mathewhe/aqua_rat huggingface dataset:
Question: The number of positive integers valued pairs (x, y) ssatisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is
(A) fifty nine
(B) 57
(C) 55
(D) 58
(E) 60
Rationale: 4x-17y=1
y=(4x-1)/17
x has to be a positive integer such that 1<=x<=1000(4x-1) is a factor of 17 so that y is also a positive integer
So we need to know how many numbers in the set {3,7,11,15,....,3999} are divisible by 17
Lets try to observe the pattern
1. 3 mod 17 = 3
2. 7 mod 17 = 7
3. 11 mod 17 = 11
4. 15 mod 17 = 15
5. 19 mod 17 = 2
6. 23 mod 17 = 6
7. 27 mod 17 = 10
8. 31 mod 17 = 14
9. 35 mod 17 = 1
10. 39 mod 17 = 5
11. 43 mod 17 = 9
12. 47 mod 17 = 13
13.51 mod 17 = 0
14. 55 mod 17 = 4
15. 59 mod 17 = 8
16. 63 mod 17 = 12
17. 67 mod 17 = 16
... and after this the remainders will repeat (this is no co-incidence that the cyclicity is also 17)
So the right choices are x=13,13+17,13+17+17,.....
The number of such numbers is 59 (highest one being 999) A
Answer: (A) fifty nine
Question: A man spends on an average Rs 269.47 for the first 7 months and Rs 281.05 for the next 5 months. Find his monthly salary if he saves Rs 308.46 during the whole year.
(A) Rs 300
(B) Rs 500
(C) Rs 840
(D) Rs 400
(E) Rs 600
Rationale: Total spending in 12 months = Rs [269.47 x 7 - 281.05 × 5] = Rs 3,291.54
Total income = Spending + Saving
= Rs 3,291.54 + Rs 308.46
= Rs 3,600.00
Monthly salary = Rs 3600/12 = Rs 300
ANSWER:A
Answer: (A) Rs 300
Question: At the library, 50 books were checked out that day from the display. 5 copies of Sandry's Book were checked out and 15 copies of Howl's Moving Castle. If only two other books were checked out (Harry Potter and the Lightning Thief) and they were both checked out in equal quantities, how many copies of the Lightning Thief were checked out?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: First, subtract the number of other books that were checked out from the total: 50-5-15=30. As the remaining two books were checked out in equal quantities, simply divide 30 by 2: 30/2=15. The answer is C, 15.
Answer: (C) 15
Question: During a clearance sale, a retailer discounted the original price of its TVs by 24% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?
(A) 40%
(B) 45%
(C) 55%
(D) 60%
(E) 62%
Rationale: VERITAS PREPOFFICIAL SOLUTION:
D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 75% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 75% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 75% sale price. Using fractions, that means they pay: 4/5*(3/4) of the original price, which nets to 3/5 of the original price, or 62%.
E
Answer: (E) 62%
Question: Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 7 skiers were CPR certified and 17 were not. How many skiers tried out for the ski patrol?
(A) 30
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Not Selected = 80%
If total is x.
Then 0.8x=7+17=24
x=30
Hence answer is A.
Answer: (A) 30
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.4 per sq m?
(A) 675, Rs.1350
(B) 575, Rs.1350
(C) 1350, Rs.675
(D) 675, Rs.2700
(E) 1550, Rs.875
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 4 = Rs.2700
ANSWER:D
Answer: (D) 675, Rs.2700
Question: In 60 litres mixture milk and water are in the ratio 3:1. After adding how many liters of water its ratio will become 3:2
(A) 1
(B) 15
(C) 7
(D) 5
(E) 12
Rationale: Milk quantity = 3/4 * 60 = 45
water quantity = 60-45 = 15
new ratio of M:W = 45:15+x = 3:2
45+3x = 90
x = 15
Answer is B
Answer: (B) 15
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
(A) 33 1/6 %
(B) 33 8/3 %
(C) 33 1/3 %
(D) 73 1/3 %
(E) 33 16/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer: C
Answer: (C) 33 1/3 %
Question: From a group of 4 boys and 4 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected?
(A) 1/2
(B) 2/3
(C) 3/5
(D) 4/7
(E) 5/9
Rationale: The total number of ways to choose 2 children from 8 is 8C2 = 28
The number of ways to choose 1 boy and 1 girl is 4*4 = 16
P(1 boy and 1 girl) = 16/28 = 4/7
The answer is D.
Answer: (D) 4/7
Question: 9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day?
(A) 18
(B) 9
(C) 10
(D) 8
(E) 11
Rationale: We have, M1D1H1 = M2D2H2
So, 9*12*4= 6*D2*8
D2 = 9*12*4/6*8 = 9
ANSWER:B
Answer: (B) 9
Question: Find the cost of fencing around a circular field of diameter 18 m at the rate of Rs.2.50 a meter?
(A) 138
(B) 132
(C) 150
(D) 140
(E) 222
Rationale: 2 * 22/7 * 9 = 56
56 * 2 1/2
= Rs.140
Answer: D
Answer: (D) 140
Question: With out any halt a train travels a certain distance with an average speed of 49 km ph , and with halts it covers the same distance at an average speed of 28 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?
(A) 48 min.
(B) 45min.
(C) 15min.
(D) 18min.
(E) 19min.
Rationale: With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 49/28 = 7/4 = 105 minutes
:. 45 minutes is the halting time per hour
ANSWER:B
Answer: (B) 45min.
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
(A) 3/4
(B) 3/8
(C) 3/1
(D) 3/2
(E) 3/9
Rationale: Explanation:
In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3,4),(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(E) = 27.
P(E) = n(E)/n(S) = 27/36 = 3/4.
Answer: A) 3/4
Answer: (A) 3/4
Question: In traveling from a dormitory to a certain city, a student went 1/2 of the way by foot, 3/5 of the way by bus, and the remaining 4 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
(A) 20
(B) 15
(C) 40
(D) 10
(E) 12
Rationale: Whole trip = distance by foot + distance by bus + distance by car
x = 1/2x + 3/5x + 4
x - 1/2x - 3/5x = 4
x=20km
Option: A
Answer: (A) 20
Question: When positive integer A is divided by positive integer B, the result is 5.15. Which of the following could be the integer A is ?
(A) 107
(B) 117
(C) 103
(D) 123
(E) 171
Rationale: the remainder will be obtained from the decimal part when A is divided by B i.e. 0.15
0.15 = 15/100 = 3/20 so possible remainders are 3,6,12,9,15.
let remainder is 3
Now when we divide option C i.e 103/20 = 5 is quotient and remainder is 3
therefore ans - C
Answer: (C) 103
Question: Three positive integers a, b, and c are such that their average is 80 and a ≤ b ≤ c. If the median is (a + 20), what is the least possible value of c?
(A) 88
(B) 89
(C) 90
(D) 92
(E) 94
Rationale: Solution
Given Data
3 positive integers
Average of a, b, and c = 80
So, a+b+c3a+b+c3 = 240 or a + b + c = 240
a ≤ b ≤ c
Median = (a + 20)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 20
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 20) + (a + 20) = 240 (b and c are equal and b, the median, is a + 20)
Or 3a = 200 or a = 66.66
So, b = c = 66.66+ 20 = 86.66
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 20) + (a + 21) = 240
Or 3a = 199. The value of the numbers is not an integer in this scenario as well.
Let us increment c again by 1. i.e., c = b + 2
Now, a + (a + 20) + (a + 22) = 240
Or 3a = 198 or a = 66
If a = 66, b = 86 and c = 88.
The least value for c that satisfies all these conditions is 88.
Correct answer is choice A.
Answer: (A) 88
Question: A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 8 books for a total of $38.00, and on Tuesday the store sold 20 maps and 12 books for a total of $60.00. At this store, how much less does a map sell for than a book?
(A)  $0.25
(B)  $0.50
(C)  $0.75
(D)  $1.00
(E)  $l.25
Rationale: 12x+8y=38
20x+12y=60
multiply eq 1 by 5 and eq 2 by 3
60x+40y=38*5
60x+36y=60*3
subtracting 1 from 2
4y=190-180
y=2.5
therefore
x=1.5
difference in price =1
D
Answer: (D)  $1.00
Question: David buys an old scooter for Rs. 2400 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 3600, his gain percent is :
(A) 20%
(B) 12%
(C) 10%
(D) 5%
(E) None of these
Rationale: Explanation :
Solution: C.P. =Rs. (2400+600) =Rs. 3000; S.P. = Rs. 3600.
Gain% = (600*100/3000) = 20%.
Answer : A
Answer: (A) 20%
Question: Mr. George paid $8,000 for 100 shares of stock A and $6,000 for 100 shares of stock B. He later sold the same shares of both stocks, gaining 3/8 the amount he paid for stock B. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
(A) A loss 1 1/2 times as much.
(B) A loss 2 times as much
(C) The same.
(D) A gain 1 1/2 times as much.
(E) A gain 1.33 times as much.
Rationale: A = 8000; B = 6000; Profit = (3/8)*6000 = 2250
After prices are reversed:
A = 6000; B =8000; Profit = (3/8)*8000 = 3000
3000 --> Gain of 1.33 times 2250
Answer: E
Answer: (E) A gain 1.33 times as much.
Question: A gold purification process cycle, is able to remove 1/16 of impurities in gold. If we have a 10 grams of gold ore dust containing 16/24 pure gold. How much impurities would have been removed from that old after 4 cycles of purification using that method?
(A) 0.72
(B) 0.74
(C) 0.76
(D) 0.78
(E) 0.82
Rationale: X is the initial quantity of impurities in that gold.
After a cycle of purification the quantity of impurities left would be X1=X-1/16X i.e. X1=15/16X
Same thing for X2, X3, X4, respectively representing the quantity of impurities left after 2, 3, 4 cycles of purification.
So we have:
X1=15/16 X
X2=15/16 X1
X3=15/16 X2
X4=15/16 X3
By multiplying both ends of the equations we get:
X1*X2*X3*X4 = (15/16)^4 X*X1*X2*X3
Simplification leaves us with:
X4 = (15/16)^4 X
X4 is the quantity of impurities left after four cycles. So the cumulative quantity of impurities (Q4) which has been removed after 4 cycles is: Q4= X-X4=X-(15/16)^4X i.e. Q4 = X (1-(15/16)^4)
In this case, given X was: X=(1-16/24) * 10 g = 3.33 g (Remember we had 16/24 pure gold)
So we have Q4 = 3.33 * (1-(15/16)^4) = 3.33 * (1-(50625/65536)) = 3.33 * (14911/65536) = 0.757 rounded gives Q4=0.76
Answer: C
Answer: (C) 0.76
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $200, by what percent is the price to be reduced?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 40%
Rationale: price of a coat in a certain store = $500
the price of the coat is to be reduced by $200
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (200)*100 / 500 = 40%
Answer: Option E
Answer: (E) 40%
Question: One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 150cm when it touches the floor on third time. What is the value of the original height?
(A) 60cm
(B) 90cm
(C) 100cm
(D) 120cm
(E) 130cm
Rationale: when Ball comes down, Then i have indicated the distance covered in green
when Ball goes up, Then i have indicated the distance covered in red
Distance travelled uptil the ball touches the floor 3rd time:h+0.5h+0.5 h+0.5*0.5 h+0.5*0.5 h
h + 2 * 0.5 * h + 2 * 0.25 * h = h (1+2*0.5+2* 0.25) = h (1+1+0.5) = 150
2.5 h = 150
h = 60.
A is the answer.
Answer: (A) 60cm
Question: If the price of gold increases by 25%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
(A) 331/8%
(B) 331/3%
(C) 631/3%
(D) 332/3%
(E) 20%
Rationale: 100
125
------
125-------25
100-------? => 20%
Answer:E
Answer: (E) 20%
Question: Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-9) = 0, then f(x) crosses the y-axis at what y-coordinate?
(A) -9
(B) -1
(C) 0
(D) 1
(E) 9
Rationale: When x = 1 and when x = -9, the expression f(x) = x² + bx + c equals 0.
Then f(x) = (x-1)(x+9)
f(0) = -9
The answer is A.
Answer: (A) -9
Question: In triangle PQR, the angle Q = 90 degree, PQ = 2 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ
(A) 1.6 cm
(B) 2.4 cm
(C) 4.8 cm
(D) 2.16 cm
(E) 3.2 cm
Rationale: Look at the diagram below:
Now, in case when QY is perpendicular to PR, two right triangles PQR and PQY are similar: QY:QP=QR:PR --> QY:2=8:10 --> QY=1.6.
Answer: A.
Answer: (A) 1.6 cm
Question: A boat having a length 5 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
(A) 100 kg
(B) 60 kg
(C) 72 kg
(D) 96 kg
(E) None of these
Rationale: Explanation:
Volume of water displaced = (5 x 2 x 0.01) m3
= 0.10 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.10 x 1000)kg
= 100 kg.
Answer: A
Answer: (A) 100 kg
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $250, by what percent is the price to be reduced?
(A) 10%
(B) 15%
(C) 50%
(D) 25%
(E) 30%
Rationale: price of a coat in a certain store = $500
the price of the coat is to be reduced by $250
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (250)*100 / 500 = 50%
Answer: Option C
Answer: (C) 50%
Question: The triplicate ratio of 1:4 is?
(A) 1:64
(B) 1:8
(C) 1:7
(D) 1:2
(E) 1:1
Rationale: 13: 43 = 1:64
Answer: A
Answer: (A) 1:64
Question: A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations X are possible?
(A) 3
(B) 4
(C) 5
(D) 6
(E) X=8
Rationale: The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6), (48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8.E
Answer: (E) X=8
Question: The respective ages of father and his son are 51 and 16 years. In how many years will the father be twice as old as his son ?
(A) 19 years
(B) 9 years
(C) 10 years
(D) 15 years
(E) 12 years
Rationale: Suppose x years later the father will be twice as old as his son.
x + 51 = 2 (x + 16)
x = 51 - 32 = 19 years
answer : A
Answer: (A) 19 years
Question: What inequality represents the condition 1<x<13?
(A) |x|<3
(B) |x+5|<4
(C) |x-7|<6
(D) |-5+x|<4
(E) |3+x|<5
Rationale: 1<x<13 represents segment with
length: 13-1 = 12
center: (13+1)/2 = 7
For any |x-a|<b a is a center and b is a half of length. So, |x-7|<12/2 represents our inequality (answer C)
Answer: (C) |x-7|<6
Question: It takes one machine 4 hours to complete a production order and another machine 9 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
(A) a) 7/12
(B) b) 2 10/13
(C) c) 1 5/7
(D) d) 3 1/2
(E) e) 7
Rationale: RT = W
Given:
R = 1/9 + 1/4 = 13/36
T = ?
W = 1
T = 1 / (13/36) = 36/13 = 2 10/13
Answer: B
Answer: (B) b) 2 10/13
Question: A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $231 for it, the cost price of the Cricket Bat for A is:
(A) 150
(B) 120
(C) 154
(D) 160
(E) 210
Rationale: 125% of 120% of A = 231
125/100 * 120/100 * A = 231
A = 231 * 2/3 = 154.
ANSWER C
Answer: (C) 154
Question: 1/[(1/0.03) + (1/0.37)] = ?
(A) 0.004
(B) 0.02775
(C) 2.775
(D) 3.6036
(E) 36.036
Rationale: Approximate.
1/.03 = 100/3 = 33
1/.37 = 100/37 = 3
Denominator becomes 33 + 3 = 36
1/36 = .02 something
Answer (B)
Answer: (B) 0.02775
Question: A basket has 5 apples and 7 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked?
(A) 2/7
(B) 4/11
(C) 5/11
(D) 7/22
(E) 15/44
Rationale: The total possible choices are 12C3 = 220
The ways to choose 3 apples: 5C3 = 10
The ways to choose 2 apples: 5C2 * 6C1 = 60
P(at least 2 apples) = 70/220 = 7/22
The answer is D.
Answer: (D) 7/22
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open,in how many hours will the tank be filled ?
(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4
Rationale: 1/5+1/10+1/30=10/30=1/3. soo 3 hrs
ANSWER:C
Answer: (C) 3
Question: A seven-digit phone number is divisible by 5. After adding the two digits of the area code the number is not divisible by 3, which of the following cannot be the area code?
(A) 05.
(B) 06.
(C) 03.
(D) 04.
(E) 02.
Rationale: Given that 7 digit number is divisible by 5
we know any number will not be divisible by 5 if the sum of all digits of the number is not the multiple of5.
Hence looking at the option we can say that the number that should be added to the seven digit number must be 06 as adding it will make it divisible by 5... hence answer is A
Answer: (A) 05.
Question: In how many ways, a committee of 5 members can be selected from
6 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 450
(B) 750
(C) 130
(D) 250
(E) 200
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1]
= 200.
Ans: E
Answer: (E) 200
Question: Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 2 inches tall. How tall are the sculpture andbase together?
(A) 3.1 feet
(B) 3.2 feet
(C) 3.3 feet
(D) 3.0 feet
(E) 3.5 feet
Rationale: we know 1 feet =12 inch then
2 feet =24 inch
24+10=34 then
34+2=36
36/12=3.0 feet
ANSWER:D
Answer: (D) 3.0 feet
Question: When Q is divided by W, the quotient is R and the remainder is r. Which of the following expressions is equal to r?
(A) RW + Q
(B) Q - RW
(C) RW - Q
(D) QW - R
(E) Q/R
Rationale: Q/W = R + r/W
Q -RW = r
Amswer: B
Answer: (B) Q - RW
Question: If a coin is tossed twice what is the probability that it will land either heads both times or tails both times?
(A) 1/8
(B) 1/6
(C) 1/4
(D) 1/2
(E) 1
Rationale: Prob to get 2 heads = 1/2*1/2 = 1/4
Prob to get 2 tails = 1/2*1/2 = 1/4
So, Prob to get either 2 heads or 2 tails = 1/4+1/4 = 1/2
Answer will be D.
Answer: (D) 1/2
Question: What is the least value of x. So that 4x569 is divisible by 3?
(A) 2
(B) 5
(C) 1
(D) 0
(E) 7
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
4 + x +5 + 6 + 9 =24 + x
Least value of x may be 0
Therefore 24+0 = 24 is divisible by 3.
D
Answer: (D) 0
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 20% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
(A) $100
(B) b $115
(C) c $125
(D) d $130
(E) e $135
Rationale: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 2/3*1500 =1000 ,Selling amount for 1000 cabbage = 1000 * 0.5 = $ 500
Remaining were sold at a price equal to 20% less than the price each head sold for on the day before i.e , (80/100)*0.5 = $ 0.4
Hence selling cost for the remaining cabbage = 500 * 0.4 = $ 200
Total selling cost = 500 + 200 = $ 700
Gross profit = $ 700 - $ 600 = $ 100
Hence Answer is A.
Answer: (A) $100
Question: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 42, what is the value of a?
(A) 24
(B) 25
(C) 28
(D) 30
(E) 32
Rationale: Let a=2k, b=3k, and c=4k.
a+b+c = 2k+3k+4k = 9k
Since the average is 42:
9k/3 = 42
3k = 42
k=14
Then a=28.
The answer is C.
Answer: (C) 28
Question: What is the remainder when 9^1 + 9^2 + 9^3 +...+ 9^9 is divided by 3?
(A) 0
(B) 3
(C) 2
(D) 5
(E) None of the above
Rationale: Notice that in the brackets we have the sum of 8 odd multiples of 3, which yields remainder of 0 upon division by 3.
Answer : A
Answer: (A) 0
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 117. What is that number?
(A) 12
(B) 29
(C) 27
(D) 17
(E) 99
Rationale: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 117
6x + 15 = 117
6x = 102
x = 17
ANSWER:D
Answer: (D) 17
Question: What will the value replace by x if 210x0 is divisible by 5?
(A) 4
(B) 3
(C) 2
(D) All the Above
(E) None
Rationale: Divisibility of 5 is Last of the digit is 0 or 5.
In 210x0 has 0.So the Number must divisible by 5.
That is any number can be replaced in the place of x
Answer is D
Answer: (D) All the Above
Question: A certain restaurant offers 7 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
(A) 8
(B) 12
(C) 15
(D) 21
(E) 35
Rationale: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:
A. 2 kinds of cheese and 2 kinds of fruits --> 7C2*2C2=21*1=21
B. 1 kind of cheese and 1 kind of fruit --> 7C1*2C1=7*2=14
A+B=21+14=35
Answer: E.
Answer: (E) 35
Question: A certain rectangular window is four times as long as it is wide. If its perimeter is 50 feet, what are its dimensions in terms of length by width?
(A) 12 by 2
(B) 11 by 3
(C) 20 by 5
(D) 10 by 4
(E) 9 by 3
Rationale: 2x+2y=50
x+y=25
x+4x=25
5x=25
x=5
Answer C
Answer: (C) 20 by 5
Question: A motorcyclist goes from Bombay to Nagpur, a distance of 600 kms at an average of 120 kmph speed. Another man starts from Bombay by car 1 Â½ hours after the first, and reaches Nagpur Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:7
(C) 1:9
(D) 3:5
(E) 1:1
Rationale: T = 600/120 = 5 h
T = 5 - 2 = 3
Time Ratio = 5:3
Speed Ratio = 3:5
Answer: D
Answer: (D) 3:5
Question: Three picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
(A) A)4^30
(B) B)2^30
(C) C)1^30
(D) D)3^30
(E) E)6^30
Rationale: Each Mango can be given to any one of the Three people or in other words..1 mango can be divided into 3 ways...so all 30 can be divided in 3^30 ways
ANS:D
Answer: (D) D)3^30
Question: 45% of 750 - 25% of 480 = ?
(A) 216
(B) 217.5
(C) 236.5
(D) 245
(E) 250
Rationale: Explanation:
Given expression = (45/100 * 750) - (25/100 * 480) = (337.50 - 120) = 217.50
Answer IS B
Answer: (B) 217.5
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 20 minutes, how much time will she spend doing yoga? (rounded to minutes)
(A) 10 min.
(B) 33 min.
(C) 17 min.
(D) 23 min.
(E) 25 min.
Rationale: The ratio is 2:3 = gym:ride, so (20)(3/2) = 30 minutes at the gym, and 30 + 20 = 50 minutes exercise, so (2/3)(50) = 33 minutes yoga.
Answer: B
Answer: (B) 33 min.