mathewhe/aqua_rat huggingface dataset:
Question: Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $99 dollar, which she typically uses for gifts and charitable causes. What is Jill’s net monthly salary?
(A) $2400
(B) $3300
(C) $6000
(D) $6400
(E) $9600
Rationale: let x be the monthly salary
15%of 1/5*x=99
x=3300
answer B
Answer: (B) $3300
Question: On a purchase of $112, a store offered a payment plan consisting of a $12 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?
(A) 10.7%
(B) 11.7%
(C) 12.7%
(D) 13.7%
(E) 14.7%
Rationale: 12*10 + 12 = 132
(12/112)* 100 = 10.7
Answer : A
Answer: (A) 10.7%
Question: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
(A) 440
(B) 440 * sqrt (2)
(C) 400 * sqrt (3)
(D) 450 * sqrt (4)
(E) 440 * sqrt (5)
Rationale: let the constant be k
F1 = 440
F2 = 440k
F3 = 440 k * k = 440 * k^2
F13= 440 * k^12
we know F13 = 2 *F1 = 2 * 440 = 880
880/440 = k^12
k = twelfth root of 2
for F7...
F7 = 440 * k^6 ( as we wrote for F2 and F3)
F7 = 440 * (twelfth root of 2) ^ 6
F7 = 440 * sqrt (2)
Answer B
Answer: (B) 440 * sqrt (2)
Question: Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 2800 envelopes.
(A) 2
(B) 3
(C) 4
(D) 6
(E) 60/7
Rationale: You can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter
1. Work done in 1 hr by A is 2000 envelopes
2. Work done in 1 hr by A and C is 3000 envelopes
3. So work done in 1 hr by C is 1000 envelopes
4. Work done in 1 hr by B and C is 2400 envelopes
5. So work done in 1 hr by B is 1400 envelopes
6. So to process 2800 envelopes B will take 2800/1400 hrs = 2 hrs
So the answer is choice A
Answer: (A) 2
Question: Two numbers are respectively 50% and 20% more than a third number. The percentage that is first of the second is?
(A) 125%
(B) 97%
(C) 118%
(D) 52%
(E) 83%
Rationale: I II III
150 120 100
120----------150
100-----------? => 125%
Answer:A
Answer: (A) 125%
Question: A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 16 inches, how many inches of framing material does the carpenter need to frame the painting?
(A) 12
(B) 22 1/2
(C) 37 1/2
(D) 88
(E) 80
Rationale: (16/2) ( 2+3) * 2 = 80=E
Answer: (E) 80
Question: In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.855 per pound?
(A) 1:3
(B) 1:2
(C) 1:1
(D) 2:1
(E) 4:5
Rationale: Using weighted average method:
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.855
0.9 – 0.1x = 0.855
x = 0.45
Thus ratio of both flours is 4:5
E
Answer: (E) 4:5
Question: A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed if two of the men refuse to serve together?
(A) 3510
(B) 2620
(C) 1404
(D) 700
(E) 635
Rationale: Committee can have either: 2 men and 4 women OR 3 men and 3 women (to meet the condition of at least 2 men and 3 women).
Ways to chose 6 members committee without restriction (two men refuse to server together): C28∗C45+C38∗C35=700C82∗C54+C83∗C53=700
Ways to chose 6 members committee with two particular men serve together: C22∗C45+(C22∗C16)∗C35=5+60=65C22∗C54+(C22∗C61)∗C53=5+60=65
700-65 = 635
Answer: E.
Answer: (E) 635
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number W of races we need to conduct to get the top 3 fastest horses?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 11
Rationale: W=7 is the correct answer.
Good solution Buneul.B
Answer: (B) 7
Question: When a train travels at a speed of 80kmph,it reaches the destination on time.when the same train travels at a speed of 50kmph,it reaches its destination 15min late.what is the length of journey?
(A) 25km
(B) 50km
(C) 60km
(D) 85km
(E) 95km
Rationale: Let x be the time reached with the speed 80km/h
50km/h ----> x+15
Distance is equal so
80(km/h)× xhr = 50(km/h) × (x+15) hr
So
80 x = 50x + 750
So the would be in km
And x = 25
ANSWER:A
Answer: (A) 25km
Question: Two pipes A and B can fill a tank in 24 and 48 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 12
(B) 16
(C) 19
(D) 20
(E) 22
Rationale: Part filled by A in 1 min. = 1/24
Part filled by B in 1 min. = 1/48
part filled by (A + B) in 1 min. = 1/24 + 1/48 = 1/16.
Both the pipes can fill the tank in 16 minutes.
Answer: B
Answer: (B) 16
Question: In Lottery,there are 10 prizes and 25 blanks.A lottery is drawn at random.What is the Probability of getting a prize?
(A) 1/7
(B) 2/7
(C) 3/7
(D) 4/7
(E) 1
Rationale: Total number of outcomes possible,n(s)=10+25=35.
Total number of prize,n(e)=10
p(e)=n(e)/n(s)=10/35=2/7
Answer is option B
Answer: (B) 2/7
Question: If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can do the same work?
(A) 32
(B) 27
(C) 26
(D) 99
(E) 11
Rationale: Given that 5 women is equal to 8 girls to complete a work.
So, 10 women = 16 girls.
Therefore 10 women + 5 girls = 16 girls + 5 girls = 21 girls.
8 girls can do a work in 84 days then 21 girls can do a work in (8*84/21) = 32 days.
Therefore 10 women and 5 girls can a work in 32 days
Answer : A.
Answer: (A) 32
Question: A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 43 percent, what is the discount rate on mysteries?
(A) 24%
(B) 25%
(C) 30%
(D) 37.5%
(E) 40%
Rationale: Let B be the discount on biographies and M be the discount on mysteries
So., B + M = 0.435 -----(1)
And
(20*5 + 12*3) - (20*5*(1-B) + 12*3*(1-M)) = 19
--> 100(1-(1-B)) + 36(1-(1-M) = 19
100B + 36M = 19 ------(2)
Solving 12., we get M = 0.375 = 37.5%
D
Answer: (D) 37.5%
Question: Two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe empties the full tank in 20 hours.If all the three pipes operate simultaneously, in how much time will the tank be filled?
(A) 7 hrs 30 min
(B) 7 hrs 45 min
(C) 8 hrs 30 min
(D) 8 hrs 45 min
(E) 8 hrs 55 min
Rationale: 1/10+1/12-1/20=2/15
so 15/2 is equal to 7:30
ANSWER:A
Answer: (A) 7 hrs 30 min
Question: A person buys an article at Rs.650. At what price should he sell the article so as to make a profit of 10%?
(A) 600
(B) 715
(C) 269
(D) 261
(E) 281
Rationale: Cost price = Rs.650
profit = 10% of 650 = Rs.65
Selling price = Cost price + Profit
= 650 + 65 = Rs.715
Answer: B
Answer: (B) 715
Question: What day of the week was 3rd January 1501
(A) Thursday
(B) Tuesday
(C) Monday
(D) Saturday
(E) Sunday
Rationale: Explanation:
3rd Jan 1501 = (1500 years + 3rd Jan 1501)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 1200 years = 0 (Since 1200 is a perfect multiple of 400)
Number of odd days in the period 1201-1500
= Number of odd days in 300 years
= 5 x 3 = 15 = 1
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
3rd Jan 1501 = 3 odd day
Total number of odd days = (0 + 1 + 3) = 4
4 odd days = Thursday
Hence 3rd January 1501 is Thursday.
Answer: Option A
Answer: (A) Thursday
Question: How many numbers from 10 to 100 are exactly divisible by 9?
(A) 7
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Option 'C'
10/9 = 1 and 100/9 = 11 ==> 11 - 1 = 10. Therefore 10 digits.
Answer: (C) 10
Question: There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is:
(A) 9
(B) 13
(C) 15
(D) 12
(E) 19
Rationale: Explanation:
abc/bcd=385/1001=>a/d=5/13
So d = 13
Option B
Answer: (B) 13
Question: The percentage profit earned by selling an article for Rs. 1720 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
(A) 3000
(B) 1230
(C) 1875
(D) 5600
(E) 3400
Rationale: Then, (1720 - x)/x * 100 = (x - 1280)/x * 100
1720 - x = x - 1280
2x = 3000 => x = 1500
Required S.P. = 125 % of Rs. 1500 = 125/100 * 1500 = Rs. 1875.
ANSWER C
Answer: (C) 1875
Question: The inner circumference of a circle race track 18 m wide is 880 m. Find the radius of the outer circle.
(A) 120m
(B) 145m
(C) 130m
(D) 140m
(E) 122m
Rationale: Let inner radius be r metres
Then 2πr = 640
2 × 22/7 r = 880
44/7 r = 880
r = 880 × 7/44 = 140 m
Answer is D.
Answer: (D) 140m
Question: 5,9,19,31,51,__
(A) 84
(B) 80
(C) 81
(D) 82
(E) 83
Rationale: (9+5) +5 = 19
(16+9) +6 = 31
(28+16)+7 = 51
(48+28)+8 = 84
ANSWER:A
Answer: (A) 84
Question: Lexi needed to save for 30 days to afford a vacation at the job that paid her $125 per day. Lexi got a new job that pays $150 per day. How many days will she need to save to afford a vacation with this job?
(A) 25
(B) 20
(C) 27
(D) 29
(E) 26
Rationale: D1 P1 = D2 P2
30*125=D2*150 => D2=25
Answer:A
Answer: (A) 25
Question: 0.001 Ã— 0.001 = ?
(A) 0.1
(B) 0.001
(C) 0.01
(D) 1.0e-06
(E) None of these
Rationale: 0.001 Ã— 0.001 = ?
or,? = 0.000001
Answer D
Answer: (D) 1.0e-06
Question: In a consumer survey, 60% of those surveyed liked at least one of three products: 1, 2, and 3. 40% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 10% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: 40 + 30 + 20 = 90
This number includes some people counted twice and some people counted three times.
90 - 60 = 30, and this number represents people counted twice or three times.
10% of the people are counted two extra times.
The percentage of people counted one extra time is 30 - 10(2) = 10.
The percentage of people who liked more than one product is 10% + 10% = 20%.
The answer is C.
Answer: (C) 20
Question: What percent of 120 are 90?
(A) 25%
(B) 50%
(C) 75%
(D) 33%
(E) 35%
Rationale: Explanation:
(?% /100) * 120 = 90
? = 75%
ANSWER IS C
Answer: (C) 75%
Question: 2.08 can be expressed in terms of percentage as
(A) 2.08%
(B) 20.8%
(C) 208%
(D) 0.208%
(E) None of these
Rationale: Explanation:
While calculation in terms of percentage we need to multiply by 100, so
2.08 * 100 = 208
Answer: Option C
Answer: (C) 208%
Question: John takes 10 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, 20 minutes
(D) 3 hours, 45 minutes
(E) 4 hours, 10 minutes
Rationale: The rate of John plus Bill is 1/10 + 1/6 = 4/15 of the job completed per hour.
If Steve worked at the same rate as John, the rate would be 4/15 + 1/10 = 11/30
The slowest possible time would be 30/11 hours = 2 hours + 8/11 hours.
If Steve worked at the same rate as Bill, the rate would be 4/15 + 1/6 = 13/30
The fastest possible time would be 30/13 hours = 2 hours + 4/13 hours.
The actual time is somewhere between these two extreme points.
The answer is B.
Answer: (B) 2 hours, 30 minutes
Question: A certain sum amounts to Rs.1550 in 2 years and Rs.1700 in 3 years. Find the rate % per annum?
(A) 5.67%
(B) 7.67%
(C) 6.67%
(D) 4.67%
(E) 8.67%
Rationale: 2 --- 1550
3 --- 1700
--------------
1 --- 150
N = 1 I = 150 R = ?
P = 1550 - 300= 1250
150 = (1250*1*R)/100
R = 6.67%
Answer: C
Answer: (C) 6.67%
Question: If 10x = 8y = 14z, then what is a possible sum of positive integers x, y, and z?
(A) 52
(B) 166
(C) 84
(D) 122
(E) 168
Rationale: 10x = 8y = 14z
5x = 4y = 7z
5(4*7) = 4(5*7) = 7(5*4)
Addition = 28+20+35 = 83
Answer would be multiple of 83 which is 166
Answer :B
Answer: (B) 166
Question: A heap of grapes is divided into groups of 3, 5 and 7 and each time one coconut is left over. The least number of grapes in the heap is?
A. 31 B. 41 C. 51 D. 61
(A) A)31
(B) B)41
(C) C)106
(D) D)61
(E) E)71
Rationale: LCM = 105
=> 105 + 1 = 106
ANSWER:C
Answer: (C) C)106
Question: A picnic attracts 240 persons. There are 40 more men than women, and 40 more adults than children. How many men are at this picnic?
(A) 240
(B) 75
(C) 110
(D) 90
(E) 200
Rationale: Adult + Children = 240
Let, Children = y
then, Adult = y+40
i.e. y+(y+40) = 240
i.e. y = 100
i.e. Adult = 100+40 = 140
Adults include only Men and Women
i.e. Men + Women = 140
Let women, W = x
then Men, M = x+40
i.e. x+(x+40) = 2x+40 = 140
i.e. x = 54
i.e. Men, M = 54+40 = 90
Answer: Option D
Answer: (D) 90
Question: What is the sum E of all 3 digit numbers that leave a remainder of '2' when divided by 3?
(A) 897
(B) 164,850
(C) 164,749
(D) 149,700
(E) 156,720
Rationale: The series is => 101+...998
Number of terms => 300
sum => 300/2 * [101+998]
hence sum E=> 164850 i.e. option B
Answer: (B) 164,850
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) s.4529
(B) s.3624
(C) s.4597
(D) s.4530
(E) s.4528
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 4
=Rs.3624
Answer: B
Answer: (B) s.3624
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) Rs.250
(B) Rs.252
(C) Rs.228
(D) Rs.208
(E) Rs.229
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer:A
Answer: (A) Rs.250
Question: Plane leaves from Chelsea every 45 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m.
At what time air hostess convey this information to Frank Lampard?
(A) 5:35 p.m
(B) 6:40p.m
(C) 7:35 p.m
(D) 8:35 p.m
(E) 9:35 p.m
Rationale: Explanation:
Time of Frank Lampard last missed plane = 7:00 p.m - 45 min = 6:15 p.m
As this information has been given to Frank Lampard 25 minutes after the plane has already left, the air hostess gave the information at 6:15 p.m + 25 min = 6:40 p.m
Answer B
Answer: (B) 6:40p.m
Question: A new model car was not selling as expected and the base retail price was lowered by 5% to increase sales. A customer haggled on the price and negotiated a final agreed price of 90% of the retail price. How much did the customer save off the retail price?
(A) 10.5%
(B) 11.5%
(C) 12.5%
(D) 13.5%
(E) 14.5%
Rationale: Quantity X Rate = Price
1 X 1 = 1
0.9 X 0.95 = 0.855
Decrease in price = (0.145/1) Ã— 100 = 14.5%
Answer = Option E
Answer: (E) 14.5%
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
(A) 28,009
(B) 28,007
(C) 28,097
(D) 28,000
(E) 28,012
Rationale: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
Answer: D
Answer: (D) 28,000
Question: If 85% of 3/5 of a number is 36, then the number is?
(A) 80
(B) 100
(C) 70.5
(D) 90
(E) None of these
Rationale: Let the number be x. Then 85% of 3/5 of x=36
85/100*3/5*x=36
x=(36*100/51)=70.5
Required number=70.5.
Correct Option: C
Answer: (C) 70.5
Question: If the average (arithmetic mean) of the four numbers 13, 15, 52, and (N + 1) is 52, then N =
(A) 1 19
(B)  120
(C) 1 21
(D)  122
(E)  127
Rationale: 13+15+52+N+1= 52 x 4 = 208
=>N +81 = 208
=>N=127
Answer E
Answer: (E)  127
Question: x is what percent of y percent of z, in terms of x, y and z? n be the value expressed in terms of x,y and z.
(A) xyz
(B) 10^4x/yz
(C) 1/xyz
(D) 10^3 xyz
(E) 10^-3 xyz
Rationale: Algebraically, y% of z is just (y/100)*z, or yz/100. So we want to answer the question: x is what percent of yz/100? Say x is equal to n% of yz/100; then we have:
x = (n/100)*(yz/100)
10,000x/yz = n
B
Answer: (B) 10^4x/yz
Question: In the list 2, 3, 4, 5, 5, 5, 5, 7, 11, 21, what fraction of the data is less than the mode?
(A) 3/10
(B) 1/3
(C) 2/5
(D) 2/3
(E) 7/9
Rationale: Mode: The mode of any set is the term which has the highest frequency (Occurrence)
Highest frequent term in the set is 5 (with frequency 4) hence
Mode = 5
three terms (2, 3, 4) out of a total of 10 terms are less than mode of the set.
Fraction of set that are less than Mode of set = 3/10
Answer: Option A
Answer: (A) 3/10
Question: In a murder case there are four suspects P,Q,R,S. Each of them makes a statement. They are p:
"I had gone to the theatre with S at the time of the murder".q: "I was playing cards with P at the time of the murder".r: "Q didn't commit the murder".s: "R is not the murderer".Assuming the only one of the above statement is false and that one of them is the murderer, who is the murderer?
(A) P
(B) Q
(C) R
(D) S
(E) T
Rationale: According to Question,
P: (s and p in theatre)
Q:(q and p playing cards)
R: q not the murderer
S: R not the murderer
IF S is false,
P has to be in theatre with S.
P playing cards with Q.
This is Impossible.
If R is false,
P has to be in theatre with S.
P playing cards with Q.
This is Impossible.
If q is False,
S and P are in theatre.
Q and R are not murderers.
This is also impossible because one of them is the murderer.
so P is false.
Q and R are not murderers.
P playing cards.
hence our murderer is S..
ANSWER:D
Answer: (D) S
Question: Three bodies X, Y and Z start moving around a circular track of length 960m from the same point simultaneously in the same direction at speeds of 12 m/s, 20 m/s and 36 m/s respectively. When will they meet for the first time after they started moving?
(A) 240 seconds
(B) 120 seconds
(C) 60 seconds
(D) 180 seconds
(E) 100 seconds
Rationale: If they all meet after T seconds, it means they covered the distances 12T, 20T, and 36T respectively.
Since they all arrive to the same spot, it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track, which is 960m. So, 8T, 16T, and 24T must all be multiples of 960. 8T multiple of 960 means T multiple of 120. The smallest T with this property is 120 and is on the list of answers.
Answer B.
Answer: (B) 120 seconds
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/4 % his yearly income diminishes by Rs. 62.50, his capital is?
(A) 24,602
(B) 25,000
(C) 24,600
(D) 24,628
(E) 24,6012
Rationale: Let the capital be Rs. x. Then,
(x * 8 * 1)/100 - (x * 31/4 * 1/100) = 62.50
32x - 31x = 6250 * 4
x = 25,000.
Answer: B
Answer: (B) 25,000
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 900 m?
(A) 122.9 m
(B) 127.5 m.
(C) 191.25 m
(D) 222.9 m
(E) 12289 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800
= 6300/8
= 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 900 m, the number of meters by which A beats C = (900 * 212.5)/1000
= 191.25 m.
Answer:C
Answer: (C) 191.25 m
Question: The perimeter of a triangle is 20 cm and the inradius of the triangle is 3 cm. What is the area of the triangle?
(A) 22
(B) 30
(C) 77
(D) 54
(E) 23
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 3 * 20/2
= 30 cm2
Answer:B
Answer: (B) 30
Question: 2, 3, 4.5, 6.75, 10.12, (...)
(A) 60
(B) 60.75
(C) 58.11
(D) 15.18
(E) 16.21
Rationale: 2
(2Ã—3)Ã· 2 = 3
(3Ã—3)Ã· 2 = 4.5
(4.5Ã—3)Ã· 2 = 6.75
(6.75Ã—3)Ã· 2 = 10.12
(10.12Ã—3)Ã· 2 = 15.78
Answer is D
Answer: (D) 15.18
Question: One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
(A) 5:4
(B) 5:6
(C) 5:0
(D) 5:4
(E) 5:1
Rationale: 45 * 5/18 = 10
25:20 => 5:4
Answer: A
Answer: (A) 5:4
Question: If a rubber ball consistently bounces back ⅔ of the height from which it is dropped, what fraction of its original height will the ball bounce after being dropped and bounced four times without being stopped?
(A) 16/81
(B) 16/81
(C) 4/9
(D) 37/81
(E) 9/12
Rationale: Step by step solution
Each time the ball is dropped and it bounces back, it reaches ⅔ of the height it was dropped from.
After the first bounce, the ball will reach ⅔ of the height from which it was dropped - let us call it the original height.
After the second bounce, the ball will reach ⅔ of the height it would have reached after the first bounce.
So, at the end of the second bounce, the ball would have reached ⅔ * ⅔ of the original height = 4/9th of the original height.
After the third bounce, the ball will reach ⅔ of the height it would have reached after the second bounce.
So, at the end of the third bounce, the ball would have reached ⅔ * ⅔ * ⅔ = 8/27th of the original height.
After the fourth and last bounce, the ball will reach ⅔ of the height it would have reached after the third bounce.
So, at the end of the last bounce, the ball would have reached ⅔ * ⅔ * ⅔ * ⅔ of the original height = 16/81 of the original height.
The correct answer is Choice A
Answer: (A) 16/81
Question: If a company sells a car with a marked price of Rs. 5,40,000 and gives a discount of 5% on Rs. 3,00,000 and 3% on the remaining amount of Rs. 2,40,000, then the actual price charged by the company for the car is :
(A) Rs.5,20,000
(B) Rs.5,17,800
(C) Rs.5,10,560
(D) Rs.5,10,100
(E) None of these
Rationale: Explanation :
Solution: M.P. = Rs. 5,40,000.
Discount = Rs. [(5% of 3,00,000) + (3% of 2,40,000)] = 15,000 + 7,200 = Rs. 22,200
.'. Actual price = Rs. (5,40,000 - 22,200) = Rs. 5,17,800
Answer : B
Answer: (B) Rs.5,17,800
Question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 8, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?
(A) 20
(B) 22
(C) 24
(D) 27
(E) 30
Rationale: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes
Answer: D.
Answer: (D) 27
Question: One scoop of fish food can feed 8 goldfish. How many goldfish can 4 scoops of fish
food feed?
(A) 12
(B) 16
(C) 8
(D) 64
(E) 32
Rationale: Each scoop of fish food can feed 8 goldfish.
Therefore, 4 scoops of fish food can feed 4x8 = 32 goldfish.
correct answer E
Answer: (E) 32