mathewhe/aqua_rat huggingface dataset:
Question: A cyclist traveled for two days. On the second day the cyclist traveled 3 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling, what was her average speed on the second day?
(A) 5 mph
(B) 10 mph
(C) 20 mph
(D) 30 mph
(E) 40 mph
Rationale: SOLUTION:
D = 280 Mi
T = 12 hrs
Day 1 time = T1
Day 2 time = T2
T2 - T1 = 4 hrs ----- (I)
T1 + T2 = 12 hrs ----- (II)
Adding I and II, T2 = 8 hrs and T1 = 4 hrs
Day 1 Rate = R1
Day 2 Rate = R2
R1 - R2 = 10 mph
i.e. R1 = 10 + R2
280 = 8R2 + 4R1
i.e. 280 = 8R2 + 4 (10 + R2)
i.e. R2 = 20 mph
ANSWER: B
Answer: (B) 10 mph
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 161 hats in this group, how many of these hats are not blue?
(A) 28
(B) 42
(C) 48
(D) 112
(E) 76
Rationale: Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be
7x+4x+12x=161 or 23x=161...here 7x,4x and 12x represent hats of each type
23x=161 so x=7...Blue hats =7*7=49...Not blue will be 161-49=112.
Ans D
Answer: (D) 112
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) 288
(B) 992
(C) 678
(D) 480
(E) 131
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer:D
Answer: (D) 480
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
(A) 3
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: (A) 3
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
(A) 1:2
(B) 1:3
(C) 2:1
(D) 1:4
(E) 1:5
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:30000×9
=45×12:30×9
=3×12:2×9
=2:1
Answer is C.
Answer: (C) 2:1
Question: 54.327 × 357.2 × 0.0057 is the same as :
(A) 5.4327 × 3.572 × 5.7
(B) 5.4327 × 3.572 × 0.57
(C) 5.4327 × 3.572 × 0.0000057
(D) None of these
(E) Cannot be determined
Rationale: Solution
Number of Decimal places in the given expression =8 .
Number of Decimal places in (a) = 8 .
Number of Decimal places in (b) =9 .
Number of Decimal places in (c) = 7 .
Number of Decimal places in (a) is the same as the given expression . Answer A
Answer: (A) 5.4327 × 3.572 × 5.7
Question: A bag contains 4 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
(A) 8/15
(B) 2/5
(C) 3/5
(D) 11/15
(E) 17/33
Rationale: Drawing two balls of same color from four green balls can be done in 4C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = 4C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 17/33
ANSWER:E
Answer: (E) 17/33
Question: If 100<x<190 and 10<y<100, then the product xy CANNOT be equal to:
(A) 18,104
(B) 18,303
(C) 18,356.732
(D) 19,502
(E) 18,909
Rationale: Correct Answer: (D)
Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 100 * 10. The largest value must be less than 190 * 100. This means that 1000 < xy < 19,000. (D) is outside of this range, so it is not a possible product of xy.
Answer: (D) 19,502
Question: A teacher prepares a test. She gives 6 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 3 questions have 3 choices and the last 3 have 4 choices.
(A) 255
(B) 1816
(C) 1872
(D) 100
(E) 144
Rationale: Two cases.
First Case: 2 Questions - 3 Choices, 2 Questions - 4 Choices
3C2 * 3C2 ways to select the questions
3C1 * 3C1 * 4C1 * 4C1 ways to answer the questions
= 3 * 3 * 3 * 3 * 4 * 4
=1296
Second Case: 1 Question - 3 Choices, 3 Questions - 4 Choices
3C1 * 3C3 ways to select the questions
3C1 * 4C1 * 4C1 * 4C1 ways to answer the questions
= 3 * 1 * 3 * 4 * 4 * 4
= 576
Total = 1296 + 576
= 1872
C
Answer: (C) 1872
Question: Find 356 x 936 - 356 x 836 = ?
(A) 35600
(B) 34500
(C) 49630
(D) 93600
(E) None
Rationale: Answer
356 x 936 - 356 x 836 = 356 x (936 - 836 )
= 356 x 100
= 35600.
Option: A
Answer: (A) 35600
Question: The milk level in a rectangular box measuring 64 feet by 25 feet is to be lowered by 6 inches. How many gallons of milk must be removed? (1 cu ft = 7.5 gallons)
(A) 100
(B) 250
(C) 750
(D) 5625
(E) 6000
Rationale: 6 inches = 1/2 feet (there are 12 inches in a foot.), so 64*25*1/2=800 feet^3 of milk must be removed, which equals to 800*7.5=6000 gallons.
Answer: E.
Answer: (E) 6000
Question: 7 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
(A) 40
(B) 48
(C) 45
(D) 42
(E) 22
Rationale: Though 2*(7C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.
The first guy has to play 2 matches with the rest of 6, so he'll play 12matches.
Similarly, second guy has to play with the rest of 5 as his 2 games with the first guy are already played. So he plays 10 matches.
This continues like this and the total matches are 12+10+8...+2
12+10+...+2 = 2(6+5+...+1) = 2((6*7)/2) = 6*7 =42.
ANSWER:D
Answer: (D) 42
Question: P can do a certain work in 16 days. Q is 60% more efficient than P. How many days does Q alone take to do the same job?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Each day, P can do 1/16 of the work.
Each day, Q can do 1.6/16 of the work = 16/160 of the work
The time taken by B alone to complete the total work is 160/16 = 10 days.
The answer is C.
Answer: (C) 10
Question: A can do a piece of work in 15 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
(A) 11 3/9
(B) 19 3/7
(C) 11 3/5
(D) 11 3/7
(E) 11 3/1
Rationale: (x – 5)/15 + x/20 = 1
x = 11 3/7 days
Answer:D
Answer: (D) 11 3/7
Question: If KING is coded as 17 and MASS is coded as 29 Then DON is coded as
(A) 21
(B) 20
(C) 18
(D) 16
(E) None of these
Rationale: KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17
MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29
DON = 4+14+15=33 i.e(3*3)+(3*3)=18
ANSWER:C
Answer: (C) 18
Question: In March, Kurt ran an average of 1.2 miles an hour. If by June he had increased his pace by 20 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June?
(A) 3590/60^2
(B) 2980/60^2
(C) 2390/60^2
(D) 3586/60
(E) 60^2/3590
Rationale: Kurt ran at an average of 1.2 miles/hour in march. So to run 1 mile he would take 1/1.2 hours = (60 * 60)/1.2 seconds = 3000 seconds.
If he increases his speed by 20 seconds, he will complete a mile in 2980 seconds. Converting in hours = 2980/(60 * 60) = 2980/(60^2)
ANSWER: B
Answer: (B) 2980/60^2
Question: A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $19 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item?
(A) $27.50
(B) $28.50
(C) $29.50
(D) $30.50
(E) $31.50
Rationale: Let x be the price that buyers see online.
The distributor wants to receive 1.2(original price) which should be 80% of x.
1.2(19) = 0.8x
x = 1.2(19) / 0.8 = 1.5(19) = $28.50
The answer is B.
Answer: (B) $28.50
Question: A person takes 5 hrs 45 min in walking to a place and riding back. He would have gained 4 hrs by riding both ways. The time he would take to walk both ways is?
(A) 5 hours 45 min
(B) 5 hours 55 min
(C) 6 hours 45 min
(D) 9 hours 45 min
(E) 10 hours
Rationale: ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 4 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 4 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 4 hours = 9 hours 45 min
D
Answer: (D) 9 hours 45 min
Question: Find the area of a parallelogram with base 12 cm and height 8 cm?
(A) 96 cm2
(B) 104 cm2
(C) 78 cm2
(D) 86 cm2
(E) 76 cm2
Rationale: Area of a parallelogram = base * height = 12 * 8
= 96 cm2
Answer:A
Answer: (A) 96 cm2
Question: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 25 p coins are there?
(A) 20
(B) 30
(C) 25
(D) 50
(E) 40
Rationale: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
Then, sum of their values = (25 x/100) + (20 x/100) + (15 x/100)
= 60 x /100
30 = 60 x / 100
x = 50 = 25 p coin
Ans - D
Answer: (D) 50
Question: A train 200 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line in seconds
(A) 12 sec
(B) 6 sec
(C) 7 sec
(D) 8 sec
(E) 9 sec
Rationale: Explanation:
Speed of the train = (60 x 5/18m / sec = 50/3 m/ sec.
Distance moved in passing the standing man = 100 m.
Required time taken = 200/(50/3) = (200 Ã—(3/50)) sec =12 sec
Answer: Option A
Answer: (A) 12 sec
Question: In a store, the profit is 320% of the cost. If the cost increases by 25% but the SP remains constant, approximately what %of the sp is the profit?
(A) 50%
(B) 70%
(C) 90%
(D) 100%
(E) 140%
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
B
Answer: (B) 70%
Question: If a - b = 5 and a2 + b2 = 29, find the value of ab.
(A) A)2
(B) B)12
(C) C)15
(D) D)18
(E) E)20
Rationale: Explanation:
2ab = (a2 + b2) - (a - b)2
= 29 - 25 = 4
ab = 2.
Answer: A
Answer: (A) A)2
Question: The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one year old child. What is the average age of the family ?
(A) 21 years
(B) 20 years
(C) 18 years
(D) 19 years
(E) 17 years
Rationale: after 5 years the average age of the two will be 28.
now the child is one year old ,
total age = 28*2 + 1 = 57
average age = total age/family members(3)
=> 57/3 = 19
ANSWER:D
Answer: (D) 19 years
Question: If n = 8^8 – 7, what is the units digit of n?
(A) 0
(B) 1
(C) 2
(D) 7
(E) 4
Rationale: 8 ^ 8 - 8 = 8 (8 ^ 7 - 1)
==> 8 (2 ^ 21 - 1)
Last digit of 2 ^ 21 is 2 based on what explanation LiveStronger is saying. 2 ^ 24 - 1 yields 2 - 1 = 1 as the unit digit. Now on multiply this with 7, we get unit digit as 7
Answer : D
Answer: (D) 7
Question: 9.009/5.005 =
(A) 1.08
(B) 1.4
(C) 1.8018
(D) 1.4014
(E) 1.8
Rationale: 9.009/5.005 = 9009/5005 = 9(1001)/5(1001) = 9/5 = 1.8
The answer is E.
Answer: (E) 1.8
Question: Which of the following describes all values of x for which 36–x^2 >= 0?
(A)  x >= 1
(B)  x <= –1
(C)  -6 <= x <= 6
(D)  x <= –1 or x >= 1
(E)  –1 <= x <= 1
Rationale: 36 - x^2 >=0
means x^2 - 36 <=0
=> (x-6)(x+6) <= 0
=> -6 <= x <= 6
Answer - C
Answer: (C)  -6 <= x <= 6
Question: In a certain accounting class of 100 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 55%, and the students on the make-up date had an average score of 95%, what was the average score for the entire class?
(A) 60%
(B) 65%
(C) 67%
(D) 70%
(E) 75%
Rationale: 70% of the class scored 55% and 30% of the class scored 95%.
The difference between 55% and 95% is 40%.
The average will be 55% + 0.3(40%) = 67%.
The answer is C.
Answer: (C) 67%
Question: If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day?
(A) 10
(B) 15
(C) 20
(D) 25
(E) None of them
Rationale: Let the required number of days be x.
More men, Less days (indirect proportion)
Less hours per day, More days (indirect proportion)
Men 18 : 15
Hours per day 8: 9 } : :16 : x
(18 x 8 x x)=(15 x 9 x 16)= x=(44 x 15)144 = 15
Hence, required number of days = 15.
Answer is B.
Answer: (B) 15
Question: The average of 50 numbers id 44. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :
(A) 22.35
(B) 33.25
(C) 22.25
(D) 11.35
(E) 43.75
Rationale: Explanation:
Total of 50 numbers = (50×44)=2200
Total of 48 numbers =(2200-(45+55)]=2100
Required average = 2100/48=43.75
Answer:E
Answer: (E) 43.75
Question: 10% of inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants let the village. The population is then reduced to 4050. Find the original inhabitants
(A) 5500
(B) 6000
(C) 6500
(D) 7000
(E) 8000
Rationale: Explanation:
Let the total number is x,
then,
(100-25)% of (100 - 10)% x = 4050
=> 75% of 90% of x = 4050
=> 75/100 * 90/100 * x = 4050
=> x = (4050*50)/27 = 6000
Answer: Option B
Answer: (B) 6000
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is?
(A) 9
(B) 11
(C) 15
(D) 12
(E) 20
Rationale: Age of the 15th student = 15*15 - (14*5+16*9) = 225-214 = 11 years
Answer is B
Answer: (B) 11
Question: Which of the following is a multiply of 4 number ?
(A) 120
(B) 130
(C) 45
(D) 82
(E) 17
Rationale: Explanation :
120 is a perfect multiply of 4
Answer : Option A
Answer: (A) 120
Question: There is a group of persons each of whom can completea piece of work in 16 days, when they are working individually. On the 1st day 1 person works, on the second day another person joins him, on the third day one more person joins them & this process continues till the work is completed. How many days are needed to complete the work?
(A) 5 1⁄2 days
(B) 5 1⁄3 days
(C) 5 1⁄6 days
(D) 6 1⁄6 days
(E) 7 1⁄6 days
Rationale: Work completed in 1st day = 1/16
Work completed in 2nd day = (1/16) + (1/16) = 2/16
Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16
…
An easy way to attack such problems is from the choices. You can see the choices are
very close to each other. So just see one by one.
For instance, The first choice given in 3 1⁄4
The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16
The work done in 4 days = (1+2+3+4)/16 = 10/16
The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?
The work done in 6 days = (1+2+3+4+5+6)/16 > 1
Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days.
(Just for your reference, work done in 5 days = 15/16.
Pending work in 6th day = 1 – 15/16 = 1/16.
In 6th day, 6 people are working and work done = 6/16.
To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.
Hence total time required = 5 + 1/6 = 5 1⁄6 days
C
Answer: (C) 5 1⁄6 days
Question: What is the units digit of 6^m(2^7+1), for a positive integer m?
(A) 1
(B) 3
(C) 4
(D) 7
(E) 0
Rationale: Equation can be re-written as
6^m( 2^7 + 1)
=6^m ( 128 + 1)
=6^m (129)
Now, putting m= 0 ; Eqn = 129
putting m= 1 ; Eqn = 129. 6
putting m= 2 ; Eqn = 129 .36
putting m= 3 ; Eqn = 129 .216
We can see that there lies a pattern while multiplying 129 with multiples of 6 , units digit is always going to be 4
ANSWER:C
Answer: (C) 4
Question: Bill has a collection of new and used trading cards that he stores in two albums. His first album contains 200 cards, 60% of which are used. If 90% of the cards in his second album are used, and 65% of all of his cards are used, what is the total number of trading cards in Bill’s collection?
(A) 290
(B) 260
(C) 254
(D) 240
(E) 156
Rationale: Let, Total Cards in second collection = B
(60/100)*200 + (90/100)*B = (65/100)*(200+B)
i.e. B = 40
i.e Total cards = 200+B = 240
Answer: OPtion D
Answer: (D) 240
Question: Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 20 days.
(A) 12 days.
(B) 17 days.
(C) 18 days.
(D) 19 days.
(E) 20 days.
Rationale: They together completed 4/10 work in 4 days.
balance 6/10 work will be completed by Arun alone in 20*6/10 = 12 days.
ANSWER:A
Answer: (A) 12 days.
Question: 9, 35, 91, 189, 341, ?
(A) 502
(B) 521
(C) 559
(D) 611
(E) 712
Rationale: Explanation :
13 + 23 = 9
23 + 33 = 35
33 + 43 = 91
43 + 53 = 189
53 + 63 = 341
63 + 73 = 559
Answer : Option C
Answer: (C) 559
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
(A) 21 (1/8)kmph
(B) 21 (1/3)kmph
(C) 21 (7/3)kmph
(D) 27 (1/3)kmph
(E) 21 (1/8)kmph
Rationale: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph
= 21 (1/3)kmph.
Answer:B
Answer: (B) 21 (1/3)kmph
Question: A team of four entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
(A) 288
(B) 329
(C) 168
(D) 127
(E) 664
Rationale: Explanation:
4 * 84 =336 - 7 = 329
Answer:B
Answer: (B) 329
Question: Product of two natural numbers is 5. Then, the sum of reciprocals of their squares is
(A) 290/289
(B) 26/25
(C) 290/90
(D) 290/19
(E) None of these
Rationale: Explanation:
If the numbers are a, b, then ab = 5,
as 17 is a prime number, so a = 1, b = 5.
1/a2+1/b2=1/1(2)+1/5(2)
=26/25
Option B
Answer: (B) 26/25
Question: In how many ways can the letters of the word WORDS be arranged in a row so that the vowels appear in alphabetic order?
(A) 210
(B) 120
(C) 180
(D) 220
(E) 160
Rationale: three letters can be arranged in ! ways.
only one combination AEI is required.
5 letters can be arranged in 5! ways.
thus 5!/ 1! * 1 = 120.
B
Answer: (B) 120
Question: Raj and Roshan has some money with them in the ratio 5:4 respectively. If Raj has Rs. 45. How much money Raj has more than Roshan?
(A) 5
(B) 9
(C) 16
(D) 12
(E) 18
Rationale: Let the money Roshan has be x then (45/x)=5/4
Upon cross multiplication and solving for x we get x=36
So Raj has Rs. 9 more than Roshan
Answer:B
Answer: (B) 9
Question: The average of seven numbers is 20. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
(A) 27
(B) 29
(C) 31
(D) 41
(E) 35
Rationale: The total of seven numbers = 7X20 = 140
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (140 - 99 ) = 41
D
Answer: (D) 41
Question: An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,395, what was the total number of pairs of contact lenses that she sold?
(A)  11
(B)  13
(C)  15
(D)  17
(E)  19
Rationale: (x+5)*150 +x*85=2395
=>x=7
total lens=7+(7+5)= 19
Answer E
Answer: (E)  19
Question: A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 km/h and the speed of the boat in still water is 14 km/h, what is the distance between A and B?
(A) 200 km
(B) 180 km
(C) 160 km
(D) 220 km
(E) None of these
Rationale: Speed of boat for downstream = 14 + 4 = 18 km/hr
Speed of boat for upstream = 14 – 4 = 10 km/hr
Distance = x
x / 18 + (x /2)/10 = 19
x = 180 km
Answer: B
Answer: (B) 180 km
Question: With the money I have , I can buy 50 pens or 150 pencils. I kept 10% aside for taxi fare. With the remaining , I purchased 54 pencils and P pens. What is the value of P?
(A) 32
(B) 30
(C) 27
(D) 25
(E) 23
Rationale: Since cost of, 50 pens = 150 pencils, With the cost of 3 pencils I can buy 1 pen. After
putting aside 10% for taxi I was left with 90% of the money , with which I can buy 135
pencils (90% of 150) or 45(90% of 50) pens, I bought 54 pencils and P pens, or I could have
bought ( 54 +3P ) pencils ,
54 +3P =135, 3P = 135-54 =81, P =27
ANSWER:C
Answer: (C) 27
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
(A) 2992
(B) 2882
(C) 1200
(D) 2999
(E) 2123
Rationale: CP* (76/100) = 912
CP= 12 * 100 => CP
= 1200
Answer: C
Answer: (C) 1200
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
(A) 3 9/16 hrs
(B) 3 9/19 hrs
(C) 3 9/17 hrs
(D) 3 3/17 hrs
(E) 4 9/17 hrs
Rationale: Net part filled in 1 hour = 1/5 + 1/6 - 1/12
= 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.
Answer:C
Answer: (C) 3 9/17 hrs
Question: A basket has 7 apples and 5 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is
(A) 45/99
(B) 43/99
(C) 42/99
(D) 49/99
(E) 52/99
Rationale: Total fruits = 12Since there must be at least two apples,(7C3 * 5C1)/12C4 + 7C4/12C4 = 42/99.Answer:C
Answer: (C) 42/99
Question: What is the product of all the prime factors of 21?
(A) 20
(B) 21
(C) 18
(D) 17
(E) 16
Rationale: factors : 1,3,7,21
3*7 =21
Answer : B
Answer: (B) 21
Question: In the Land of Oz only one or two-letter words are used. The local language has 67 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?
(A) 65
(B) 66
(C) 67
(D) 131
(E) 134
Rationale: The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...
The number of 1 letter words (X) that can be made from 67 letters is 67;
The number of 2 letter words (XX) that can be made from 67 letters is 67*67, since each X can take 67 values.
Total: 67+67*67.
Similarly:
The number of 1 letter words (X) that can be made from 66 letters is 66;
The number of 2 letter words (XX) that can be made from 66 letters is 66*66, since each X can take 66 values.
Total: 66+66*66.
The difference is (67+67*67)-(66+66*66)=134.
Answer: E.
Answer: (E) 134
Question: Two whales are moving in the same direction at 18 mps and 15 mps. The faster whale crosses the slow whale in 15 seconds. What is the length of the slower whale in meters?
(A) 45 m
(B) 56 m
(C) 39 m
(D) 33 m
(E) 62 m
Rationale: Relative speed = (18 - 15) = 3 mps.
Distance covered in 15 sec = 15 * 3 = 45 m.
The length of the faster train = 45 m.
Answer: A
Answer: (A) 45 m
Question: Little Krish had $200.50. He spent $35.25 on sweets and gave to his two friends $25.20 each. How much money was left?
(A) $220.85
(B) $214.85
(C) $ 114.85
(D) $314.85
(E) $104.85
Rationale: Krish spent and gave to his two friends a total of
35.25 + 25.20 + 25.20 = $85.65
Money left
200.50 - 85.65 = $114.85
correct answer is C) $ 114.85
Answer: (C) $ 114.85
Question: The salary of A, B, C, D, E is Rs. 9000, Rs. 5000, Rs. 11000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is
(A) Rs. 7000
(B) Rs. 8200
(C) Rs. 8500
(D) Rs. 9000
(E) None
Rationale: Answer
Average salary
= 9000 + 5000 + 11000 + 7000 + 9000 / 5
= Rs. 8200
Correct Option: B
Answer: (B) Rs. 8200
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 14 cm
(A) 178 cm2
(B) 179 cm2
(C) 266 cm2
(D) 167 cm2
(E) 197 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (14)
= 266 cm2
Answer: C
Answer: (C) 266 cm2
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) 338
(B) 77
(C) 298
(D) 540
(E) 882
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer: D
Answer: (D) 540