mathewhe/aqua_rat huggingface dataset:
Question: Look at this series: 2, 1, (1/2), (1/4), (1/8), ... What number should come next?
(A) (1/3)
(B) (1/5)
(C) (1/6)
(D) (1/10)
(E) (1/16)
Rationale: This is a simple division series; each number is one-half of the previous number.
In other terms to say, the number is divided by 2 successively to get the next result.
4/2 = 2
2/2 = 1
1/2 = 1/2
(1/2)/2 = 1/4
(1/4)/2 = 1/8
(1/8)/2= 1/16 and so on.
Answer is E
Answer: (E) (1/16)
Question: A girl swims downstream 40 km and upstream 16 km taking 4 hours each time, what is the speed of the girl in still water?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 40 --- 4 DS = 10
? ---- 1
16 ---- 4 US = 4
? ---- 1 M = ?
M = (10 + 4)/2 = 7
Answer:E
Answer: (E) 7
Question: On my sister's birthday, she was 143 cm in height, having grown 10% since the year before. How tall was she the previous year?
(A) 140 cm
(B) 136 cm
(C) 130 cm
(D) 127 cm
(E) 125 cm
Rationale: Let the previous year's height be x.
1.1x = 143
x = 130
The answer is C.
Answer: (C) 130 cm
Question: A goods train runs at the speed of 72 kmph and crosses a 350 m long platform in 26 seconds. What is the length of the goods train?
(A) 230 m
(B) 140 m
(C) 160 m
(D) 170 m
(E) None of these
Rationale: Explanation:
Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,[ (x+350)/26 ]= 20
=> x + 350 = 520
=> x = 170. Answer: D
Answer: (D) 170 m
Question: How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated?
(A) 60
(B) 41
(C) 42
(D) 62
(E) 61
Rationale: Three digit numbers will have unit's, ten's and hundred's place.
Out of 5 given digits any one can take the unit's place.
This can be done in 5 ways ------- (i)
After filling the unit's place, any of the four remaining digits can take the ten's place.
This can be done in 4 ways ------- (ii)
After filling in ten's place, hundred's place can be filled from any of the three remaining digits.
This can be done in 3 ways ------- (iii)
=> By counting principle, the number of 3 digit numbers =5×4×3==5×4×3= 60
Option is A
Answer: (A) 60
Question: M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3, 4}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
(A) 0
(B) 1/3
(C) 2/5
(D) 1/2
(E) 4/7
Rationale: We will have a negative product only if 1, 2, 3, or 4 are selected from set T.
P(negative product) = 4/7
The answer is E.
Answer: (E) 4/7
Question: Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 7 weeks have been $406, $413, $420, $436, $395, $410, $360. What must his average (arithmetic mean) income over the next two weeks be to decrease his average weekly income to $400 over the 9-week period?
(A) $360
(B) $380
(C) $430
(D) $290
(E) $520
Rationale: OFFICIAL SOLUTION:
(B) First, we need to add up the wages over the past 7 weeks: $406 + $413 + $420 + $436 + $395 + $410 + $360 = $2840.
To average $400 over 9 weeks, the salesman would need to earn: $400 × 9 = $3600.
Subtract $2840 from $3600 to determine how much he would need to earn, in total, over the next 2 weeks to average $400 for the 9 weeks: $3600 – $2840 = $760.
Dividing $760 by 2 will give us the amount he needs to earn on average over the next 2 weeks: $760/2 = $380.
The correct answer is choice (B).
Answer: (B) $380
Question: In order to obtain an income of Rs. 600 from 12% stock at Rs. 106, one must make an investment of
(A) 5363
(B) 6240
(C) 2368
(D) 7632
(E) 7732
Rationale: To obtain Rs. 10, investment
= Rs. 106.
To obtain Rs. 600, investment =
= Rs. 7632
Answer: D
Answer: (D) 7632
Question: What are the odds that you will draw a Queen or Spades from a well-shuffled standard deck of cards?
(A) 1 in 13
(B) 1 in 12
(C) 1 in 5
(D) 4 in 52
(E) 4 in 13
Rationale: Using a simple equation with a common denominator being the number of cards in the deck (52), the equation can be written this way:
13/52 + 4/52 = 17/52
17/52 - 1/52 = 16/52
16/52 = 4/13
Correct answer is E.
Answer: (E) 4 in 13
Question: Truck P and Truck Q drive on the highway in the same direction at respective rates of 72 kph and 80 kph. If Truck Q is 5 km behind Truck P, by how much does Truck P need to increase the speed to catch up with Truck P in 20 minutes?
(A) 6 kph
(B) 7 kph
(C) 8 kph
(D) 9 kph
(E) 10 kph
Rationale: Truck Q needs to gain 5 km in 20 minutes.
The relative speed difference needs to be 5 km / 20 minutes = 15 km/hour
Truck Q needs to increase up to 87 kph, thus an increase in 7 kph.
The answer is B.
Answer: (B) 7 kph
Question: The ratio of two numbers is 3:4 and their H.C.F. is 4. Their L.C.M. is?
(A) 12
(B) 16
(C) 24
(D) 48
(E) None of these
Rationale: Let the numbers be 3x and 4x. Then, their H.C.F. = x., So, x=4
so, the numbers are 12 and 16.
L.C.M. of 12 and 16=48.
Correct Option: D
Answer: (D) 48
Question: A lady builds 7cm length, 18cm width, and 3cm height box using 9cubic cm cubes. What is the minimum number of cubes required to build the box?
(A) 42
(B) 45
(C) 47
(D) 49
(E) 56
Rationale: Number of cubes required = Volume of box/Volume of cube
= 7*18*3/9
=42 cubes
ANSWER:A
Answer: (A) 42
Question: In 1990 a total of c earthquakes occurred worldwide, some but not all of which occurred in Asia. If e o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
(A) c/e
(B) e/c
(C) e/(c-e)
(D) c/(c-e)
(E) 1- (e/c)
Rationale: We're given a couple of facts to work with:
1) There were a total of c earthquakes
2) Of those earthquakes, e of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Let's TEST VALUES
c = 5 total earthquakes
e = 2 occurred in Asia
Thus, there were 3 earthquakes that DID NOT occur in Asia....
The answer to the question is 2:3
We just need to plug in the values for c and e and find the match...
Answer A: c/e = 5/2 NOT a match
Answer B: e/c = 2/5 NOT a match
Answer C: e/(c-e) = 2/(5-2) = 2/3 This IS a match
Answer D: c/(c-e) = 5/(5-2) = 5/3 NOT a match
Answer E: 1 - (e/c) = 1-2/5 = 3/5 NOT a match
C
Answer: (C) e/(c-e)
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit?
(A) 3029
(B) 3199
(C) 3120
(D) 3000
(E) 3123
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
Answer:D
Answer: (D) 3000
Question: Sheik Abdullah decides to buy 2 new cars for his collection. If he has to choose between eight different cars, what is the number of purchasing possibilities he has?
(A) A)148
(B) B)158
(C) C)168
(D) D)178
(E) E)188
Rationale: Sheik Abdullah decides to buy 2 new cars for his collection. He has to choose between eight different cars
8C3= 8*7*6/(2*1) = 168 ANS:C
Answer: (C) C)168
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer M that must divide n is?
(A) 6
(B) 12
(C) 24
(D) 36
(E) 48
Rationale: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer M that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B
Answer: (B) 12
Question: A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 400 shares of the company's stock?
(A) $208
(B) $96
(C) $104
(D) $120
(E) $240
Rationale: EPS Actual> EPS expected.
each gets and additional .12 per share.
Thus .52*400 --> $208
answer is A
Answer: (A) $208
Question: Alfred buys an old scooter for $4700 and spends $800 on its repairs. If he sells the scooter for $6000, his gain percent is?
(A) 9.1%
(B) 6.23%
(C) 7%
(D) 8.12%
(E) 10%
Rationale: C.P. = 4700+800 = $5500
S.P. = $6000
Gain = 6000-5500 = $500
Gain% = 500/5500 * 100 = 9.1%
Answer is A
Answer: (A) 9.1%
Question: An unbiased die is tossed .find the probability of getting a multiple of 3
(A) 3/4
(B) 1/3
(C) 2/7
(D) 1/7
(E) 1/6
Rationale: Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(E)=n(E)/n(S)=2/6=1/3
Option B
Answer: (B) 1/3
Question: If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-2) ∆ (2 ∆ −2) ?
(A) −1
(B) 0
(C) 1
(D) 9
(E) 25
Rationale: (-2) ∆ (2 ∆ − 2) =
(-2) ∆ (4^2/2^2) =
(-2) ∆ (4) =
(-6^2) / (-2)^2 = 9
The answer is D.
Answer: (D) 9
Question: What is the difference between the place value and the face value of 6 in the numeral 296827?
(A) None of these
(B) 5999
(C) 994
(D) 5994
(E) 995
Rationale: Explanation:
Place value of 6 = 6000
Face value of 6 = 6
Difference = 6000 - 6 = 5994
Answer: D
Answer: (D) 5994
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) Rs.3944
(B) Rs.3921
(C) Rs.3927
(D) Rs.3297
(E) Rs.3929
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs.3944.
Answer: A
Answer: (A) Rs.3944
Question: The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 11m 95 cm is
(A) 2
(B) 7
(C) 5
(D) 8
(E) 9
Rationale: Explanation:
Required Length = H.C.F of 700 cm, 385 cm and 1195 c
= 5 cm.
Answer: C)5 cm
Answer: (C) 5
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.24, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]
(A)  0.32
(B)  0.44
(C)  32
(D)  44
(E)  55
Rationale: A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 24 cents;
A half-liter of kerosene costs as much as 8 eggs --> 8 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 16 eggs = 16/12*24 = 32 cents.
Answer: C.
Answer: (C)  32
Question: 8873 + x = 13200, then x is ?
(A) 3327
(B) 4327
(C) 3337
(D) 2337
(E) None of these
Rationale: Answer
x = 13200 - 8873 = 4327
Option: B
Answer: (B) 4327
Question: If Compound Interest on a certain sum for 2 years at 5% p.a. is Rs.328, the Simple interest will be ?
(A) Rs. 320
(B) Rs. 321
(C) Rs. 322
(D) Rs. 323
(E) Rs. 324
Rationale: Solution:
Suppose, Compound Interest for first year = Rs. 100
Then, Compound Interest for second year =100 + 5% (100) = Rs. 105
Total Compound Interest for two years = (Rs. 100 + Rs. 105) = Rs. 205
And Simple Interest for two years = 2 x Rs. 100 = Rs. 200
If Compound Interest is Rs. 205, Simple Interest = Rs. 200
If compound interest is Rs.1, then simple interest = 200/205
If Compound Interest is Rs. 328, Simple Interest = Rs.328×200/205= Rs. 320
Answer A
Answer: (A) Rs. 320
Question: In a camp, there is a meal for 60 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
(A) 41
(B) 16
(C) 18
(D) 20
(E) 15
Rationale: E
15
There is a meal for 200 children.
150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children 60 men.
50 children = (60/200)x 50 = 15 men.
Answer: (E) 15
Question: The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 65 terms of set X?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: 65*4 + 64*40 + 63*400 = 260 + 2560 + 25200 = 28020
The hundreds digit is 0.
The answer is A.
Answer: (A) 0
Question: An article is sold at a certain price. By selling it at 2/3 of that price one loses 10%. Find the gain percent at original price?
(A) 25%
(B) 20%
(C) 35%
(D) 40%
(E) 50%
Rationale: Let the original S.P. be $x
Then, New S.P. = $ 2/3 x
Loss = 10%
C.P. = 100/90 * 2/3 x = 20x/27
C.P. = 20x/27
Gain = x - 20x/27 = 7x/27
Gain% = 7x/27 * 27/20x * 100 = 35%
Answer is C
Answer: (C) 35%
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?
(A) 17/90
(B) 87/20
(C) 17/28
(D) 17/20
(E) 57/20
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: (D) 17/20
Question: In how many different number of ways 6 men and 2 women can sit on a shopa which can accommodate persons?
(A) 170
(B) 180
(C) 200
(D) 1680
(E) 220
Rationale: Option 'D'
8p4 = 8 x 7 x 6 x 5 = 1680
Answer: (D) 1680
Question: A company, Chauncy Co., has an annual travel budget of $58,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
(A) Expenses will not go over the budget.
(B) $2,725
(C) $4,225
(D) $5,725
(E) $60,725
Rationale: annual travel budget of $58,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 55000-60725 = 2725
Answer: Option B
Answer: (B) $2,725
Question: In a class there are 60% of girls of which 25% poor. What is the probability that a poor girl is selected is leader?
(A) 22
(B) 15
(C) 77
(D) 17
(E) 11
Rationale: Assume total students in the class = 100
Then Girls = 60% (100) = 60
Poor girls = 25% (60) = 15
So probability that a poor girls is selected leader = Poor girls / Total students = 15/100 = 15%
Answer:B
Answer: (B) 15
Question: Find the middle one when The sum of three consecutive even numbers is 36?
(A) 10
(B) 12
(C) 14
(D) 15
(E) 18
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: (B) 12
Question: Sum of two numbers prime to each other is 12 and their L.C.M. is 35. What are the numbers?
(A) 8 and 4
(B) 7 and 5
(C) 6 and 5
(D) 8 and 5
(E) 6 and 5
Rationale: As two numbers are prime, only options satisfy ie option B and C and D,E
but option A will not make the product of numbers i.e 35
ANSWER:B
Answer: (B) 7 and 5
Question: If the charge of staying in a student youth hostel $18.00/day for the first week, and $14.00/day for each additional week, How much does it cost to stay for 23 days?
(A) $160
(B) $350
(C) $282
(D) $274
(E) $286
Rationale: Total number of days of stay = 23
Charge of staying in first week = 18*7 = 126 $
Charge of staying for additional days =(23-7)*14 = 16*14 = 224 $
Total charge =126 +224 = 350$
Answer B
Answer: (B) $350
Question: The difference of 6 hours 45 minutes and 3 hours 15 minutes is approximately what percent of a day?
(A)  approx 15%
(B)  approx 16%
(C)  approx 24%
(D)  approx 28%
(E)  approx 72%
Rationale: Since the question is asking for an approximate percentage
6:45 - 3:15 ~ 3:30 hours
% of day = 3.5*100/24 ~ 15%
Answer is A.
Answer: (A)  approx 15%
Question: A and B together have Rs. 1210. If of A's amount is equal to of B's amount, how much amount does B have?
(A) 484
(B) 448
(C) 844
(D) 848
(E) 884
Rationale: 4/15 A = 2/5 B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
Therefore, B's share = Rs. (1210 x 2/5)= Rs. 484.
Answer is A.
Answer: (A) 484
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 9 years and that for 15 years?
(A) 2:6
(B) 3:5
(C) 1:4
(D) Data inadequate
(E) None of these
Rationale: Let the principal be P and rate of interest be R%.
∴ Required Ratio = [(P×R×9/100) /(P×R×15/100)]=9PR/15PR=9/15=3:5
Answer B
Answer: (B) 3:5
Question: 5% people of a village in a country died by violence, 15% of the remaining left the village on account of fear. If now the population is reduced to 3553, how much was it at the beginning?
(A) 5000
(B) 4400
(C) 3400
(D) 5500
(E) 6000
Rationale: x=> x*95/100*85/100 = 3553
= x = 4400
ANSWER B
Answer: (B) 4400
Question: In what time will a train 100 m long cross an electric pole, it its speed be 90 km/hr?
(A) 2.5 sec
(B) 2.8 sec
(C) 8.5 sec
(D) 2.2 sec
(E) 4 sec
Rationale: Speed = 90 * 5/18
= 25 m/sec
Time taken = 100/25
= 4 sec.
Answer:E
Answer: (E) 4 sec
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 8 boys when a boy gets any no. of prizes?
(A) 55
(B) 512
(C) 510
(D) 540
(E) 70
Rationale: Ans.(B)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 8 ways, i.e. (8 x 8x 8) ways = 83 ways = 512 ways Or nr ways = 83 ways = 512 ways
Answer: (B) 512
Question: The train consists of 6 carriages, 20 meters long each. The gap between the carriages is 1 meter. If the train is moving at a constant speed of 60 km/h, how much time will it take the train to run through a 1 kilometer tunnel?
(A) 1^1/8 minutes
(B) 1^1/2minutes
(C) 1^3/4 minutes
(D) 2 minutes
(E) 2^1/4 minute
Rationale: The length of the train is 6∗20 plus five 1 meter gaps, so it's 6∗20+5=125 meters;
The length that should be traveled by train is 1+0.125=1.125 kilometers;
Time=Distance/ Rate=1.125/60 hours or 1.125/60∗60=1.125=1^1/8minutes.
Answer: A
Answer: (A) 1^1/8 minutes
Question: The compound ratio of 2:3, 3:4 and 4:5?
(A) 1:2
(B) 2:5
(C) 3:4
(D) 3:5
(E) 3:9
Rationale: 2/3 * 3/4 * 4/5 = 2/52:5Answer: B
Answer: (B) 2:5
Question: On a baseball team, 6 players including Alice want to play 1st base, 2nd base, or 3rd base. Before every game, the coach chooses a name randomly from a bag and this person plays 1st base. Then the coach chooses the next name randomly and this person plays 2nd base. The coach then chooses a third name randomly and this person plays 3rd base. What is the probability that Alice plays 1st, 2nd, or 3rd base?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: The total number of ways to choose three players is 6C3=20.
Excluding Alice, the number of ways to choose three players is 5C3=10.
P(Alice is not chosen)=10/20=1/2.
P(Alice is chosen)=1 - 1/2 = 1/2.
The answer is C.
Answer: (C) 1/2
Question: If a man travels f miles an hour for t hours and r kilometers an hour for s hours, what is his average rate in kilometers per hour for the entire distance traveled?
(A) ft + rs kms/hr
(B) (ft + rs)/2 kms/hr
(C) t/f + s/r kms/hr
(D) (ft + rs)/(t + s) kms/hr
(E) (ft + rs)/(t - s) kms/hr
Rationale: Average Speed = Total Distance /Total Time Taken
Total Distance travelled in t hours = ft
Total Distance travelled in s hours = rs
Total Time taken = t+s
Therefore , Average Speed = (ft+ts)/(t+s) kms/hr
Answer D
Answer: (D) (ft + rs)/(t + s) kms/hr
Question: In Arun's opinion, his weight is greater than 65 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?
(A) 55.5 kg
(B) 66.5 kg
(C) 77.5 kg
(D) 88.5 kg
(E) None of these
Rationale: Explanation:
Let Arun's weight be X kg.
According to Arun, 65 < X < 72.
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg Answer: B
Answer: (B) 66.5 kg
Question: A palindrome is a number that reads the same forward and backward, such as 124. How many odd, 4-digit numbers are palindromes?
(A) 40
(B) 45
(C) 50
(D) 60
(E) 2500
Rationale: A palindrome is a number that reads the same forward and backward. Examples of four digit palindromes are 1221, 4334, 2222 etc
You basically get to choose the first two digits and you repeat them in opposite order. Say, you choose 45 as your first two digits. The next two digits are 54 and the number is 4554.
Also, you need only odd palindromes. This means that you need an odd digit at the end i.e. 1/3/5/7/9. This means that you need to start the number with an odd digit. Only then will it end with an odd digit.
In how many ways can you pick two digits such that the first one is an odd digit?
The first digit can be selected in 5 ways.(1/3/5/7/9)
The second digit can be selected in 10 ways.(0/1/2/3...8/9)
Total = 5*12 = 60 ways
D
Answer: (D) 60
Question: . A boy has four trousers and 7 shirts. In how many different ways can he select a trouser and a shirt?
(A) 18
(B) 20
(C) 26
(D) 28
(E) 30
Rationale: Explanation:
The boy can select one trouser in four ways.
The boy can select one shirt in 7 ways.
The number of ways in which he can select one trouser and one shirt is 4 * 7 = 28 ways.
Answer: Option E
Answer: (E) 30
Question: A train passes a station platform in 32 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) 160
(B) 180
(C) 200
(D) 220
(E) 240
Rationale: The speed of the train is 54 * 5/18 m/s = 15 m/s
The length of the train is 15 x 20 = 300 m
platform + 300 = 15 * 32
platform = 480 - 300 = 180
The answer is B.
Answer: (B) 180
Question: Every day Daniel drives 100 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?
(A) 10%
(B) 28%
(C) 33%
(D) 42%
(E) 52%
Rationale: Let's TEST X = 4....
On Sunday, Daniel drove 100 miles at 4 miles/hour.
D = (R)(T)
100 = (4)(T)
100/4 = 25 = T
It takes 25 hours to drive home
On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (68 miles) at 4/2 = 2 miles/hour
D = (R)(T)
32 = (8)(T)
32/8 = 4 = T
It takes 4 hours for the first part
D = (R)(T)
68 = (2)(T)
68/2 = 34 = T
It takes 34 hours for the second part
Total time to drive home on Monday = 4+34 = 38 hours
We're asked by what percent 38 hours is greater than 25 hours.
38/25 = 1.52, so it is 52% greater.
E
Answer: (E) 52%
Question: a percent of b is c and c percent of d is e, then a is what percent of e?
(a, b, c, d, e > 0)
(A) bd/1000
(B) 10000/bd
(C) 10000 bd
(D) bd/1000
(E) 1000000/bd
Rationale: Given:
a/100∗b=c
c/100∗d=e
substitute c in 2nd equation with LHS of the first
a∗b/100∗d/100=e
abd/100=100e
a=100e∗100/bda
convert this into a percent
1000000/bd of e.
Answer- E
Answer: (E) 1000000/bd