mathewhe/aqua_rat huggingface dataset:
Question: A and B together can complete work in 6 days. A alone starts working and leaves it after working for 3 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?
(A) 3
(B) 8
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
(A+B) one day work =1/6
now A does half of the work in 3 days so A can complete the whole work in 6 days
A’s one day work =1/6
B’s one day work=1/6 - 1/6= 1/6
B alone can complete the work in 6 days so half of the work in 3 days
Answer: Option A
Answer: (A) 3
Question: If TEAR is coded as 4657 and BOX is coded as 125. How is BETA coded?
(A) 1465
(B) 1645
(C) 1654
(D) 1456
(E) 1546
Rationale: e=6 t-4 a-5 from the code TEAR, b-1 from the code BOX, ANSWER:B
Answer: (B) 1645
Question: If 20 typists can type 44 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
(A) 63
(B) 72
(C) 198
(D) 216
(E) 400
Rationale: 20 typists can type 44 letters, so 30 typists can type = 44*30/20
44*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 44*30*60/20*20= 198
C is the answer
Answer: (C) 198
Question: What is the 29th digit to the right of the decimal point in the decimal form of 4/11?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 4/11 = 0.363636...
The odd numbered positions in the decimal expansion are all 3.
The answer is C.
Answer: (C) 3
Question: 20 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?
(A) 30
(B) 32
(C) 60
(D) Data inadequate
(E) None of these
Rationale: Capacity of the tank = 20 × 13.5= 270 litres
When the capacity of each bucket = 9 litres, then the required no. of buckets
= 270⁄9 = 30
Answer A
Answer: (A) 30
Question: Mane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Mane or Thomas is to be selected?
(A) 28
(B) 46
(C) 55
(D) 63
(E) 70
Rationale: Ans:C
Solution:
M+T+6 = total 8 ,
we need to select at least one of the M and T or both= total 4 out of 8 - 4 out of 6
8C4 - 6C4
=55
Answer: (C) 55
Question: There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 855. How many houses are there?
(A) 155
(B) 161
(C) 154
(D) 156
(E) 158
Rationale: So it starts from 545 and goes like 547, 549,...... 855. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.
i.e., ([855-545][/2]+1 = 156
Ans D
Answer: (D) 156
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 musthe travel to reach A at 1 PM?
(A) 8 kmph
(B) 10 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: If the average (arithmetic mean) of x and y is 60, and z – x = 80, what is the average of y and z?
(A) 100
(B) 120
(C) 125
(D) 115
(E) 90
Rationale: x+y/2 = 60
=> x+y = 120
x = z - 80...sub this value
z-80+y = 120
=>z+y = 200
=>z+y/2 = 100
Answer : A
Answer: (A) 100
Question: At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
(A) 16 4/17
(B) 16 4/16
(C) 16 4/12
(D) 16 4/11
(E) 16 4/13
Rationale: At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
To be coincident, it must gain 15 min. spaces.55 min. are gained in 60 min.
15 min. are gained in
= (60/55 x 15)min
=16+4/11
The hands are coincident at 16 + 4/11 min past 3
Answer: D
Answer: (D) 16 4/11
Question: In a shower, 9 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
(A) 75 cu. m
(B) 1350 cu. m
(C) 7500 cu. m
(D) 75000 cu. m
(E) 7.50 cu. m
Rationale: 1 hectare = 10000 sq mtr
The volume of water that falls on 1.5 hectares of ground = 0.09*1.5*10000 =1350 cub mtr .
ANSWER:B
Answer: (B) 1350 cu. m
Question: Find the odd man out. 3576, 1784, 888, 440, 216, 105, 48
(A) 105
(B) 216
(C) 888
(D) 1784
(E) 48
Rationale: Explanation :
3576
(3576-8)/2 = 1784
(1784-8)/2 = 888
(888-8)/2 = 440
(440-8)/2 = 216
(216-8)/2 = 104
(104-8)/2 = 48
Hence, 105 is wrong. 104 should have come in place of 105
Answer : Option A
Answer: (A) 105
Question: A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?
(A) 1500
(B) 2000
(C) 3000
(D) 3500
(E) 2500
Rationale: Profit as x
since 5% and 95% of x will be divided b/w A and B ration 3:2
=>profit 95x/100 * 3/5
given that A's share is Rs 855 =>
95x/100 * 3/5 = 855
hence x = 1500
ANSWER A
Answer: (A) 1500
Question: The price of stock decreased by 5% last year and rose by 10% this year. What is the net percentage change in the price of the stock?
(A) 0.2%
(B) 0.8%
(C) 1.2%
(D) 1.6%
(E) 4.5%
Rationale: (100% - 5%) * (100% + 10%) = 0.95 * 1.10 =1.045 = 104.5%.
The net percentage change in the price of the stock is (+) 4.5%
The answer is E
Answer: (E) 4.5%
Question: x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xyz is divisible by 6
2. (z-x)(y-x+2) = 4
3. xy is odd
(A) I only
(B) II only
(C) III only
(D) I only
(E) I, II, and III
Rationale: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1
Statement 1 would be true as at least one of the three numbers is divisible by 2 and one by 3 so xyz would be divisible by 6.
Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+2) = 2*3 = 6 So, not true
Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.
So, I is always true and hence answer is
D.
Answer: (D) I only
Question: Concentrated pineapple juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated pineapple juice, at the most, can fit into 3 wooden boxes?
(A) 24.
(B) 28.
(C) 36.
(D) 42.
(E) 48.
Rationale: concentrated pineapple juice since height of a tube is 15 inches , the tubes can fit only in one way .
now, diameter of each tube = 5 inches
therefore, 4*2 can be put in each wooden box
in 3 boxes 3*4*2 can be accommodated
= 24=A
Answer: (A) 24.
Question: Mary works 9 hours per day on Monday, Wednesday and Friday, and 5 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $407 per week. How much does she earn in dollars per hour?
(A) 12
(B) 10
(C) 9
(D) 8
(E) 11
Rationale: So, she works 27 hours in 3 days
So, she works 10 hours in 2 days
So in a week she works 37 hours ( 27 + 10 ) and earns $407
So, Hourly wage is 407/37 => 11
Hence answer will be (E) 11
Answer: (E) 11
Question: If x, y, and z are positive integers such that x is a factor of y and y is a factor of z, which of the following is NOT necessarily an integer?
(A) (x + y)/z
(B) (y + z)/x
(C) yz/x
(D) (2y + 3z)/x
(E) (xy + z)/y
Rationale: As per the question, let x = 2, y = 6, and z = 12. Plugging these into the answer choices, only A does not yield an integer.
Answer: (A) (x + y)/z
Question: A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.300 more. What was the Sum?
(A) s.1200
(B) s.1300
(C) s.600
(D) s.800
(E) s.1200
Rationale: At 5% more rate, the increase in S.I for 10 years = Rs.300 (given)
So, at 5% more rate, the increase in SI for 1 year = 300/10 = Rs.30/-
i.e. Rs.30 is 5% of the invested sum
So, 1% of the invested sum = 30/5
Therefore, the invested sum = 30 × 100/5 = Rs.600 Answer: C
Answer: (C) s.600
Question: If y is a given positive integer,.What is the remainder if y is divided by 25, since when y divided by 7 and 12 the remainders are 4 and 3 respectively.
(A) 12
(B) Between 1 and5, inclusive
(C) Between 10 and 15, inclusive
(D) Between 6 and 9, inclusive
(E) 10
Rationale: Given the integer y
7y+4= 12y+3
Start 7y+4 -->11, 18, 25,32,39,...
Of these only 39 fit the description 12y+3. The remainder when divided by 25 is 14. So answer is C).
Answer = C)
Answer: (C) Between 10 and 15, inclusive
Question: If a certain sample of data has a mean of 25.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
(A) (19.0; 26.5)
(B) (14.5; 28.0)
(C) (23.0; 28.5)
(D) (22.5; 26.0)
(E) (19.0; 30.5)
Rationale: The standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5.
The values between 20 and 30 are within 2.5 standard deviations from the mean.
The answer is E.
Answer: (E) (19.0; 30.5)
Question: Two teams participating in a competition had to take a test in a given time. Team
B chose the easier test with 300 questions, and team A the difficult test with 10%less questions. Team A completed the test 3 hours before schedule while team B completed it 6 hours before schedule. If team B answered 7 questions more than
team A per hour, how many questions did team B answer per hour?
(A) 21
(B) 22
(C) 23
(D) 25
(E) 27
Rationale: If t hrs is normal time,
then
270/(t-3) + 7 = 300/(t-6)
so t = 18
so Qns done by team A per hour = 270/15 = 18 qns.
Qns done by team B per hour = 300/12 = 25 qns.
ANSWER:D
Answer: (D) 25
Question: A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 44 days, then together ,all will finish the work in :
(A) 13 3/3 days
(B) 12 1/3 days
(C) 15 days
(D) 20 days
(E) 30 days
Rationale: C alone can finish the work in 44 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
Aâ€™s 1 dayâ€™s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 dayâ€™s work = (1/60) + (1/30) + (1/44) = 1/(13 3/4)
All the three together will finish it in = 13 and 3/4 days.
ANSWER:A
Answer: (A) 13 3/3 days
Question: A person spends 1/5th of his income on the education of his children, and 20% of the remaining on food. If he is left with Rs.576 find his income?
(A) 900
(B) 197
(C) 176
(D) 107
(E) 727
Rationale: X * 4/5 * 80/100 = 576
X = 14400/16
X = 900
Answer: A
Answer: (A) 900
Question: Evaluate combination
99C97=99!/(97)!(2)!
(A) 6170
(B) 4851
(C) 4171
(D) 3170
(E) None of these
Rationale: Explanation:
nCr=n!/(r)!(n−r)!
99C97=99!/(97)!(2)!
=99∗98∗97!/(97)!(2)!
=99∗98/2∗1
=4851 Option B
Answer: (B) 4851
Question: A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 2 buckles is how many times that of 5 buckles and 6 buttons?
(A) 7/15
(B) 4/9.
(C) 6/11
(D) 5/9
(E) 8/15
Rationale: 2 buttons + 2 buckles = 1/3(11 buckles + 3buttons)
6 buttons + 6 buckles = 11 buckles + 3buttons
3buttons = buckles
Weight of 3buttons and buckles = 5buckles + 2buckles = 7buckles
Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles
(3buttons and 2buckles) = x * (6buttons and 5buckles)
7 = x*15
x = 7/15
Answer: A
Answer: (A) 7/15
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336, 528
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Also, 5184 is not divisible by 11.
Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.
Answer: B
Answer: (B) 5
Question: Ram was asked to multiply a number by 441 and he came with an answer 70229. His
Teacher told him that all the digits except the 2’s in his answer are correct. Which of the following could be the correct answer?
(A) 70119
(B) 70110
(C) 70117
(D) 70112
(E) 71119
Rationale: 441*158 = 69678
441*159 = 70119
441*160 = 70560
441*161 = 71001
since all the digits except 2 are correct , second number will be 159 and answer = 70119
ANSWER:A
Answer: (A) 70119
Question: A man sitting in a train which is travelling at 20 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?
(A) 52 kmph.
(B) 62 kmph.
(C) 72 kmph.
(D) 92 kmph.
(E) None
Rationale: Solution
Relative Speed	= (280 / 9)m/sec
= (280/9 x 18/5)
= 112 kmph.
Speed of the train	= (112 - 20)kmph
= 92 kmph.
Answer D
Answer: (D) 92 kmph.
Question: If the two-digit integers L and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of L and N?
(A) 181
(B) 165
(C) 121
(D) 99
(E) 44
Rationale: Since the question asks for the answer that CANNOT be the sum of L and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.
We're told that L and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of L and N.
Let's start with the 'easiest' answer first:
44. Can we get to 44 in the manner described?
Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E
Now let's work through the rest of the list....
Can we get to 99 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D
Can we get to 121 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C
Can we get to 165 in the manner described?
Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B
There's only one answer left....
A
Answer: (A) 181
Question: A tester rejects 0.08% of the meters as defective, How many meters he tested to reject 2 meters ?
(A) 1200
(B) 2400
(C) 1400
(D) 2500
(E) 5400
Rationale: Explanation :
It means that 0.08% of x = 2
=>(8/100100x)=2
=>x=2100100/8
=>x=2500
Answer : D
Answer: (D) 2500
Question: In a lottery, there are 12 prizes and 48 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: P(winning a prize) = 12 / (12+48) = 12/60 = 1/5
The answer is D.
Answer: (D) 1/5
Question: A train 300 m long, running with a speed of 90 km/hr will pass a tree in?
(A) 17 sec
(B) 16 sec
(C) 18 sec
(D) 14 sec
(E) 12 sec
Rationale: Speed = 90 * 5/18
= 25 m/sec
Time taken = 300 * 1/25
= 12 sec
Answer: E
Answer: (E) 12 sec
Question: The difference between the simple interest received from two different sources on Rs.1700 for 3 years is Rs.13.50. The difference between their rates of interest is
(A) 0.16%
(B) 0.26%
(C) 0.36%
(D) 0.46%
(E) 0.56%
Rationale: (1700xR1x3)/100-(100xR2x3)/100 =13.50
5100(R1-R2)=1350
R1-R2 = 1350/5100=0.26%
answer : B
Answer: (B) 0.26%
Question: Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 1:2 and 3:2 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
(A) 99:61
(B) 1:1
(C) 61:160
(D) 61:99
(E) 99:160
Rationale: Vessel A = 300 gallons --> milk = 100, water = 200;
Vessel B = 500 gallons --> milk = 300, water = 200;
Vessel A + B = 800 gallons --> milk = 400, water 400.
The ratio = 400/400 --> 1:1
Answer: B
Answer: (B) 1:1
Question: The flowerman sale, all of the prices of the flowers sold were different. If the price of a radio sold at the flowerman sale was both the 17th highest price and the 42th lowest price among the prices of the slowers sold, how many flowers were sold at the flowerman sale?
(A) 38
(B) 34
(C) 58
(D) 63
(E) 73
Rationale: 16+41+1= 58
Answer: C
Answer: (C) 58
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 15%. What is the effect on its area?
(A) 1288
(B) 1299
(C) 10625
(D) 10000
(E) 2887
Rationale: 100 * 100 = 10000
125 * 85 = 10625
Answer: C
Answer: (C) 10625
Question: A person crosses a 1080 m long street in 12 minutes. What is his speed in km per hour?
(A) 4.1
(B) 4.5
(C) 4.8
(D) 5.4
(E) 5.5
Rationale: Speed = 1080/(12x60) m/sec
= 1.5 m/sec.
Converting m/sec to km/hr =1.5 x(18/5) km/hr
= 5.4 km/hr.
ANSWER :D
Answer: (D) 5.4
Question: A certain school implemented a reading program for its students, with the goal of getting each student to read 3 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year?
(A) 20cs
(B) cs/2
(C) 36cs
(D) (2cs)/12
(E) (24c)/s
Rationale: Ans: C
Solution: simple multiplication s students , c classes , 3 books/ month= 36 books a year
total number of books = 36cs
Answer: (C) 36cs
Question: the number of zeros at the end of product of prime numbers between 1 and 999999
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 1 zero at the end because multiplication of 2 and 5 leads to an answer which is a multiple of 10
ANSWER:A
Answer: (A) 1
Question: 7 girls earn equal to as many boys as are equal to 9 men. All of them earn Rs.105 only. Girl's earnings are?
(A) 6
(B) 5
(C) 2
(D) 7
(E) 2
Rationale: 7g=xb=9m
7g+xb+9m ----- 105Rs.
7g+7g+7g ----- 105 Rs.
21g ------ 105 Rs. => 1Mg= 5Rs.
Answer: B
Answer: (B) 5
Question: How many even multiples of 65 are there between 649 and 1301?
(A) 5
(B) 6
(C) 9
(D) 10
(E) 11
Rationale: 650 = 10*65
1300 = 20*65
The even multiples are 65 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B.
Answer: (B) 6
Question: At a meeting of the local computer user group, each member brought two nonmembers. If a total of 27 people attended, how many were members and how many were nonmembers?
(A) 10
(B) 13
(C) 24
(D) 22
(E) 18
Rationale: Let x= number of members and 2x= number of non-members
x+ (2x)= 27
3x=27
3x/3=27/3
x=9
The number of non-members is 2x = 2(9)=18 people, the answer is E)
Answer: (E) 18
Question: How many minutes does it take James to type 8 words if he types at the rate of 4 words per minute?
(A) 4
(B) 1
(C) 2
(D) 6
(E) 3
Rationale: time*rate=job --> time*4=8 --> time=8/4=2.
Answer: C.
Answer: (C) 2
Question: The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?
(A) 5
(B) 4
(C) 3
(D) 6
(E) 7
Rationale: 100 ---- 300 --- 3
900 --- 3
----
6 years
Answer: D
Answer: (D) 6
Question: In how many ways can you seat 7 people on a bench if one of them does not want to sit at either end?
(A) 3500
(B) 3600
(C) 3700
(D) 3800
(E) 3900
Rationale: One person can choose 5 possible chairs to sit. The remaining 6 people can sit in 6! ways.
The number of arrangements is 5*6! = 3600.
The answer is B.
Answer: (B) 3600
Question: Nine persons went to a hotel for taking their meals. Eight of them spent 11 each on their meals and the ninth spend 8 more than the average expenditure of all the nine. What was the total money spent by them?
(A) 108
(B) 117
(C) 119
(D) 122
(E) None of the above
Rationale: Let the average expenditure of all the nine be x.
Then, 11 × 8 + (x + 8) = 9x or 8x = 96 or x = 12.
∴ Total money spent = 9x = (9 × 12) = 108.
Answer A
Answer: (A) 108
Question: Two trains of length 120 meter and 150 meter crosses a stationary man in 10 and 15 seconds respectively. In what time they will cross each other when they are moving in same direction.
(A) 120 sec
(B) 125 sec
(C) 135 sec
(D) 140 sec
(E) None of these
Rationale: Explanation :
120 = a*10, a = 12 m/sec (speed of first train)
150 = b*15, b = 10 m/sec (speed of second train)
270 = (2)*T, T = 135 seconds
Answer – C
Answer: (C) 135 sec
Question: In an election between two candidates first candidate got 60% of votes polled and second Candidate got 280 votes. The total number of votes polled was?
(A) 700 votes
(B) 900 votes
(C) 1000 votes
(D) 1100 votes
(E) 1300 votes
Rationale: Total = 100 %,
First person got 60%
second person got remaining 40 % of votes.
than 40 % = 280
40% = 40×7 = 280
100% =100×7 =700 votes
A)
Answer: (A) 700 votes
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/18 hours
(B) 37/13 hours
(C) 80/13 hours
(D) 30/13 hours
(E) 30/43 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream
= d/s = 60/26
= 30/13 hours.
Answer: D
Answer: (D) 30/13 hours
Question: A pharmaceutical company received $5 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
(A) 8%
(B) 15%
(C) 45%
(D) 52%
(E) 67%
Rationale: Solution:
This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.
We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales, and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.
First 20 Million
royalties/sales = 5/20 = 1/4
Next 108 Million
royalties/sales = 9/108 = 1/12
Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents.
First 20 Million
royalties/sales = (5/20) x 12 = 3
Next 108 Million
royalties/sales = 9/108 = (1/12) x 12 =1
We can plug 15 and 5 into our percent change formula:
(new – old)/old x 100
[(1 – 3)/3] x 100
-200/3 x 100
At this point we can stop and consider the answer choices. Since we know that 200/3 is just a bit less than ½, we know that -200/3 x 100 is about a 67% decrease.
Answer E.
Answer: (E) 67%
Question: Find the odd man out. 6, 13, 18, 25, 30, 37, 40
(A) 40
(B) 30
(C) 37
(D) 25
(E) 13
Rationale: Explanation :
The difference between two successive terms from the beginning are 7, 5, 7, 5, 7, 5
Hence, in place of 40, right number is 37+5=42
Answer : Option A
Answer: (A) 40
Question: A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 191 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
(A) 7,251
(B) 8406
(C) 9216
(D) 10,348
(E) can not be determined
Rationale: Let the side for growing cabbages this year be X ft. Thus the area is X^2.
Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2.
The area would have increased by 191 sq ft as each cabbage takes 1 sq ft space.
X^2 - Y^2 = 191
(X + Y)(X - Y) = 191
191 is a prime number and thus it will be (96+95)*(96-95).
Thus X = 96 and Y = 95
X^2 = 96^2 = 9216
The answer is C.
Answer: (C) 9216
Question: If x = 3z, where z is a prime number greater than 2, how many different positive even divisors does x have, including x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) It cannot be determined from the information given
Rationale: z is prime greater than 2 thus z is odd
3z is odd
Thus no even factors
Ans:A
Answer: (A) 0