mathewhe/aqua_rat huggingface dataset:
Question: If the simple interest on a sum of a money for 1 years at 4% per annum is rs 70 what is the compound interest on the sum of the same rate and same time
(A) $856.38
(B) $752.36
(C) $523.98
(D) $1822.8
(E) $523.65
Rationale: sum= 70*100/1*4=1750
amount=$(1750(1+4/100)^2)
=1700*26/25*26/25
=$1892.8
C.I=Rs.(1892.8-70)=$.1822.8
Answer (D)
Answer: (D) $1822.8
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
(A) 7500
(B) 3388
(C) 2665
(D) 2888
(E) 2661
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
Answer: A
Answer: (A) 7500
Question: In how many ways the word "CALORIES" can be arranged?
(A) 40322
(B) 40320
(C) 45340
(D) None
(E) Cannot be determined
Rationale: Explanation :
The required number of ways = 8!
= 40320
Answer : B
Answer: (B) 40320
Question: (0.15)(power 3) - (0.1)(power 3)/ (0.15)(power 2) + 0.015 + (0.1)(power 2) is:
(A) 0.68
(B) 0.08
(C) 0.05
(D) 0.06
(E) None of them
Rationale: Given expression
= (0.15) (power 3) - (0.1)(power 3) / (0.15)(power 2) + (0.15 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.15 - 0.1)
= 0.05
Answer is C.
Answer: (C) 0.05
Question: In a certain pond, 55 fish were caught, tagged, and returned to the pond. A few days later, 55 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
(A) 400
(B) 625
(C) 1250
(D) 1528
(E) 10 000
Rationale: The percent of tagged fish in the second catch is 2/55*100 = 3.64%.
We are told that 3.64% approximates the percent of tagged fish in the pond. Since there are 55 tagged fish, then we have 0.036x = 55 --> x = 1,528.
Answer: D.
Answer: (D) 1528
Question: A businessman earns $27800 in December, thus decreasing his average annual (January to December) earnings by $1200. His average annual earnings would be
(A) $29000
(B) $33500
(C) $40200
(D) $41000
(E) $42300
Rationale: (x - 27,800)/11 - x/12 = 1,200
x = 492,000
x/12 = 41,000
Answer: D.
Answer: (D) $41000
Question: How many kg of pure salt must be added to 30kg of 2% solution of salt and water to increase it to 10% solution ?
(A) 3/5
(B) 4/3
(C) 5/7
(D) 2/3
(E) 8/3
Rationale: Amount of salt in 30kg solution = [(20/100)*30]kg=0.6kg
Let x kg of pure salt be added
Then , (0.6+x)/(30+x)=10/100
60+100x=300+10x
90x=240
x=8/3.
Answer is E.
Answer: (E) 8/3
Question: A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 15 cm by 13 cm. The total number of bricks required is :
(A) 16000
(B) 18078
(C) 11076
(D) 11456
(E) None of these
Rationale: Explanation:
Number of bricks =Courtyard area /1 brick area
=(1800Ã—1200 /15Ã—13)=11076
Option C
Answer: (C) 11076
Question: Which one of the following numbers is exactly divisible by 11?
(A) 417269
(B) 315624
(C) 615624
(D) 715624
(E) 415624
Rationale: E
415624 is exactly divisible by 11.
Answer: (E) 415624
Question: If a person walks at 25 km/hr instead of 10 km/hr, he would have walked 31 km more. The actual distance traveled by him is?
(A) 30
(B) 25
(C) 20.67
(D) 12.33
(E) 19.48
Rationale: Let the actual distance traveled is 'x' km
Then by given conditions, we have
x/10 = (x+31)/25
25x = 10x + 310
x = 20.67 km
Ans- C
Answer: (C) 20.67
Question: X, Y and Z invested Rs.3600, Rs.4800 and Rs.5400 respectively, in a partnership business. Find the share of X in profit of Rs.23000 after a year?
(A) 6300
(B) 6200
(C) 6100
(D) 6400
(E) 6000
Rationale: Explanation:
3600:4800:5400
6:8:9
6/23 * 23000 = 6000
E)
Answer: (E) 6000
Question: A buffet consists of 5 main dishes and 4 side dishes. If a plate is created with 2 main dishes and 2 side dishes, in how many ways can the plates be formed?
(A) 36
(B) 60
(C) 66
(D) 180
(E) 575
Rationale: Choose 2 main dishes from 5 main dishes and 2 side dishes from 3 side dishes:
2C5 * 2C4 = 10*6 = 60
Ans: B
Answer: (B) 60
Question: 46080, 3840, 384, 48, 8, 2, ?
(A) 0.5
(B) 1
(C) 1.5
(D) 2
(E) 2.5
Rationale: 46080 ÷ 12 = 3840
3840 ÷ 10 = 384
384 ÷ 8 = 48
48 ÷ 6 = 8
8 ÷ 4 = 2
2 ÷ 2 = 1
Answer is B.
Answer: (B) 1
Question: A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $7.00. If the company’s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order?
(A) $960
(B) $1,350
(C) $1,725
(D) $2,100
(E) $2,250
Rationale: Total Volume is 288000
Given LBH = 8*10*12.
the number of hats inside it = 288000/10 * 8 * 12 = 300.
price of each hat is 7.5 $ then total value is 300 * 7.0 = 2100.
IMO option D is correct answer..
Answer: (D) $2,100
Question: The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 12348 pi cubic centimeters, what is hte surface area of the balloon in square centimeters?
(A) a. 40
(B) b. 100
(C) c. 400
(D) d. 1,000
(E) e. 5,000
Rationale: The surface area is 4.pi.r^2 (its area remember not volume)
as 4/3.pi.r^3=12348pi
r=21
so area = 4.pi.r^2= 1764.pi= 1764 x 3.14 = 5000 (approx)
E
Answer: (E) e. 5,000
Question: What is the range of all the roots of |x^2 - 6| = x ?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 5
Rationale: we get 2 quadratic equations here ..
1) x^2-x-2=0 ....... roots 2 , -1
2) x^2+x-2=0 ........ roots -2, 1
Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations .
So value of x for given equation .... x=6 or x=1
I guess range is 6-1 =5
E
Answer: (E) 5
Question: Kailash loses 20% of his pocket money. After spending 25% of the remainder he has Rs 480 left. What was his pocket money?
(A) Rs 600
(B) Rs 800
(C) Rs 900
(D) Rs 1000
(E) none of these
Rationale: Let A be the pocket money,
A ( 1 + x/100) ( 1 + y/100) = 480 (Given)
Here x = - 20, y = - 25
Therefore,
A( 1 - 20/100) ( 1 - 25/100) = 480
A = (480 x 100 x 100) / (80 x 75) = Rs 800
ANSWER:B
Answer: (B) Rs 800
Question: Two persons starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
(A) 17 hrs
(B) 22 hrs
(C) 25 hrs
(D) 12 hrs
(E) 14 hrs
Rationale: The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs
Answer : A.
Answer: (A) 17 hrs
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 324 metres
(D) 228 metres
(E) 150 metres
Rationale: Speed= 60 x	5/18	m/sec	= 50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3	x 9	m = 150 m.
Option E
Answer: (E) 150 metres
Question: The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 8th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?
(A) 45
(B) 40
(C) 35
(D) 30
(E) 25
Rationale: 1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))
2ndyear : 1-2 (age), we take age = 1
3rd year : 2-3 (age), we take age = 2
4th year : 3-4 (age), we take age = 3
5th year : 4-5 (age), we take age = 4
6th year : 5-6 (age), we take age = 5
7th year : 6-7 (age), we take age = 6
8th year : 7-8 (age), we take age = 7
Thus for the 3rd year = 50,
4th year = 50 -3 = 47
5th year = 47-4 = 43
6th year = 43-5 = 38.
7th year =38-6 = 32
8th year =32-7 = 25
The correct answer is E.
Answer: (E) 25
Question: In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?
(A) 1/5
(B) 1/25
(C) 2/5
(D) 3/5
(E) Data inadequate
Rationale: Explanation:
A = 2B => B = 1/2 A, so, AB = 2/25
1/2 A2 = 2/25
A2 = 4/25
A = 2/5
ANSWER IS C
Answer: (C) 2/5
Question: The measures of the 2 acute angles of a triangle are in the ratio of 3 : 6. What arethe measures of the 2 angles?
(A) 20°
(B) 70°
(C) 60°
(D) 120°
(E) 140°
Rationale: If the ratio of the two angles is 3:6, then the measures of two angles can be written as 3x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence
3x + 6x = 90
9x = 90
x = 10
Measures of the two acute angles are
3x = 3 × 10 = 30°
6x = 6 × 10 = 60°
C
Answer: (C) 60°
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 37
(B) 27
(C) 44
(D) 26
(E) 27
Rationale: Explanation:
g% = 20 + 20 + (20*20)/100
= 44%
Answer: C
Answer: (C) 44
Question: 49 Ã— 49 Ã— 49 Ã— 49 x 49 Ã— 49 Ã— 49 Ã— 49= 7?
(A) 4
(B) 7
(C) 8
(D) 16
(E) None of these
Rationale: 49 Ã— 49 Ã— 49 Ã— 49 x 49 Ã— 49 Ã— 49 Ã— 49 = 7?
or, 7(2) Ã— 7(2) Ã— 7(2) Ã— 7(2) x 7(2) Ã— 7(2) Ã— 7(2) Ã— 7(2)= 7^?
or 7(16) = 7? or, ? =16
Answer D
Answer: (D) 16
Question: 5/9= 25/45 . which method did you use to determine whether this proportion is true or false?
(A) true
(B) neutral
(C) false
(D) not sure
(E) none
Rationale: 5/9= 25/45. cross multiplication: 5 * 45= 225, 25 * 9 = 225,
we see that 225 are not equal to 225. so there is proportion. corrcet answer: (A)
Answer: (A) true
Question: The sum of the number of boys and girls in a school is 150. if the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is ?
(A) 60
(B) 38
(C) 26
(D) 29
(E) 11
Rationale: Explanation:
We have : x + x% of 150 = 150
Answer: A) 60
Answer: (A) 60
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 86.49, the number of the member is the group is:
(A) 93
(B) 67
(C) 77
(D) 87
(E) 97
Rationale: Money collected =(86.49 x 100) paise = 8649 paise
numbers of members = 8649 squareroot = 93
Answer A
Answer: (A) 93
Question: 2. Abhishek started a business investing 50,000. After one year he invested another 30,000 and Sudin also joined him with a capital of 70,000. If the profit earned in three years from the starting of business was 87,500, then find the share of Sudin in the profit
(A) 37,500
(B) 32,500
(C) 38,281
(D) 52,500
(E) None of these
Rationale: Ratio of Abhishek and Sudin for one month
= (50,000 × 36) + (30,000 × 24) : (70,000 × 24)
= (18,00,000 + 7,20,000) : 16,80,000 = 3 : 2
Hence share of Sudin in the profit earned from the business.
= 87,500/(3+2)×2 = 35,000
Answer E
Answer: (E) None of these
Question: Which of the following is two more than the square of an odd integer?
(A) 14,173
(B) 14,361
(C) 14,643
(D) 14,737
(E) 14,981
Rationale: one of the given options should be a square if 2 is subtracted from it.
the options would be
(A) 14,171
(B) 14,359
(C) 14,641
(D) 14,735
(E) 14,979
We can solve this question with many approaches. Here are the 2 easiest methods.
Method 1:-
If a square has odd unit's digit, then it's ten's digit will always be even.
Only 14,641 satisfies this condition.
Method 2:-
If you know about palindromic numbers,
then you can clearly see that 14,641 is a palindromic square.
Answer:- C
Answer: (C) 14,643
Question: E and F have a data plan which gives them 200 GB every month. If E uses 7 GB every 9 days and F uses 5 GB every 4 days, how many GB will be unused after a 30 day month? Answer in fractions.
(A) 365/6
(B) 73/6
(C) 35/6
(D) 835/6
(E) 200/6
Rationale: Number of GB that E uses every day: 7/9
Number of GB that F uses every day: 5/4
Number of GB that E and F use every day: 7/9+5/4=73/36
Number of GB that E and F use in 30 days: 30x(73/36)=365/6
Number of GB remaining: 200-365/6=835/6
Answer is D
Answer: (D) 835/6
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 12 minutes earlier. How far is the office from his house?
(A) 4 1/5 Km
(B) 4 1/7 Km
(C) 3 1/5 Km
(D) 3 1/7 Km
(E) 4 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 20/6
= 24/2 * 20/60
= 10 * 2/5
= 20/5 = 4 Km
E)
Answer: (E) 4 Km
Question: If the average (arithmetic mean) of x and y is 80, and z – x = 100, what is the average of y and z?
(A) 140
(B) 100
(C) 110
(D) 120
(E) 130
Rationale: x+y/2 = 80
=> x+y = 160
x = z - 100...sub this value
z-100+y = 160
=>z+y = 260
=>z+y/2 = 130
Answer : E
Answer: (E) 130
Question: John has taken four (4) tests that have an average of 83. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?
(A) 87
(B) 90
(C) 92
(D) 95
(E) 97
Rationale: Traditional Method:
Total scored till now 83*4=332
Total score to avg 87 in 6 tests = 87*6=522
Total to be scored on 2 tests = 522-332=190
Avg on 2 tests = 190/2 = 95
Answer: D
Answer: (D) 95
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 60 white marbles. How many red marbles could be in bag A?
(A) 1
(B) 3
(C) 4
(D) 12
(E) 8
Rationale: 6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:4
Let W in bag B be 4k
W = 60 = 6K+4k
=> k =6
Total Red's in bag A will be 2K = 12
D
Answer: (D) 12
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
(A) 5.2%
(B) 5.4%
(C) 5.6%
(D) 6%
(E) 6.5%
Rationale: Cost Price of 1 toy = Rs. 375 = Rs. 31.25
12
Selling Price of 1 toy = Rs. 33
So, Gain = Rs. (33 - 31.25) = Rs. 1.75
Profit % = 1.75	x 100	%	=	28	% = 5.6%
C)
Answer: (C) 5.6%
Question: Sachi invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Sachi will get on the maturity of the fixed deposit.
(A) 8000
(B) 8500
(C) 8820
(D) 8870
(E) 8900
Rationale: CI = (800*(1+5/100)^2
==> 8820
ANSWER C
Answer: (C) 8820
Question: At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 15 males did not bring gifts to the party, how many females did bring gifts?
(A) 18
(B) 28
(C) 50
(D) 68
(E) 70
Rationale: the correct method
total = 300..
70% of 300 = 210 got gifts..
90 did not get gift, out of which 15 are males, so remaining 90-15=75 are females..
But 40% females brought gift, so 60% did not get it..
so 60% = 75, 100%= 75*100/60=125..
ans 40% of 125 =50
C
Answer: (C) 50
Question: If a is the sum of b and c, then which one of the following must equal b – c?
(A) a+2c
(B) a+c
(C) a-c
(D) a-2c
(E) a+2c
Rationale: Given a= b+c if you subtracts both side with -2c
a-2c = b-c
Answer : D
Answer: (D) a-2c
Question: Husband has prepared for a candle light dinner on the honeymoon for his wife. While they were having the dinner, a strong breeze flew through the open window and four candles out of ten were extinguished. After that, the husband closed the window.
How many candles were left in the end?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Solution:
Four
As the window was closed it is obvious that the six candles that were not extinguished were lit till they melted away entirely. Thus only four candles that were extinguished remain at the end.
Answer C
Answer: (C) 4
Question: Mr. Jones is the Chairman of a committee. In how many ways can a committee of 5 be chosen from 10 people given that Mr. Jones must be one of them?
(A) 126
(B) 252
(C) 459
(D) 3024
(E) 4126
Rationale: Total Ways of choosing the committee = Total Ways of choosing 4 out of 9 candidates leaving Mr.Jones as one of the selected candidate in advance
Total Ways of choosing 4 out of 9 candidates = 9C4 = 9!/(5!*4!) = 126
Answer: option A
Answer: (A) 126
Question: There are cats got together and decided to kill the mice of 999975. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?
(A) 941,1009
(B) 991,1001
(C) 995,1005
(D) 791,1009
(E) 931,1009
Rationale: 999975 can be written as 1000000 â€“ 25
= 10002 â€“ 52 ie of the form a2-b2=(a+b)(a-b)
=(1000+5)*(1000-5)
= (1005)*(995)
Given that number of cats is less than number if mice.
So number of cats is 995 and number of mice were 1005
Answer C
Answer: (C) 995,1005
Question: The average of six numbers is 3.95. The average of two of them is 3.2, while the average of the other two is 3.85. What is the average of the remaining two numbers?
(A) 4.5
(B) 4.6
(C) 4.7
(D) 4.8
(E) 4.9
Rationale: Sum of the remaining two numbers
= (3.95 × 6) – [(3.2 × 2) + (3.85 × 2)]
= 23.70 – (6.4 + 7.7)
= 23.70 – 14.1 = 9.60
∴ Required average = (9.6⁄2) = 4.8
Answer D
Answer: (D) 4.8
Question: How many shots of 1cm radius can be prepared from a sphere of 3cm radius?
(A) 33
(B) 77
(C) 27
(D) 88
(E) 121
Rationale: 4/3 π * 3 * 3 * 3 = 4/3 π * 1 * 1 * 1 * x
x = 27
Answer: C
Answer: (C) 27
Question: A club wants to mix 30 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Let number of pounds of 5$ candy to be used be w
6 = (30*8 + 5*w)/(30 +w)
=>180 + 6w = 240 + 5w
=> w = 60
Answer D
Answer: (D) 60
Question: How many even multiples of 25 are there between 249 and 501?
(A) 5
(B) 6
(C) 9
(D) 10
(E) 11
Rationale: 250 = 10*25
500 = 20*25
The even multiples are 25 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B.
Answer: (B) 6
Question: How many two letter words are formed using the letters of the word RAM?
(A) 8
(B) 1
(C) 6
(D) 4
(E) 9
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 3P2
= 3 * 2 = 6.
Answer: C
Answer: (C) 6
Question: Jim is able to sell a hand-carved statue for $550 which was a 35% profit over his cost. How much did the statue originally cost him?
(A) $407.41
(B) $412.40
(C) $455.40
(D) $474.90
(E) $488.20
Rationale: 550 = 1.35*X
X = 550/1.35 = 407.407407...
which rounds to $407.41, which is (A).
Answer: (A) $407.41
Question: Can you deduce the pattern and find the next number in the series?
2,6, 12, 20, 30, __?
(A) 41
(B) 45
(C) 56
(D) 49
(E) 42
Rationale: Solution:
42
Explanation:
2=1*1+1
6=2*2+2
12=3*3+3
20=4*4+4
30=5*5+5
Thus the next number will be
6*6+6=42
Answer E
Answer: (E) 42
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 37
(B) 240
(C) 288
(D) 267
(E) 211
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: B
Answer: (B) 240
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak’s share is :
(A) Rs. 5400
(B) Rs.7200
(C) Rs. 8400
(D) Rs. 9600
(E) Rs. 8600
Rationale: Ratio of their shares = 22500 : 35000 = 9 : 14.
Deepak’s share = Rs. 13800 * 14/23
= Rs. 8400
ANSWER:C
Answer: (C) Rs. 8400
Question: A man walking at a rate of 10km/hr crosses a bridge in 3 minutes. The length of the bridge is?
(A) 500
(B) 650
(C) 250
(D) 111
(E) 236
Rationale: Speed = 10*5/18 = 50/18 m/sec
Distance covered in 5 minutes = 50/18 * 5 *60 = 500 m
Answer is A
Answer: (A) 500
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $6.00 per hour and a standard tip rate of 35% of the cost of the orders she serves. If she worked four 10-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
(A) 280
(B) 300
(C) 320
(D) 350
(E) 1120
Rationale: Jill earns 6 dollars/hour and the hourly tip is (7/20)*40.
Jill thus earns 6*10+10*14 per day(or 6(10)+14(10)=20(14)=280).
Jill has worked for 4 days ->280*4=1120.
This matches answer choice E.
Answer: (E) 1120
Question: A BAG CONTAINS 6 WHITE AND 4 BLACK BALLS .2 BALLS ARE DRAWN AT RANDOM. FIND THE PROBABILITY THAT THEY ARE OF SAME COLOUR.
(A) 7/15
(B) 4/8
(C) 15/7
(D) 6/7
(E) 9/5
Rationale: LET S BE THE SAMPLE SPACE
THEN N(S)=NO OF WAYS OF DRAWING 2 BALLS OUT OF (6+4)=10C2=(10*9)/(2*1)=45
LET E=EVENT OF GETTING BOTH BALLS OF SAME COLOUR
THEN N(E)=NO OF WAYS(2 BALLS OUT OF SIX) OR(2 BALLS OUT OF 4)
=(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=N(E)/N(S)=21/45=7/15
Ans: A
Answer: (A) 7/15
Question: A team bought a total of 355 balls. If each player on the team bought at least 16 balls, then what is the greatest possible number of players on the team?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: 355/16=22 plus remainder.
The answer is B.
Answer: (B) 22
Question: A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 10 days respectively. They worked together for five days and then C completed the remaining work all alone. If $720 was the net sum to be paid for the entire work, what was the average daily wage of B?
(A) $144
(B) $90
(C) $72
(D) $54
(E) $48
Rationale: The correct answer is C.
Answer: (C) $72
Question: John takes 18 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?
(A) 2 hours, 10 minutes
(B) 2 hours, 30 minutes
(C) 3 hours, 10 minutes
(D) 3 hours, 45 minutes
(E) 4 hours, 10 minutes
Rationale: The rate of John plus Bill is 1/18 + 1/6 = 4/18 of the job completed per hour.
If Steve worked at the same rate as John, the rate would be 4/18 + 1/18 = 5/18
The slowest possible time would be 18/5 hours = 3 hours, 36 minutes.
If Steve worked at the same rate as Bill, the rate would be 4/18 + 1/6 = 7/18
The fastest possible time would be 18/7 hours = 2 hours + 4/7 hours.
The actual time is somewhere between these two extreme points.
The answer is C.
Answer: (C) 3 hours, 10 minutes
Question: If the speed of Y meters per minute is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
(A) 15y/18
(B) 6y/5
(C) 18y/5
(D) 6y/100
(E) 3600000y
Rationale: If the speed of Y meters per second is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
We need to find an equation with y in the answer...
convert all measurements so they are alike (i.e. convert km to m, minutes to hours, etc)
Speed = y/t
y meters/second
(60) x meters/hour
Speed = x/t
x KM/hour
Speed = x(1000m)/hour
x(1000meters)/hour = (60) x meters/hour
x(1000)/1hour = y(60) / 1 hour
x(1000) = y(60)
x = 0.06y
Answer: D. 6y/100
Answer: (D) 6y/100
Question: An item is being sold for $10 each. However, if a customer will “buy at least 3” they have a promo discount of 17%. Also, if a customer will “buy at least 10” items they will deduct an additional 8% to their “buy at least 3” promo price. If Sam buys 10 pcs of that item how much should he pay?
(A) $92.00
(B) $88.00
(C) $87.04
(D) $80.96
(E) $75.00
Rationale: Without any discount Sam should pay 10*10=$100. Now, the overall discount would be slightly less than 27%, thus he must pay slightly more than $73. Only answer choice E fits.
Answer: E
Answer: (E) $75.00