mathewhe/aqua_rat huggingface dataset:
Question: A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 3 miles per day and it will take them two days, how many miles long is the route down the mountain?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: On the way down, the rate is 1.5*3 = 4.5 miles per day.
The distance of the route down the mountain is 2*4.5 = 9 miles.
The answer is C.
Answer: (C) 9
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 2.91 m
(B) 3 m
(C) 5.82 m
(D) 4.65 m
(E) None of these
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
Answer: Option B
x = 3.
Answer: (B) 3 m
Question: A man is facing west. He turns 45 degree in the clockwise direction and then another 180 degree in the same direction and then 270 degree in the anticlockwise direction. Find which direction he is facing now ?
(A) south-west
(B) west
(C) south
(D) east-south
(E) east
Rationale: Please refer to the explanation image.
The man firstly faces the direction OA. On moving 45 degree clockwise[Please check carefully always if clockwise or anticlockwise], he faces the direction OB.
Now again he moved 180 degree clockwise, now he will be facing OC. From here he moved 270 degree anticlockwise, Finally he is facing OD, which is South west.
ANSWER A
Answer: (A) south-west
Question: It is required to seat 5 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible?
(A) 2880
(B) 2148
(C) 3680
(D) 3280
(E) 3680
Rationale: Total number of candidates = 5 + 4 = 9. In the row of 9 positions, the even places are 2nd, 4th, 6th and 8th.
Now, number of even places = 4.
Number of girls to occupy the even places = 4.
Even places can be filled = P (4, 4) ways.
Number of boys = 5.
The remaining 5 places can be filled by 5 boys = P (5, 5) ways
By the fundamental principle of counting:
The required number of seating arrangements
P(4, 4) x P(5, 5) = 4! x 5! = 24 x 120 = 2,880
ANSWER:A
Answer: (A) 2880
Question: The polynomial P(x) = x4 + 4x3 + 8x2 + 8x + 4 is the square of another polynomial Q(x) =
ax2 + bx + c with positive coecients a, b, and c. Compute 4a + 2b + c.
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Note that Q(2) = 4a+2b+c and P(2) = [Q(2)]2 = 24+4*23+8 * 22+8* 2+4 = 100.
Since a, b, and c are positive, we have Q(2) > 0. Taking the positive square root, we get
Q(2) =√P(2) =√100 = 10 .
correct answer E
Answer: (E) 10
Question: 96 +97+98+99=390. How many such 4 consecutive numbers are there less than 5000 when added gives a sum which is divisible by 10?
(A) 100
(B) 300
(C) 500
(D) 1000
(E) 1500
Rationale: since 1+2+3+4=10 & 6+7+8+9=30
any combination with these no be will give u desirable result...
so total no in 100 will be 20 & that's why in in 5000,it will be 1000
ANSWER:D
Answer: (D) 1000
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
(A) 1500
(B) 3900
(C) 2600
(D) 3100
(E) 7400
Rationale: Explanation:
Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x =4y or y=5/2x.
15x + 2y = 4000
15x + 2 x	5/2x = 4000
20x = 4000
x = 200.
So, y =5/2x 200= 500.
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
Answer is B
Answer: (B) 3900
Question: Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 14, and 19, what is the value of r?
(A) 20
(B) 21
(C) 26
(D) 27
(E) 33
Rationale: From the triangle inequality rule, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, the three inequalities are:
1. q + 14 > 19
2. 14 + 19 > q
3. q + 19 > 14
Equation 3 is true for any positive value of q.
From equation 1, q > 5
From equation 2, 33 > q
Then 33 > q > 5 so q can be any value from 6 to 32 inclusive.
The number of possible values is 27.
The answer is D.
Answer: (D) 27
Question: If 6 persons can do 6 times of a particular work in 6 days, then, 7 persons can do 7 times of that work in?
(A) 3 days
(B) 4 days
(C) 6 days
(D) 7 days
(E) 8 days
Rationale: That is, 1 person can do one time of the work in 6 days.
Therefore, 7 persons can do 7 times work in the same 6 days itself
C)
Answer: (C) 6 days
Question: A baker filled with a measuring cup with 7/8 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
(A) 1/8 cup
(B) 3/8 cup
(C) 1/4 cup
(D) 1/2 cup
(E) 8/8 cup
Rationale: 3/4 is the original water in cup .half in batter.So left is 3/8 out which 1/8 is spilled out.So again left with 2/8.
so 50% more than what he started was = 7/8+1/2*(3/4)=10/8
Amount of water needed to add = 10/8 - 2/8=8/8
ANSWER:E
Answer: (E) 8/8 cup
Question: . By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 7
(C) 5
(D) 3
(E) 1
Rationale: Explanation:
80% --- 12
120% --- ?
80/120 * 12 = 8
Answer:A
Answer: (A) 8
Question: On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
(A) 18 1/6%
(B) 16 2/3%
(C) 10 2/3%
(D) 29 1/3%
(E) 16 2/3%
Rationale: E
Clearly, the retailer gets 1 dozen out of 6 dozens free.
Equivalent discount = 1/6 * 100 = 16 2/3%.
Answer: (E) 16 2/3%
Question: What is the next number of the following sequence
12, 6, 24, 12, 48, 24, (...)
(A) 66
(B) 72
(C) 84
(D) 96
(E) 102
Rationale: The series is
12/2=6
6*4=24
24/2=12
12*4=48
48/2=24
24*4=96
ANSWER: D
Answer: (D) 96
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 16. What is the value of x?
(A) 20
(B) 40
(C) 80
(D) 160
(E) 320
Rationale: y = 0.5*0.5*x = x/4
y%*x = 16
(y/100)*x = 16
(x/400)*x = 16
x^2 = 16*400
x = 80
The answer is C.
Answer: (C) 80
Question: Insert the missing number
10, -20, 40, -80, 160, (....)
(A) 320
(B) -420
(C) 420
(D) -320
(E) 0
Rationale: 10*-2=-20
-20*-2=40
40*-2=-80
-80*-2=160
160*-2=-320
ANSWER:D
Answer: (D) -320
Question: Each week, Harry is paid X dollars per hour for the first 30 hours and 1.5X dollars for each additional hour worked that week. Each week, James is paid X dollars per hour for the first 40 hours and 2X dollars for each additional hour worked that week. Last week James worked a total of 56 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 58
Rationale: Amount earned by James = 40*x + 16*2x = 72x
Therefore, Amount earned by Harry = 72x
But we know the amount Harry earned assuming working y hours (y>30) is 30*x + (y-30)*1.5x
[[We know y>30 because in 30h the most Harry could earn is 30x, but he has earned 72x]]
So x*(1.5y -45 +30) = 72x
Or x*(1.5y - 15) = 72x
So 1.5y - 15 = 72
So 1.5y = 87
So y = 58
Answer is E
Answer: (E) 58
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 110,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?
(A) 77,500
(B) 1,760,000
(C) 2,480,000
(D) 3,720,000
(E) 4,960,000
Rationale: 110,000 × 2 × 2×2×2 = 110,000 × 16 = B
Answer: (B) 1,760,000
Question: The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 5 per metre approximately
(A) 4457
(B) 4567
(C) 4235
(D) 4547
(E) 7429
Rationale: Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 5) = Rs. 7429.
Answer: Option E
Answer: (E) 7429
Question: There are 3 identical pens and 5 identical books. In how many ways can a person select at least one object from this set?
(A) 23
(B) 25
(C) 31
(D) 15
(E) 45
Rationale: total ways = 6*4=24..
But we are looking for ATLEAST 1, so subtract 1 way when both are 0..
ans 24-1=23..
Answer is A
Answer: (A) 23
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 36 kilometers, Maxwell's walking speed is 2 km/h, and Brad's running speed is 4 km/h. What is the distance traveled by Maxwell when they meet in the middle?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 9
Rationale: Consider Max starts from Point A and Brad Starts from Point B and move towards each other.
Assume they shall meet at point O after Time 'T'. The question asks us to find OA.
From the question stem we can make out :- Distance OA = 50km - Distance OB
=> 2xT = 36 - 4xT (i.e distance =Speed x Time)
=> 6T = 36
Hence T = 6
OA = 2 x 6 = 12 Km
Answer : C
Answer: (C) 12
Question: The output of a factory was increased by 5% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?
(A) 20%
(B) 24%
(C) 30%
(D) 32%
(E) 79%
Rationale: The original output increases by 5% and then 20%.
Total % change = a + b + ab/100
Total % change = 5 + 20 + 5*20/100 = 26%
Now, you want to change it to 0, so,
0 = 26 + x + 26x/100
x = -26(100)/126 = 20% approximately
Answer is A
Answer: (A) 20%
Question: Three grades of milk are 1 percent, 2.7 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2.7 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 2.5 percent grade, what is x in terms of y and z?
(A) y + 3z
(B) (y +z) / 4
(C) 2y + 5z
(D) 3y + z
(E) 3y + 4.5z
Rationale: Based on the given information, the following equation could be dervied: 1% * x + 2.7% * y + 3% * z = 2.5% * (x+y+z) [equation*].
Then use algebra to figure out 1.5%*x = 0.2%*y + 0.5%*z. Thus, 15x = 2y + 5z.
C
Answer: (C) 2y + 5z
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 87 liters
(B) 17 liters
(C) 10 liters
(D) 17 liters
(E) 16 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
Answer: C
Answer: (C) 10 liters
Question: The diagonal of a square is 4 ?2 cm. What will be the diameter of another square if their area is double that of the first square?
(A) 8cm
(B) 9cm
(C) 10cm
(D) 11cm
(E) 12cm
Rationale: d1=4 ? 2 => area = 1/2d12=1/2 * (4 ? 2)2 = 16cm2
Area of new square = (2*16)cm2 = 32 cm2
Therefore 1/2*d22=32 =>d22=64 => d2=8cm
Answer A
Answer: (A) 8cm
Question: A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance Q that he will have a matched pair?
(A) Q=2/5
(B) Q=3/5
(C) Q=1/5
(D) 1/2
(E) 7/5
Rationale: P(both doves) + P(both rabbits) = p(matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5
Hi How did you get the probability 2/4 and 1/4???
You have 3 doves and 2 rabbits i.e. a total of 5 animals.
The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)
The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)
Similarly,
The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)
The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. Also only 4 animals are left to choose from)
Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
Answer: (A) Q=2/5
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
(A) 33
(B) 30
(C) 77
(D) 66
(E) 12
Rationale: Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 6 hours.
His speed = 180/6 = 30 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken = 0.5 hours = 30 minutes.
Answer: B
Answer: (B) 30
Question: Richard,Kenn, Jerk, Dave and Paster line up at a ticket window. In how many ways can they arrange themselves so that Dave is first in line from the window?
(A) a 20
(B) b 12
(C) c 9
(D) d 24
(E) e 3
Rationale: D
Dave's position is fixed. Now we need to arrange all others around Dave.
There are 4x3x2x1= 24 ways to arrange four people.
Answer: (D) d 24
Question: The average expenditure of a labourer for 6 months was 80 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i
(A) 70
(B) 72
(C) 75
(D) 78
(E) 80
Rationale: Income of 6 months = (6 × 80) – debt
= 480 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 750
Average monthly income = 750 ÷ 10 = 75
Answer C
Answer: (C) 75
Question: Last year, for every 100 million vehicles that travelled on a certain highway, 98 vehicles were involved in accidents. If 3 billion vehicles travelled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
(A) 288
(B) 320
(C) 2,940
(D) 3,200
(E) 28,800
Rationale: To solve we will set up a proportion. We know that “100 million vehicles is to 98 accidents as 3 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 3,000 million rather than 3 billion. Creating a proportion we have:
100/98 = 3,000/x
Cross multiplying gives us:
100x = 3,000 * 98
x = 30 * 98 = 2,940
Correct answer is C.
Answer: (C) 2,940
Question: find the next number in the sequence
12, 20, 40, 72, 116, 172 ?
(A) 500
(B) 250
(C) 240
(D) 350
(E) 400
Rationale: C
240
40 { diff 20 + 12 =>32 add to it}
72 { diff 32 + 12 =>44 add to it}
116 { diff 44 + 12 =>56 add to it}
172 { diff 56 + 12 =>68 add to it}
240
Answer: (C) 240
Question: In how many different ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?
(A) 70
(B) 288
(C) 576
(D) 10,080
(E) 20,160
Rationale: Glue the ladies together so that they create one unit, so we would have 5 units: {M1}, {M2}, {M3}, {M4}, and {W1,W2,W3,W4} --> # of different arrangements of nn objects around the table (circular arrangements) is (n−1)!(n−1)!, so our 5 objects can be arranged in (5−1)!=4!(5−1)!=4! ways.
On the other hand 4 women within their unit also can be arranged in 4! ways --> total 4!∗4!=5764!∗4!=576.
Answer: C.
Answer: (C) 576
Question: On dividing 100 by a number, the quotient is 9 and the remainder is 1. Find the divisor?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: d = (D-R)/Q
= (100 - 1)/9
= 99/9 = 11
B)
Answer: (B) 11
Question: A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?
(A) 40
(B) 45
(C) 49
(D) 51
(E) 43
Rationale: A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=175×(9/35)=5×9=45
Answer is B.
Answer: (B) 45
Question: The cricket team of 11members is 26yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?
(A) 21
(B) 22
(C) 23
(D) 25
(E) 28
Rationale: Let the average age of the whole team be x years.
11x - (26 + 29) = 9 (x - 1)
=> 11x - 9x = 46
=> 2x = 46
=> x = 23.
So, average age of the team is 23 years.
C
Answer: (C) 23
Question: A man purchased a carriage and horse in Rs. 1500. By selling the horse at 10% loss and carriage at 20% profit he earned a profit of 8% on the whole transaction.
(A) 900
(B) 376
(C) 197
(D) 167
(E) 191
Rationale: ANSWER: A
Answer: (A) 900
Question: pooja travels from A to B a distance of 800 miles in 10 hours. He returns to A in 5 hours. Find his average speed?
(A) 123.07mph
(B) 100mph
(C) 150.07mph
(D) 200mph
(E) 300mph
Rationale: Speed from A to B = 800/8 = 100 mph
Speed from B to A = 800/5 = 160 mph
Average speed = 2*100*160 / 260 = 123.07mph
Answer is A
Answer: (A) 123.07mph
Question: The speed of a car is 20 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 79 kmph
(B) 40 kmph
(C) 34 kmph
(D) 23 kmph
(E) 14 kmph
Rationale: S = (20 + 60)/2
= 40 kmph
Answer:B
Answer: (B) 40 kmph
Question: A sum of money at simple interest amounts to Rs. 2240 in 2 years and to Rs. 2600 in 5 years. The sum is:
(A) Rs. 1500
(B) Rs. 2000
(C) Rs. 1000
(D) Rs. 1200
(E) Rs. 1800
Rationale: S.I. for 3 years = Rs. (2600 - 2240) = Rs. 360.
S.I. for 1 year = Rs. 360/3 = Rs. 120.
S.I. for 2 years = Rs. (120 x 2) = Rs.240.
Principal = Rs. (2240 - 240) = Rs. 2000.
Answer: Option B
Answer: (B) Rs. 2000
Question: If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 500. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 512.50. What is the value of X?
(A) 8000
(B) 6000
(C) 5000
(D) 4000
(E) 3000
Rationale: Simple way to solve this question is to use options.
From SI, we know that X*y=25,000.
Now, put the value of X = 5000, we will have y = 5%
To calculate CI,
Now, we know 1st year Amount= 5000+5% of 5000= 5250.
2nd year, Amount = 5250 + 5% of 5250 = 5512.50.
We can see after 2 years Interest = 5512.50-5000= 512.50 hence, it satisfies the question. Hence C is the correct answer
Answer: (C) 5000
Question: The ratio of flour to water to sugar in a recipe is 11:8:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 4 cups of water, how much sugar is required?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: The ratio of flour to water is 22:8=11:4.
The ratio of flour to sugar is 5.5:1=11:2.
The new ratio of flour to water to sugar is 11:4:2
If we need 4 cups of water, then we need 2 cups of sugar.
The answer is D.
Answer: (D) 2
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
(A) 42
(B) 57
(C) 27
(D) 29
(E) None of these
Rationale: The total of seven numbers = 7 Ã— 18 = 126
The total of first 3 and last 3 numbers is = 3 Ã— 14+3 Ã— 19 = 99
So, the middle number is (126 - 99 ) = 27
ANSWER IS C
Answer: (C) 27
Question: A group consists of 4 men, 6 women and 6 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
(A) 400
(B) 720
(C) 287
(D) 278
(E) 281
Rationale: Explanation:
Two men, three women and one child can be selected in â´Câ‚‚ * â¶Câ‚ƒ * âµCâ‚ ways
= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 6
= 720 ways.
Answer:B
Answer: (B) 720
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
(A) 1
(B) 5
(C) 6
(D) 7
(E) 3
Rationale: Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/3
3 --------- ? è 1 hour
Answer: A
Answer: (A) 1
Question: Without stoppages a train travels a certain distance with an average speed of 160 kmph and with stoppages it covers the same distance with an average speed of 80 kmph. What is the time in minutes per hour for which train stops?
(A) 10 min/hr
(B) 25 min/hr
(C) 27 min/hr
(D) 30 min/hr
(E) 33 min/hr
Rationale: Pick a smart number for the distance. lets say LCM 160
Without = 160/160 = 1 hours
With = 160/80= 2 hours
So in a trip of 2 hours, 1 hour is spent in stoppages
Hence, 60/2 = 30 min/hr on stoppages
Answer : D
Answer: (D) 30 min/hr
Question: A train 700 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 510
(B) 540
(C) 500
(D) 520
(E) 600
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (700 + x)/60 = 65/3
x = 600 m.
Answer: Option E
Answer: (E) 600
Question: In covering a distance of 48 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
(A) 5 kmph
(B) 6 kmph
(C) 6.25 kmph
(D) 7.5 kmph
(E) 8 kmph
Rationale: Let Abhay's speed be x km/hr.
Then,	48/X	-	48/2X	= 3
6x = 48
x = 8 km/hr. Answer: Option E
Answer: (E) 8 kmph
Question: Positive integers from 1 to 45, inclusive are placed in 5 groups of 9 each. What is the highest possible average of the medians of these 5 groups?
(A) 25
(B) 31
(C) 15
(D) 26
(E) 23
Rationale: Answer
We need to maximize the median in each group in order to maximize the average of all the medians.
The highest possible median is 41 as there should be 4 numbers higher than the median in a group of 9.
So, if we have a group that has a, b, c, d, 41, 42, 43, 44, 45, the median will be 41.
In this set, it is essential not to expend any more high values on a, b, c, or d as these do not affect the median.
The median of a group that comprises 1, 2, 3, 4, 41, 42, 43, 44, 45 will be 41.
The next group can be 5, 6, 7, 8, 36, 37, 38, 39, 40. The median will be 36.
Extrapolating the findings in the two sets listed above, to maximize medians in all the 5 groups, the medians of the 5 groups will have to be 21, 26, 31, 36 and 41.
The average of the highest possible medians will be the average of these 5 numbers = 31.
Answer B
Answer: (B) 31
Question: If cement, gravel and sand are to be mixed in 7:10:13 and 6 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.
(A) 35 7/8
(B) 40
(C) 34 2/7
(D) 25 5/7
(E) 34 6/7
Rationale: Cement:Gravel:Sand = 6:10:13 --> total of 6+10+13 = 30 parts.
If we use 8 tons of cement, then we'll get 6/7*30 = 25 5/7 tons of mixture.
Answer: D.
Answer: (D) 25 5/7
Question: If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true?
I. ab is even
II. ab > 0
III. c is even
(A) l only
(B) ll only
(C) l and ll
(D) l and lll
(E) l,ll,and lll
Rationale: Given: a, b, and c are integers and ab^2/c is a positive even integer.
Evaluate each option:
I. ab is even.
ab^2/c to be positive even integer ab^2 must be even, from which it follows that either a or b must be even, thus ab has to be even.
II. ab > 0
Since b is squared in our expression, then we can say nothing about its sign, thus we cannot say whether ab is positive.
III. c is even
The easiest one: ab^2/c = integer/c = even --> c could be even as well as odd.
Answer: A.
Answer: (A) l only
Question: ((-1.9)(0.6) – (2.6)(1.2))/4.0 = ?
(A) 1.07
(B) 1.0
(C) -1.065
(D) 1.71
(E) 2.71
Rationale: Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option.
-1.065
Answer C
Answer: (C) -1.065