mathewhe/aqua_rat huggingface dataset:
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) 17/26
(B) 17/22
(C) 17/22
(D) 17/29
(E) 17/12
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) 17/29
Question: In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent of her bushes have only yellow roses?
(A) 20
(B) 30
(C) 50
(D) 70
(E) 80
Rationale: let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x
if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T
we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers
so, 0.8T+x=T
x=0.2T
so, 1.5x=0.3T
30% flowers are yellow flowers
ANSWER:B
Answer: (B) 30
Question: It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill one sixteenth of the dish?
(A) 16 days
(B) 26 days
(C) 27 days
(D) 28 days
(E) 29 days
Rationale: The bacteria doubles each day, so after 29 days, the dish was half full.
After 28 days, the dish was one quarter full.
After 27 days, the dish was one eighth full.
After 26 days, the dish was one sixteenth full.
The answer is B.
Answer: (B) 26 days
Question: A bullet train passes a station platform in 36 seconds and a man standing on the platform in 21 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?
(A) 240 m
(B) 220 m
(C) 260 m
(D) 225 m
(E) 239 m
Rationale: A
225 M
Speed = 54 x 5/18 = 15 m/s
Length of the bullet train = (15 x 21)m = 315 m.
Let the length of the platform be x metres.
Then, (x + 315)/36 = 15
--> x + 315 = 540
x = 225m. D
Answer: (D) 225 m
Question: There was one mess for 30 boarders in a certain hostel. The number of boarders being increased by 10, the expenses of the mess were increased by Rs 40 per month while the average expenditure per head diminished by Rs 2. Find the original monthly expenses.
(A) Rs 390
(B) Rs 410
(C) Rs 360
(D) Cannot be determined
(E) None of these
Rationale: Let X rupees be the average of 30 boarders
30X + 40= (X - 2) x 40
X = 12
Hence, original expenditure
= Rs 12 x 30 = Rs 360.
ANSWER:C
Answer: (C) Rs 360
Question: In the biology lab of "Jefferson" High School there are 3.24*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?
(A) 300
(B) 200
(C) 500
(D) 1000
(E) 5000
Rationale: 3.24*10^6/ 10800==> 32.4*10^3/108==> 32400/108= 300
ANSWER:A
Answer: (A) 300
Question: A person crosses a 1440 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) 7.2
Rationale: Speed = 1440/(12x60) m/sec
= 2 m/sec.
Converting m/sec to km/hr =2 x(18/5) km/hr
= 7.2 km/hr.
ANSWER :E
Answer: (E) 7.2
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.
(A) profit of Rs. 202
(B) profit of Rs. 211
(C) profit of Rs. 128
(D) profit of Rs. 200
(E) profit of Rs. 219
Rationale: Explanation:
Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
Answer:E
Answer: (E) profit of Rs. 219
Question: There are 12 dozen mangoes in a box. If there are 25
such boxes, how many mangoes are there in all the
boxes together?
(A) 3600
(B) 3096
(C) 6192
(D) 628
(E) None
Rationale: Number of mangoes = 12 dozens
= 12 × 12 = 144
∴ Number of mangoes in 25 boxes
= 25 × 144 = 3600
Answer A
Answer: (A) 3600
Question: Marge has Z candies, where Z is an integer such that 20 < Z< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: If Marge divides the candies equally among 5 children, she will have 2 candies remaining.
This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47
If she divides the candies among 6 children, she will have 1 candy remaining.
this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49
ONLY 37 is common, so candies are 37 in number..
if 37 is divided in 7 kids, remainder Z= 2
C
Answer: (C)  2
Question: 9, 16, 17, 25, 36,49
(A) 9
(B) 16
(C) 17
(D) 25
(E) 36
Rationale: Each of the numbers except 17, is perfect square.
Answer: Option C
Answer: (C) 17
Question: What distance (in meters) will be covered by a bus moving at 72 km/hr in 38 seconds?
(A) 720
(B) 760
(C) 800
(D) 840
(E) 880
Rationale: 72 km/hr = 72 * 5/18 = 20 m/s
distance = 20 * 38 = 760 meters
The answer is B.
Answer: (B) 760
Question: If $200 invested at a certain rate of simple interest amounts to $240 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years?
(A) $190
(B) $180
(C) $200
(D) $240
(E) $210
Rationale: 200 amounts to 240 in 3 years.
i.e (principal + interest ) on 120 in 3 years = 240
200 + 200*(r/100)*(3) = 240 => r = 20/3
150 in 6 years = principal + interest
= 150 + 150*(r/100)*(6)
=210
Answer is E.
Answer: (E) $210
Question: Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements W.
(A) a) 48
(B) b) W=144
(C) c) W=240
(D) d) W=288
(E) e) 120
Rationale: One specificboy is seated to either of end seat, lets call him b1
One specificgirl is seated in the middle, lets call her g1
Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.
b1 can be seated 2 different seats : 2!
g1 is seated on the seat #4, fixed (no other alternative) : 1
the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!
2! x 1 x 5! = 240
Answer C
Answer: (C) c) W=240
Question: Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 222 grams of compound X?
(A) 54
(B) 185
(C) 250
(D) 270
(E) 322
Rationale: total number of fractions =2+10=12
element B constitutes =10 out of 12 parts of X
So in 222 gms of X have 222*10/12=185 gms of B
and 222-185=37 gms of A.
cross check:- A/B = 37/185 =2/10 (as given)
Ans B
Answer: (B) 185
Question: If positive integers x and y are not both odd, which of the following must be even?
(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1
Rationale: Positive integers x and y are NOT both odd, means that either both x and y are even or one is even and the other one is odd. In either case xy must be even.
Answer: A.
Answer: (A) xy
Question: In a coconut grove, (x + 2) trees yield 30 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 10
Rationale: (x+2)×30+x×120+(x−2)×180/(x+2)+x+(x−2)=100
⇒ 330x−300/3x = 100
⇒ 30x = 300 ⇒ x = 10
Answer E
Answer: (E) 10
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio T of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
(A) 8:3
(B) 3:2
(C) 4:3
(D) 2:3
(E) 3:8
Rationale: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio T of Ann's time to Bob's time is 3:2.
Answer: B.
Answer: (B) 3:2
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
(A) 5 : 2
(B) 7 : 3
(C) 9 : 2
(D) 13 : 4
(E) None of these
Rationale: Explanation:
Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⇒ 3x + 20 = 2x + 40
⇒ x = 20.
⇒ Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
Answer: B
Answer: (B) 7 : 3
Question: A train covers a distance of 12 km in 10 min. If it takes 12 sec to pass a telegraph post, then the length of the train is?
(A) 100
(B) 260
(C) 120
(D) 240
(E) 140
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 12 = 240 m.
Answer: Option D
Answer: (D) 240
Question: If a and b are negative integers, which of the following statements must be true?
I. (-a)^b is positive.
II. (-a)^(-b) is positive.
III. a^(-b) is positive.
(A) None
(B) II only
(C) I and II only
(D) I and III only
(E) I, II and III
Rationale: Let's a = -2 and b = -3
I. (-a)^b = (2)^(-3) = 1/(2^3) --> Positive
II. (-a)^(-b) is positive. = 2^3 --> Positive
III. a^(-b) is positive. = -2^3 --> Negative
Answer: C
Answer: (C) I and II only
Question: Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
(A) 1 hour
(B) 2 hours
(C) 6 hours
(D) 8 hours
(E) 9 hours
Rationale: If A takes x hrs, then B takes x+6 hrs
1/x + 1/ (x+6) = 1/4
solving it, we get
x= 6 hours
ANSWER:C
Answer: (C) 6 hours
Question: Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 5 weeks have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) income over the next five weeks be to increase his average weekly income to $500 over the 10-week period?
(A) $570
(B) $586
(C) $630
(D) $686
(E) $715
Rationale: OFFICIAL SOLUTION:
(B) First, we need to add up the wages over the past 5 weeks: $406 + $413 + $420 + $436 + $395 = $2070.
To average $500 over 10 weeks, the salesman would need to earn: $500 × 10 = $5000.
Subtract $2070 from $5000 to determine how much he would need to earn, in total, over the next 5 weeks to average $500 for the 10 weeks: $5000 – $2070 = $2930.
Dividing $2930 by 5 will give us the amount he needs to earn on average over the next 5 weeks: $2930/5 = $586.
The correct answer is choice (B).
Answer: (B) $586
Question: A certain list of 100 data has an average (arithmetic mean) of 10 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 110 data with standard deviation less than d?
(A) -10 and 0
(B) 10 and 10
(C) 0 and 10
(D) 0 and 20
(E) 6 and 6
Rationale: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 10 and 10 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.
Answer: B.
Answer: (B) 10 and 10
Question: If q and k are integers whose product is 400, which of the following statements must be true?
(A) n + k > 0
(B) n is not equal to k.
(C) Either n or k is a multiple of 10.
(D) If n is even, then k is odd.
(E) If q is odd, then k is even.
Rationale: If q and k are integers whose product is 400, which of the following statements must be true?
A.n + k > 0n and k should have the same sign, but that means that they can also both be negative
B.n is not equal to k.20 x 20 = 400[i]
C.Either n or k is a multiple of 10. [i]25 x 16 = 400
D.If n is even, then k is odd.k can also be even since even x even will be even
E. If q is odd, then k is even.k must be even since odd x even = even
Answer: (E) If q is odd, then k is even.
Question: A certain number of workers can do a work in 65 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there?
(A) 55
(B) 30
(C) 28
(D) 24
(E) 32
Rationale: number of workers = 10* (65-10)/10 = 55
Answer is A
Answer: (A) 55
Question: Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 100kmph. When will Raghu overtake Anup?
(A) 8:30am
(B) 9:40am
(C) 10:00am
(D) 12:00pm
(E) 11:10am
Rationale: Suppose bike is overtaken by car xhrs after 6am
Distance covered by the bike in x hrs = distance covered by the car in x-1 hr
60x = 100(x-1)
40x = 100
x = 2.5 hrs
Required time = 6+2.5 = 8:30am
Answer is A
Answer: (A) 8:30am
Question: The average score of a cricketer for eleven matches is 45 runs. If the average for first five matches is 28, then average for last six matches is
(A) 33.25
(B) 32.25
(C) 59
(D) 60
(E) 65
Rationale: Explanation:
=(45×11)−(28×5)/6
=(495−140)/6=59
Answer: Option C
Answer: (C) 59
Question: Three table runners have a combined area of 224 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?
(A)  18 square inches
(B)  20 square inches
(C)  24 square inches
(D)  28 square inches
(E)  30 square inches
Rationale: Total = a + b + c - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither
80%*175 = 224 - 24 - 2*(all three) + 0
2*(all three) = 224 - 24 - 140
all three = 30
Answer: E
Answer: (E)  30 square inches
Question: Find the missing figures: 0.3% of ? = 0.15
(A) 50
(B) 45
(C) 150
(D) 450
(E) 500
Rationale: Let 0.3% of x = 0.15. Then , 0.30*x/100 = 0.15
X= [(0.15*100)/0.3] = 50.
Answer is A.
Answer: (A) 50
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
(A) 810
(B) 1440
(C) 2880
(D) 50400
(E) 5760
Rationale: Explanation:
In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters =	7!	= 2520.
2!
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
in	5!	= 20 ways.
3!
Required number of ways = (2520 x 20) = 50400.
ANSWER IS D
Answer: (D) 50400
Question: In 10 years,A will be 4 times as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :
(A) 13 Years
(B) 29 Years
(C) 39 Years
(D) 49 Years
(E) 59 Years
Rationale: Solution
Let B's present age = x years.Then,A's present age =(x +9) years.
âˆ´ (x + 9)+ 10 = 4 (x - 10) â‡” x + 19 = 4x- 40 â‡”3 x = 39. x=13 Answer A
Answer: (A) 13 Years
Question: If after 400 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
(A) 180 grams
(B) 220 grams
(C) 400 grams
(D) 800 grams
(E) 950 grams
Rationale: The 24% alcohol solution decreases by 1/3 once the 400 grams of water is added so 400/.08 =5000*.16% (2/3 of 24%) is 800 grams, thus answer is D.
Answer: (D) 800 grams
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
(A) 199 sec
(B) 190 sec
(C) 726 sec
(D) 127 sec
(E) 128 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10
= 190 sec.
Answer: B
Answer: (B) 190 sec
Question: In a certain pond, 80 fish were caught, tagged, and returned to the pond. A few days later, 80 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A)  400
(B)  625
(C)  3,200
(D)  4,500
(E)  10,000
Rationale: total fish = x
percentage of second catch = (2/80)*100 = 2.5%
so, x * 2.5% = 80
x = 3200 ans C.
Answer: (C)  3,200
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 2/18%
(B) 18 2/11%
(C) 18 2/91%
(D) 18 9/11%
(E) 12 2/11%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: (B) 18 2/11%
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 180 grams of water?
(A)  160
(B)  72
(C)  112
(D)  128
(E)  142
Rationale: Solution:
We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is 180
18x = 180
x = 10
Since x is 10, we know that there are 16 x 10 = 160 grams of oxygen in 180 grams of water.
Answer A.
Answer: (A)  160
Question: Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 2 minute each, how soon will the tank be filled?
(A) 2 hours
(B) 4 hours
(C) 3 hours
(D) 5 hours
(E) 6 hours
Rationale: in three minute 1/20+1/30-1/15=1/60 part is filled
6 min--------1/60 parts
x min--------- 1 part(full)
x=360 min =6 hours
ANSWER:E
Answer: (E) 6 hours
Question: If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers is :
(A) 2 :3
(B) 3 :4
(C) 3:20
(D) 20:3
(E) 22:1
Rationale: Expl : 0.4A = 0.06B -> A/B = 0.06/0.40 = 6/40 = 3/20
:. A : B = 3 : 20
Answer: C
Answer: (C) 3:20
Question: One pump drains one-half of a pond in 1 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
(A) 1 hour
(B) 1.2 hour
(C) 3 hours
(D) 5 hours
(E) 6 hours
Rationale: The tricky part here, I believed is one half hour = 1/2. Then everything would be easy.
We have the 1st pump working rate/hour = 1/2 : 1 = 1/2
Working rate of 2 pumps: 1/2 : 1/2 = 1.
Working rate of 2nd pump: 1 -1/2 = 1/2 --> Time taken for the 2nd pump to finish: 1 : 1/2 = 2/1 = 2 hours.
C
Answer: (C) 3 hours
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
(A) 27%
(B) 25%
(C) 26%
(D) 35%
(E) 29%
Rationale: 800 --- 200
100 --- ? => 25%
Answer: B
Answer: (B) 25%
Question: Efrida and Frazer who live 10 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is four miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?
(A) 6
(B) 7
(C) 8
(D) 10
(E) 11
Rationale: It's a simple geometry problem. Look at the diagram below:
Answer: A.
Answer: (A) 6
Question: Two numbers are in the ratio of 1 : 2. If 7 be added to both, their ratio changes to 3 : 5. The greater number is
(A) 20
(B) 24
(C) 28
(D) 32
(E) 36
Rationale: Let the ratio be X : Y,
Given X/Y = 1/2 ,
(X + 7)/(Y + 7) = 3/5
=> X = 14
And Y = 28
ANSWER:C
Answer: (C) 28
Question: During a trip, Francine traveled x percent of the total distance at an average speed of 25 miles per hour and the rest of the distance at an average speed of 50 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
(A) (180-x)/2
(B) (x+60)/4
(C) (300-x)/5
(D) 5000/x+100
(E) 12,000/(x+200)
Rationale: total distance =100 ;total time = T
t1 = x/25 t2 = 100-x /50
T =t1+t2 = x/25 + 100-x/50 = (50x + 2500- 25x)/1250
= (25x+2500)/1250
= x +100 / 50
av speed = 100*50/x+100 = 5000/x+100
D
Answer: (D) 5000/x+100
Question: A train passes a station platform in 42 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) 180 m
(B) 240 m
(C) 330 m
(D) 280 m
(E) 380 m
Rationale: Speed = 54 x 5/18 = 15 m/s
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/42 = 15
--> x + 300 = 630
x = 330m.
Answer : C.
Answer: (C) 330 m
Question: A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 300
(B) 266
(C) 230
(D) 288
(E) 271
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 50/3
3(x + 300) = 1800 è x = 300m.
Answer: A
Answer: (A) 300
Question: In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 4 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
(A) 23,400
(B) 60,840
(C) 67,600
(D) 45,697,600
(E) 676,000
Rationale: The choices give us the answer without any calculations--
4 one digits places can take 10*10*10*10 ways..
2 letters places can be filled up in 26*26 ways
ans= 26*26*10*10*10*10=45,697,600
ans D
Answer: (D) 45,697,600
Question: In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
(A) 3!*8!*4!*4! Ways
(B) 8!*4!*4! Ways
(C) 8!*3!*4! Ways
(D) 3!*4!*4! Ways
(E) 4!*4! Ways
Rationale: Taking all person of same nationality as one person, then we will have only three people.
These three person can be arranged themselves in 3! Ways.
8 Indians can be arranged themselves in 8! Way.
4 American can be arranged themselves in 4! Ways.
4 Englishman can be arranged themselves in 4! Ways.
Hence, required number of ways = 3!*8!*4!*4! Ways.
Option A
Answer: (A) 3!*8!*4!*4! Ways
Question: A tyre has two punctures. The first puncture alone would have made the tyre flat in 8 minutes and the second alone would have done it in 5 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
(A) 3 1/5min
(B) 3 2/5min
(C) 3 3/5min
(D) 3 4/5min
(E) 3 1/13min
Rationale: Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(1/8+1/5)=(13/40)
So both punctures will make the type flat in
(40/13)mins=3 1/13mins
Option E
Answer: (E) 3 1/13min
Question: A train 110 m long is running with a speed of 24 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 6 sec
(C) 8 sec
(D) 14 sec
(E) 13.2 sec
Rationale: Speed of train relative to man = 24 + 6
= 30 km/hr.
= 30 * 5/18 = 8.33 m/sec.
Time taken to pass the men = 110 /8.33
= 13.2 sec.
Answer:E
Answer: (E) 13.2 sec
Question: Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 29 skiers were CPR certified and 35 were not. How many skiers tried out for the ski patrol?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Not Selected = 80%
If total is x.
Then 0.8x=29+35=64
x=80
Hence answer is E.
Answer: (E) 80
Question: If the product of two positive integers is 60, which of the following could be the LCM and HCF of the two numbers? a. LCM 10 : HCF 6 b. LCM 30 : HCF 2 c. LCM 15 : HCF 4
(A) a only
(B) b only
(C) c only
(D) a,b only
(E) a,c only
Rationale: b is the correct answer.
Answer : B
Answer: (B) b only