits at even places and at odd places is 0 or multiple of 11
The given number is N183.
(Sum of digits at EVEN places) – (sum of digits at ODD places)=0
(8 + N)- (3+1)= 0
(8 + N) - 4 = 0
Here the value of N must be 7
B
Answer: (B) 7
Question: A’s speed is 20/12 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
(A) 1/17
(B) 3/17
(C) 1/10
(D) 6/20
(E) 3/10
Rationale: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 20 meters, B covers 12 meters in that time. So if the race is 20 meters long, when A reaches the finish line, B would be 8 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 8 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 20 meters) would be the same as the time required by B (to cover 12 meters) to reach the finish line.
So B should get a head start of 8/20th of the race.
Answer (D)
Answer: (D) 6/20
Question: If x is an odd integer, which of the following is an even integer?
(A) 2x-x
(B) x+1
(C) 2x+3
(D) x^3
(E) 3x+2x
Rationale: Plug in an odd integer; in this case 3
(2*3)-3 = 3 Odd
3+1 = 4 Even
(2*3)+3 = 9 Odd
3^3 = 27 Odd
(3*3)+(2*3) = 9 + 6 = 15 Odd
Answer: B
Answer: (B) x+1
Question: Two trains 120 meters and 150 meters long are running in the same direction with speeds of 92 km/hr, 56km/hr. In how much time will the first train cross the second
(A) 37 sec
(B) 22 sec
(C) 27 sec
(D) 35 sec
(E) 36 sec
Rationale: Explanation:
Relative speed of the trains = (92 - 56) km/hr = 36 km/hr
= (36× 5/18) m/sec = 10 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (120 + 150) m at 10 m /sec = (270/10) sec = 27 sec.
Answer: Option C
Answer: (C) 27 sec
Question: Two trains of length 150 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 100/7 sec
(B) 80/7 sec
(C) 57/7 sec
(D) 110/7 sec
(E) 50/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (150 + 100 + 300)/35
= 550/35 = 110/7 sec.
ANSWER:D
Answer: (D) 110/7 sec
Question: What is 0.05 percent of 12,356?
(A) 0.6178
(B) 61.78
(C) 6.178
(D) 0.06178
(E) 0.006178
Rationale: Since, Percent=1/100, what=something(s), and is:=. We can write the question as s=0.05(1/100)12,356. The answer is 6.178. Hence, the correct answer is C.
Answer: (C) 6.178
Question: 1. Internet: $80, with no sales tax, plus $10 shipping fee
2. Store X: $90, a 10% discount, plus 10% tax on discounted price
3. Store Y: $90, no tax
4. Store Z: $90, a 20% sales tax, and $10 rebate after tax
Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?
(A) 88.1
(B) 89.0
(C) 89.1
(D) 89.5
(E) 90.0
Rationale: Option 2 = (90 - 9) + 0.1 * 81
= 81 + 8.1 = 89.10
Option 4 = 90 + 0.2 * 90 - 10
= 98
So the OA is correct - C
Answer: (C) 89.1
Question: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 16, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?
(A)  4/11
(B)  1/2
(C)  15/22
(D)  144/17
(E)  11/4
Rationale: P1 takes 12 hrs
Rate for P2P3 together = 1/16 + 1/18 = 17/144
Therefore they take 144/17
Ratio = 144/17 = D
Answer: (D)  144/17
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2376?
(A) 2277
(B) 2400
(C) 2200
(D) 2766
(E) 2998
Rationale: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2376.
=> (90%) of (110%) of x = Rs. 2376.
=> (90/100)(110/100)x = 2376
=> x = (2376 * 100)/(9 * 11)
=> x = Rs. 2400
Answer: B
Answer: (B) 2400
Question: Three liquids were mixed in 5:4:1 ratios. If cost per kg for ach of them is 4.50,
3.75& 5.10. Then in what price mixture should be sold to get 25% profit?
(A) 52.25
(B) 53.25
(C) 54.25
(D) 55.25
(E) 56.25
Rationale: cp of the liquid=5*4.50+4*3.75+1*5.10=42.6
In order to gain 25%profit
Sp=1.25*42.6=53.25
ANSWER:B
Answer: (B) 53.25
Question: A committee is composed of w women and m men. If 4 women and 5 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by
(A) w/m
(B) w/(w+m)
(C) (w+4)/(m+5)
(D) (w+4)/(w+m+5)
(E) (w+4)/(w+m+9)
Rationale: The number of women is w+4.
The total number of people is w+m+9.
P(a woman is selected) = (w+4) / (w+m+9)
The answer is E.
Answer: (E) (w+4)/(w+m+9)
Question: Speed of trains A and B are 29 & 56 km/hr travelling in the same direction. Man in slower train passes in 16 min.
Find the length of the train.?
(A) 100 m
(B) 110 m
(C) 120 m
(D) 220 m
(E) 130 m
Rationale: let length of 2 trains = 2x
Relative speed= 56-29 = 27 km/hr
= (27*5)/18 m/sec
= 15/2 m/sec
so, 2x/16=15/2
2x=120
ANSWER:C
Answer: (C) 120 m
Question: A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 18 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
(A) 14
(B) 16
(C) 21
(D) 32
(E) 48
Rationale: I treat such problems as work ones.
Work=Rate*Time
Mileage(m)=Rate(mpg)*Gallons(g)
X gallons is a full tank
{462=RX
{336=(R-18)X solve for R, R=66
66-18=48 mpg
E
Answer: (E) 48
Question: In what ratio must tea worth Rs. 60 per kg be mixed with tea worth Rs. 65 a Kg such that by selling
the mixture at Rs. 68.20 a Kg ,there can be a gain 10%?
(A) 3 : 2
(B) 2 : 3
(C) 4 : 3
(D) 3 : 4
(E) None of these
Rationale: Explanation :
Cost Price(CP) of 1 Kg mixture = Rs. 68.20
Profit = 10%
Cost Price(CP) of 1 Kg mixture= 100(100+Profit%)×SP=100(100+10)×68.20=100110×68.20=68211=Rs.62
By the rule of alligation:
CP of 1 kg tea of 1st kind CP of 1 kg tea of 2nd kind
60 65
Mean Price
62
65 - 62 = 3 62 - 60 = 2
Hence required ratio = 3 : 2
Answer : Option A
Answer: (A) 3 : 2
Question: The positive integer n is divisible by 16. If n√n is greater than 16, which of the following could be the value of n16?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: The positive integer n is divisible by 16
=> n = 16k where k is a positive integer
Sqrt(n) > 16
=> Sqrt (16k) > 16
=> Sqrt (k) > 4
=> k > 16
Therefore n/16 = k must be greater than 16. From the given options, it can only be 17. Option E.
Answer: (E) 17
Question: Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following T must be true?
I. At least 50% of the numbers in Z are smaller than the median.
II. Less than 50% of the numbers in Z are greater than the median.
III. The median of Z is greater than the average of the largest and smallest numbers in Z.
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) T=None of the above
Rationale: Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3.
Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect.
Even if not, we can rule them both out. So, E.
Answer: (E) T=None of the above
Question: An error 2.5% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
(A) 6.04%
(B) 5.14%
(C) 5.23%
(D) 5.0625%
(E) 5.5%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102.5 x 102.5) cm2.
(A2 - A1) = [(102.5)2 - (100)2]
= (102.5 + 100) x (102.5 - 100)
= 506.25 cm2.
Percentage error = 5.0625
D
Answer: (D) 5.0625%
Question: Three unbiased coins are tossed. What is the probability of getting at most 2 heads?
(A) 7/8
(B) 5/8
(C) 3/8
(D) 7/5
(E) 3/5
Rationale: Here S={TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E=event of getting at least two heads ={TTT, TTH, THT, HTT, THH, HTH, HHT}
P(E) = n(E)/n(S) = 7/8.
Answer A.
Answer: (A) 7/8
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 878 in 4 years. The sum is:
(A) 500
(B) 698
(C) 626
(D) 910
(E) None
Rationale: Sol.
S.I. for 1 year = Rs. (878 - 815) = Rs. 63.
S.I. for 3 years = Rs. (63 * 3) = Rs. 189.
âˆ´ Principal = Rs. (815 - 189) = Rs. 626
Answer C
Answer: (C) 626
Question: A car covers a distance of 630 km in 6 hours. Find its speed?
(A) 105
(B) 7778
(C) 266
(D) 288
(E) 121
Rationale: 624/6 = 105 kmph
Answer:A
Answer: (A) 105
Question: Express a speed of 90 kmph in meters per second?
(A) 10 mps
(B) 76 mps
(C) 26 mps
(D) 97 mps
(E) 25 mps
Rationale: 90 * 5/18
= 25 mps
Answer:E
Answer: (E) 25 mps
Question: An article is sold at a profit of 14%. If both the cost price and selling price are Rs 132 less, the profit would be 12% more. Find the cost price.
(A) Rs276
(B) Rs268
(C) Rs266
(D) Rs286
(E) Rs296
Rationale: Let cost price was X.
SP = X + 14% of X = 1.14X.
If CP and SP were Rs. 132 less, the profit would be (14 +12)%.
New, CP = ( X - 132)
SP = 1.14X - 132
SP - CP = 26% of (X - 132)
1.14X - 132 - X + 132 = [26*(X -132)]/100
0.14X * 100 = 26X – 3432
14X – 26X = - 3432
12X = 3432
X = 286.
So, CP was Rs 286.
ANSWER : OPTION C
Answer: (C) Rs266
Question: Roy is now 8 years older than Julia and half of that amount older than Kelly. If in 2 years, Roy will be three times as old as Julia, then in 2 years what would be Roy’s age multiplied by Kelly’s age?
(A) 72
(B) 84
(C) 88
(D) 96
(E) 108
Rationale: R = J+8 = K+4
R+2 = 3(J+2)
(J+8)+2 = 3J+6
J = 2
R = 10
K = 6
In 2 years (R+2)(K+2) = 12*8 = 96
The answer is D.
Answer: (D) 96
Question: Complete the sequence:
A D I P ?
(A) M
(B) C
(C) S
(D) D
(E) Y
Rationale: A+3=D
D+5=I
I+7=P
P+9=Y
E
Answer: (E) Y
Question: A couple spent $158.40 in total while dining out and paid this amount using a credit card. The $158.40 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food. What was the actual price of the food before tax and tip?
(A) $115
(B) $120
(C) $125
(D) $130
(E) $135
Rationale: Let the price of the meal be x.
After a 10% sales tax addition, the price is 1.1*x
After a 20% tip on this amount, the total is 1.2*1.1*x = 1.32x
1.32x = 158.40
x = 120
The correct answer is B.
Answer: (B) $120
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed must he travel to reach A at 1 PM?
(A) 8 kmph
(B) 9 kmph
(C) 12 kmph
(D) 14 kmph
(E) 16 kmph
Rationale: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C
Answer: (C) 12 kmph
Question: Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 8 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
(A) 7/15
(B) 11/25
(C) 17/35
(D) 23/45
(E) 27/55
Rationale: Tom paints 1/6 of the room in the first hour.
Tom and Peter paint 1/6+1/3 = 1/2 of the room in the next hour for a total of 4/6.
The three people then paint the remaining 2/6 in a time of (2/6) / (15/24) = 8/15 hours
Peter worked for 23/15 hours so he painted 23/15 * 1/3 = 23/45 of the room.
The answer is D.
Answer: (D) 23/45
Question: If Suresh distributes his pens in the ratio of 1/2 : 1/4 : 1/5 : 1/7 between his four friends A, B, C and D, then find the total number of pens Suresh should have?
(A) 153
(B) 156
(C) 186
(D) 158
(E) 191
Rationale: Here, A : B : C : D = 1 / 2 : 1 / 4 : 1 / 5 : 1 / 7
1) L.C.M of 2, 4, 5, 7 is 140
2) Find the number of pens each friend received --------- (To find no. of pens each friend has, multiply the ratio with the L.C.M. calculated)
A = (1/2) x 140 = 70
B = (1/4) x 140 = 35
C = (1/5) x 140 = 28
D = (1/7) x 140 = 20
3) Total number of pens = (70 x + 35 x + 28 x + 20 x) = 153 x
Minimum number of pens (x) = 1
Therefore, total number of pens = 153 pens.
Correct option :A
Answer: (A) 153
Question: P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 60 days to complete the same work. then Q alone can do it in
(A) 20
(B) 24
(C) 25
(D) 27
(E) 30
Rationale: Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/60
Work done by P, Q and R in 1 day = 1/10 + 1/60 = 7/60
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day Ã— 2 = 7/60
=> Work done by P in 1 day = 7/120
=> Work done by Q and R in 1 day = 7/120
Hence work done by Q in 1 day = 7/120 â€“ 1/60 = 1/24
So Q alone can do the work in 24 days
Answer is B.
Answer: (B) 24
Question: If a shopkeeper gets profit of 2% while selling a pair of shoes at $15. What is the cost price for that pair of shoes ?
(A) $14.60
(B) $14.00
(C) $14.50
(D) $14.40
(E) $14.70
Rationale: Cost Price = ?
Profit % = 2
Selling Price = 15
Cost Price = 100 * Selling Price / (100 + profit %)
= 100 * 15 / (100 + 2)
= 14.70
Answer is E
Answer: (E) $14.70
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 135 grams of water?
(A) 120
(B) 116
(C) 112
(D) 108
(E) 104
Rationale: (16/18)*144 = 120 grams
The answer is A.
Answer: (A) 120
Question: What is 995*995?
(A)  974,169
(B)  974,219
(C)  974,549
(D)  985,019
(E)  990,025
Rationale: if you take a base of 1000 then 995 is 5 less than 1000
to get the product of 995 x 995 write like this
995- 5( as 5 less than base1000)
995- 5
now 5 x 5 = 25
and 995-5 = 990
so 995 x 995 = 990025 ... (bingo the answer is E . you can even have a shortcut ...... 5 x 5 = 25 ... only answer choice has last three digits as 25.. so no need to calculate 995-5 . after you get 5 x 5 you can straight way pick answer choice E.
Answer: (E)  990,025
Question: For the positive integers x, x + 2, x + 4, x + 7, and x + 17, the mean is how much greater than the median?
(A) 0
(B) 1
(C) 2
(D) 4
(E) 7
Rationale: Mean = (x + x+2 + x+4 + x+7 + x+17)/5
=(5x+30)/5
=x+6
Median = x+4
Thus Mean - Median = x+6 - (x+4)
=2
Answer = C
Answer: (C) 2
Question: The compound interest accrued on an amount of Rs.44000 at the end of two years is Rs.1193.60. What would be the simple interest accrued on the same amount at the same rate in the same period?
(A) Rs.10569
(B) Rs.10522
(C) Rs.10,560
(D) Rs.10533
(E) Rs.10584
Rationale: Let the rate of interest be R% p.a.
4400{[1 + R/100]2 - 1} = 11193.60
[1 + R/100]2 = (44000 + 11193.60)/44000
[1 + R/100]2 = 1 + 2544/1000 = 1 + 159/625
[1 + R/100]2 = 784/625 = (28/25)2
1 + R/100 = 28/25
R/100 = 3/25
Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100
=Rs.10560
Answer:C
Answer: (C) Rs.10,560
Question: If the GCD of two numbers (both integers, greater than 1) is 1, then which of the following cannot be true?
A. They are prime.
B. They are consecutive.
C. They have a common prime factor.
D. They do not have a common factor other than 1.
(A) Only A
(B) Only B
(C) Only C
(D) Only B and C
(E) A, B, C, and D
Rationale: The GCD of two numbers (both integers, greater than 1) is 1 means that they don't share factors other than 1. This also means that they cannot be equal.
We can take examples :
A. They can be prime. Example: 5 and 7
B. They can be consecutive. Example: 4 and 5
C. They cannot have a common prime factor. The only common factor is 1, which by definition is not prime.
D. They do not have a common factor other than 1. This is defined in the question.
Therefore, only (C) cannot be true.
Answer: (C) Only C
Question: In how many ways can the letters {U, U, U, R, R} be arranged?
(A) 10
(B) 20
(C) 120
(D) 720
(E) 840
Rationale: There is 5! ways to arrange those letters in total, however letter U repeats 3! times and letter R repeats 2! times
=> the way to arrange without repeating = 5!/ [3!x2!] = 10
answer : A
Answer: (A) 10
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/8%
(B) 33 3/3%
(C) 33 1/3%
(D) 39 1/3%
(E) 33 4/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: The average of first 10 natural numbers is?
(A) 5.6
(B) 5.5
(C) 5.1
(D) 5.8
(E) 5.2
Rationale: Sum of 10 natural no.
= 110/2 = 55
Average = 55/10
= 5.5
Answer:B
Answer: (B) 5.5
Question: The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 40 minutes after it was poured was how many degrees Fahrenheit?
(A) 67.5
(B) 75
(C) 80
(D) 85
(E) 90
Rationale: Answer: B
The temperature of coffee 10 minutes after it was poured (120 F) will help in solving the constant “a”.
120 = 120(2 ^ 10a) + 60
2 ^ -1 = 2 ^ 10a
a = -1/10
The temperature of coffee 40 minutes after it was poured is:
F = 120 ( 2 ^ -40/10) + 60
F = 120 * 1/ 16 + 60
F = 15/2 + 60
F = 135/2=67.5
A
Answer: (A) 67.5
Question: Charlene's annual bonus is calculated in the following manner: Charlene receives 20 percent of her first $11,000 in sales and 30 percent of her sales in excess of $11,000. If Charlene received a bonus of $8,900, what were her annual sales?
(A) $ 20,000
(B) $ 22,000
(C) $ 24,000
(D) $ 26,000
(E) $ 28,000
Rationale: Let x be the total sales in $.
For the 1st 11,000 you get 20% ---> 0.2*11000 = 2200$
For the remaining (x-11000) $, you get 30% ---> 0.3*(x-11000)
Thus, 0.3*(x-11000) + 2200 = 8900 ----> x= 26,000 $
D is thus the correct answer.
Answer: (D) $ 26,000
Question: Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes T, each draining water at the same constant rate, will be needed to drain the pool in 4 days?
(A)  6
(B)  9
(C)  10
(D)  12
(E)  15
Rationale: This is an inverse proportional problem......
5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15
So, T=15-5 = 10.C
Answer: (C)  10
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) 245
(B) 77
(C) 88
(D) 99
(E) 22
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) 88
Question: Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
(A) 229
(B) 270
(C) 877
(D) 266
(E) 281
Rationale: Let xx be the total number of pages in the book, then she finished 23⋅x23⋅x pages.
Then she has x−23⋅x=13⋅xx−23⋅x=13⋅x pages left.
23⋅x−13⋅x=9023⋅x−13⋅x=90
13⋅x=9013⋅x=90
x=270x=270
So the book is 270 pages long.
Answer:B
Answer: (B) 270
Question: By selling 16 pens for a rupee a woman loses 5%. How many for a rupee should he sell in order to gain 18%?
(A) 12
(B) 14
(C) 45
(D) 13
(E) 65
Rationale: D
95% --- 16
118% --- ?
95/118 * 16 = 13
Answer: (D) 13
Question: Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 45 km/hr. For how many minutes does the bus stop per hour?
(A) 15
(B) 88
(C) 77
(D) 20
(E) 99
Rationale: In 1hr, the bus covers 60 km without stoppages and 45 km with stoppages.
Stoppage time = time take to travel (60 - 45) km i.e 15 km at 60 km/hr.
stoppage time = 15/60 hrs = 15 min.
Answer: A
Answer: (A) 15
Question: If two-third of a bucket is filled in one minute then the time taken to fill the bucket completely will be .
(A) 90 seconds
(B) 70 seconds
(C) 60 seconds
(D) 100 seconds
(E) 120 seconds
Rationale: 2/3 filled in 1 mint
1/3 filled in 1/2 mint
thn 2/3+1/3=1 in mint 60 sec+30 sec=90 sec
ANSWER:A
Answer: (A) 90 seconds