mathewhe/aqua_rat huggingface dataset:
Question: Mercury travels around the sun at a speed of approximately 30 miles per second. The approximate speed is how many miles per hour?
(A) 108,000
(B) 96,000
(C) 84,000
(D) 72,000
(E) 60,000
Rationale: 30 * 3600 = 108,000
The answer is A.
Answer: (A) 108,000
Question: A certain bag contains 100 balls â€” 50 white, 25 green, 10 yellow, 7 red, and 8 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
(A) 0.9
(B) 0.85
(C) 0.6
(D) 0.8
(E) 0.5
Rationale: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (50 + 25 + 10)/100 =85/100 = 0.85.
Answer is B
Answer: (B) 0.85
Question: What is the are of an equilateral triangle of side 4 cm?
(A) 2√3
(B) 3√3
(C) 5√3
(D) 4√3
(E) 8√3
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 4, Area of triangle = √3/4 * 4 * 4
= 4√3 cm2;
Answer:D
Answer: (D) 4√3
Question: Two trains are moving at 40 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 41/2 sec
(B) 5/2 sec
(C) 61/2 sec
(D) 71/6 sec
(E) 49/6 sec
Rationale: 70 + 40 = 110 * 5/18 = 275/9mps
D = 150 + 100 = 250 m
T = 250 * 9/275 = 49/6 sec
Answer:E
Answer: (E) 49/6 sec
Question: What is the least common multiple of 12,15,18,27
(A) 640
(B) 540
(C) 691
(D) 385
(E) 789
Rationale: factors of 12 =2*2*3
factors of 27= 3*3*3
factors of 15 =3*5
factors of 18 =2*3*3
thus the l.c.m is 2*3*2*3**1*5*3=540
the answer is B
Answer: (B) 540
Question: 2 trains starting at the same Ɵme from 2 stations 200 km apart and going in opposite direction cross
each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?
(A) 11:9
(B) 13:9
(C) 17:9
(D) 21:9
(E) None of these
Rationale: Explanation:
We know total distance is 200 Km
If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km
[110+90=200km]
So raƟo of their speed = 110:90 = 11:9
Answer: A
Answer: (A) 11:9
Question: he two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 76 Kmph
(B) 68 Kmph
(C) 87 Kmph
(D) 56 Kmph
(E) 10 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer:B
Answer: (B) 68 Kmph
Question: how much percentage 80 is of 480?
(A) 16.5
(B) 14.33
(C) 12.5
(D) 15.8
(E) 16.66
Rationale: 80*100/480=16.66%
answer E
Answer: (E) 16.66
Question: Cream costs twice as much as skim milk. A certain brand of milk is 1/5 cream and 4/5 skim milk. What fraction of the cost of this brand is due to the cream?
(A) 1/3
(B) 2/3
(C) 1/4
(D) 3/4
(E) 2/5
Rationale: Let x be the cost of the skim milk in the mixture.
The cost of the cream is (1/4)*x*2 = x/2.
The total cost is x+x/2 = 3x/2 and the fraction due to the cream is (x/2) / (3x/2) = 1/3
The answer is A.
Answer: (A) 1/3
Question: City A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
(A) 56
(B) 57.5
(C) 58.9
(D) 61.3
(E) 67.23
Rationale: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,
Average Speed=(Total DistanceTotal Time)=2304=57.5
B
Answer: (B) 57.5
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 10 kmph
(B) 15 kmph
(C) 20 kmph
(D) 22 kmph
(E) 25 kmph
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer:C
Answer: (C) 20 kmph
Question: The distance between a school and the closest grocery store is approximately 9.2 x 10^4 inches. Which of the following is closest to the distance between the school and the store, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
(A) 2.9
(B) 3.2
(C) 2.7
(D) 2.4
(E) 1.9
Rationale: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).
We also know that the distance between the school and the store is approximately 9.2x10^4 inches. To convert inches to kilometers, we need to multiply 9.2x10^4 inches by the ratio we just found out.
kilometers = 9.2x10^4 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]
km = 9.2x10^4/3.9x10^4 km
km = 2.36 = 2.4 km
Therefore, we can see that the closest answer is D.
Answer: (D) 2.4
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 50
(B) 40
(C) 70
(D) 80
(E) 30
Rationale: C
70%
Let C.P. = $100. Then, profit = $320, S.P. = $420
New C.P. = 125% of $100 = $125.
New S.P. = $420
Profit = 420 - 125 = $295
Required percentage = 295/420 * 100 = 1475/21 = 70%
Answer: (C) 70
Question: If 4-X < 2-5X, which of the following is correct?
(A) X < -1/2.
(B) X > -5.
(C) X > 5.
(D) -5 < X < 0.
(E) 0 < X < 5.
Rationale: 4-X < 2-5X
2 < -4X
-10/2>X
-5>X
A is the answer
Answer: (A) X < -1/2.
Question: For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.30 – 6.30*?
(A) 1.5
(B) 0.5
(C) 6.25
(D) 0.25
(E) 0.3
Rationale: Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.30* =6 (the greatest positive even integer less than or equal to 6.30 is 6).
Hence, 6.30 – 6.30* = 6.30 - 6 = 0.30
Answer: E.
Answer: (E) 0.3
Question: The present population of a town is 3744. Population increase rate is 20% p.a. Find the population of town before 2 years?
(A) 2500
(B) 2600
(C) 3500
(D) 3600
(E) 2050
Rationale: P = 3744
R = 20%
Required population of town = P/(1 + R/100)^T
= 3744/(1 + 20/100)^2
= 3744/(6/5)^2
= 2600(approximately)
Answer is B
Answer: (B) 2600
Question: An association of mathematics teachers has 1,600 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?
(A) 75%
(B) 58%
(C) 42%
(D) 14.5%
(E) 19.6%
Rationale: Total umber of members = 1600
Number of members that cast votes = 525
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100)*525 = 315
Percent of total membership that voted for winning candidate = (315/1600)*100 = 19.6%
Answer E
Answer: (E) 19.6%
Question: A ratio between two numbers is 5:4 and their L.C.M. is 80. The first number is
(A) 60
(B) 45
(C) 20
(D) 15
(E) None
Rationale: Sol.
Let the required numbers be 5x and 4x. Then, their L.C.M. is 20x.
∴ 20x = 80⇔ x = 4. Hence, the first number is 20.
Answer C
Answer: (C) 20
Question: A train 110 m long is running with a speed of 60 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) 1
(B) 6
(C) 7
(D) 9
(E) 3
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer: B
Answer: (B) 6
Question: Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?
(A) 689
(B) 569
(C) 123
(D) 512
(E) 456
Rationale: Explanation:
Let total number of children be x
Then, x x1/8X=x/2*16,x=64
Number of notebooks =1/8x^2=(1/8*64*64)=512
Answer:D
Answer: (D) 512
Question: The sum of the mean, the median, and the range of the set {5, 7, 9} equals which one of the following values?
(A) 27
(B) 45
(C) 62
(D) 22
(E) 10
Rationale: set {5, 7, 9}
Mean = (5+7+9)/3 = 7
Meadian = Middle term = 7
Range = Highest - Lowest = 9-1 = 8
Mean+Median+Range = 7+7+8 = 22
Answer: Option D
Answer: (D) 22
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
(A) Tuesday
(B) Wednesday
(C) Friday
(D) Monday
(E) Sunday
Rationale: The year 2004 is a leap year. It has 2 odd days.
The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.
Hence, this day is Sunday.
Answer: E
Answer: (E) Sunday
Question: What is the length of a bridge (in meters), which a train 166 meters long and travelling at 45 km/h can cross in 40 seconds?
(A) 310
(B) 318
(C) 326
(D) 334
(E) 342
Rationale: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s
In 40 seconds, the train can travel 25/2 * 40 = 500 meters
500 = length of train + length of bridge
length of bridge = 500 - 166 = 334 meters
The answer is D.
Answer: (D) 334
Question: I have Rs.450 in my pocket. I would like to give my mother, my brother and my friend the same amount, how much should I give to each of them?
(A) 120
(B) 70
(C) 90
(D) 150
(E) 60
Rationale: 450/3 = 150
The answer is D.
Answer: (D) 150
Question: The average of 10 numbers is calculated as 46. It is discovered later on that while calculating the average, the number 65 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?
(A) 48
(B) 50
(C) 54
(D) 66
(E) 86
Rationale: The total sum of the numbers should be increased by 40.
Then the average will increase by 40/10 = 4.
The correct average is 50.
The answer is B.
Answer: (B) 50
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/4 min
(B) 28 1/7 min
(C) 17 1/7 min
(D) 17 1/8 min
(E) 17 5/7 min
Rationale: 1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer:C
Answer: (C) 17 1/7 min
Question: The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above condition is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let the required numbers be 33a and 33b.
Then 33a +33b= 528 \inline \fn_jvn \Rightarrow a+b = 16.
Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).
\inline \fn_jvn \therefore Required numbers are ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)
The number of such pairs is 4
Answer: A
Answer: (A) 4
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
(A) 750
(B) 277
(C) 262
(D) 231
(E) 123
Rationale: 1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
Answer: A
Answer: (A) 750
Question: If a can complete a work in x days and b can complete a work in y days. In how many days that they will work together simultaneously?
(A) xy/(x+y)
(B) (x+y)/xy
(C) 1/xy
(D) xy
(E) x+y
Rationale: A's one day work=1/x
B's one day work=1/y
a+b=1/x+1/y=(x+y)/xy(for one day)
Total days=xy/(x+y)
Answer is option A
Answer: (A) xy/(x+y)
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 50 km/hr
(B) 15 km/hr
(C) 6 km/hr
(D) 8 km/hr
(E) 12 km/hr
Rationale: Explanation:
Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==>
x = 50 km/hr.
Answer: A) 50 km/hr.
Answer: (A) 50 km/hr
Question: The speed of a boat in still water is 40kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
Rationale: Speed downstream = 40 + 20 = 60 kmph
Speed upstream = 40 - 20 = 20 kmph
Answer:B
Answer: (B) kmph
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 80%?
I will see what is the quickest way to solve it then I will provide the explanation
(A) 6
(B) 7
(C) 9
(D) 10
(E) 11
Rationale: The following approach might be the easiest one and less error prone.
We need on-time departure rate to be higher than 8/10, so it should be at least 9/11, which means that 9 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 9-3=6 subsequent flights need to depart on-time.
Answer: A
Answer: (A) 6
Question: The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?
(A) 2000
(B) 4000
(C) 5000
(D) 1000
(E) 5500
Rationale: Let monthly income A = a
monthly income of B = b
monthly income C= c
a+b=2*5050 --- 1
b+c=2*6250----2
a+c=2*5200----3
add 3 eqns
a=4000
monthly income of A = 4000
ANSWER B
Answer: (B) 4000
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
(A) 1/8
(B) 1/3
(C) 1/9
(D) 1/2
(E) 1/4
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
Answer:B
Answer: (B) 1/3
Question: Tina’s cat weighs 2.6 kilograms. Her dog weighs 4 times as much as her cat. How much does her dog weigh in kilograms?
(A) 10.4kg
(B) 38kg
(C) 22kg
(D) 48kg
(E) 20kg
Rationale: 2.6*4=10.4kg.Answer is A.
Answer: (A) 10.4kg
Question: Which of the following numbers is the biggest => [-4/7 , -7/8 , -9/10 , -12/13 , -34/35]
(A) A)-4/7
(B) B)-7/8
(C) C)-9/10
(D) D)-12/13
(E) E)-34/35
Rationale: If we observe all the fractions just differ by one i.e denominator vs numerate.. in such case the biggest will be with large values... here all values are with -ve value...the least value is biggest. i.e. -4/7..
Hence A is correct answer...
Answer: (A) A)-4/7
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days . how many hours a day must 4 pumps work to empty the tank in 1 day?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: the required number of working hours per day x, more pumps , less working hours per day(indirect)
less days , more working hours per day (indirect)
pumps 4:3, days 1:2 } :: 8:x
therefore 4*1*x= 3*2*8, x= (3*2*8)/4
x=12
correct answer(D)
Answer: (D) 12
Question: If the average (arithmetic mean) of x, x + 2, and x + 4 is 103, what is the value of x?
(A) 95
(B) 97
(C) 101
(D) 85
(E) 87
Rationale: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2
Given that x + 2 = 103
x = 101
Answer : C
Answer: (C) 101
Question: If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 6 children have two children of the same sex and one of the opposite sex?
(A) 1/3
(B) 2/3
(C) 1/4
(D) 3/16
(E) 3/5
Rationale: No of ways of selecting a gender - 2C1
No of ways of selecting any 2 children out of 6 = 6C2
Total possible outcomes - 2^6 (each child can be either a girl or a boy)
Probability=2C1*6C2/2^6= 2*6/2*2*2*2*2*2=12/64=3/16
Ans=D
Answer: (D) 3/16
Question: Walking at 70% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?
(A) 30
(B) 36
(C) 42
(D) 48
(E) 56
Rationale: speed is inversly proprtional to time
walking at 70% of speed meand 7/10s takes 10/7t.
It takes 24 minutes extra to cover the distance. then
10/7t=t+24
10t=7t+168
3t=168
t=56.
Option E is correct
Answer: (E) 56
Question: Twelve identical machines, running continuously at the same constant rate, take 9 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by three days?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 9
Rationale: From the question you know that 12R = 1/9. The question asks you (partially) to make the rate from 1/9 to 1/6 (drop from 9 day to 6). So the only thing that you need to do is to find the magic number than can convert 1/9 to 1/6.
So 1/9 * x = 1/6 (1 equation with one unknown). So by solving this you get x = 9/6 or 3/2. Thats it then! Take the magic number 4/3 and multiply BOTH sides of the original equation and you have:
12*(3/2)*R = (3/2) * 1/9
6 * 3 * R = 1/6, Hence 18R = 1/6, therefore 6 more machines!
D
Answer: (D) 6
Question: The security gate at a storage facility requires a five-digit lock code. If the lock code must consist only of digits from 1 through 6, inclusive, with no repeated digits, and the first and last digits of the code must be even, how many lock codes are possible?
(A) 144
(B) 240
(C) 360
(D) 720
(E) 1440
Rationale: X-X-X-X-X --> there are 3 even digits from 1 to 6, inclusive thus options for the first and the last X's are: 3-X-X-X-2. Other X's can take following values: 3-4-3-2-2 --> 3*4*3*2*2=144..
Answer: A.
Answer: (A) 144
Question: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
(A) Sunday
(B) Saturday
(C) Friday
(D) Wednesday
(E) None
Rationale: EXPLANATION
On 31st December, 2005 it was Saturday.
Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday.
Answer C
Answer: (C) Friday
Question: Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes?
(A) 56678
(B) 16789
(C) 17576
(D) 35142
(E) None of these
Rationale: Explanation :
The first letter from the right can be chosen in 26 ways because there are 26 alphabets.Having chosen this, the second letter can be chosen in 26 ways.=> The first two letters can be chosen in 26*26=676 waysHaving chosen the first two letters, the third letter can be chosen in 26 ways.=> All the three letters can be chosen in 676*26=17576 ways.It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
Answer : C
Answer: (C) 17576
Question: There are cats got together and decided to kill the mice of 999984. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?
(A) 941,1009
(B) 991,1001
(C) 996,1004
(D) 791,1009
(E) 931,1009
Rationale: 999984 can be written as 1000000 â€“ 16
= 10002 â€“ 42 ie of the form a2-b2=(a+b)(a-b)
=(1000+4)*(1000-4)
= (1004)*(996)
Given that number of cats is less than number if mice.
So number of cats is 996 and number of mice were 1004
Answer C
Answer: (C) 996,1004
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 45 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 287
(B) 279
(C) 270
(D) 278
(E) 379
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (45 -40) = 8 hours
So, the two trains meet at 6 p.m. The two trains meet 6 * 45 = 270 km away from Mumbai.
Answer:C
Answer: (C) 270
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
(A) 1/4
(B) 1/7
(C) 2/4
(D) 2/3
(E) 1/3
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
ANSWER:E
Answer: (E) 1/3
Question: A can do a piece of work in 4 days. B can do it in 8 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 87 days
(B) 20 days
(C) 8 days
(D) 19 days
(E) 36 days
Rationale: C = 1/2 - 1/4 - 1/8 = 1/8
=> 8 days
Answer:C
Answer: (C) 8 days
Question: A soccer team plays games only against the other five teams in its league and always in the following order: Gary, Howard, Robin, Fred and Jackie. If the team’s final game of the season is against Fred, which of the following could be the number of games in the team’s schedule?
(A) 24
(B) 66
(C) 56
(D) 72
(E) 81
Rationale: IMO 'A' is the answer.
Matches will be in multiples of 5x+4. The answer that satisfies this condition is A
Answer: (A) 24
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is?
(A) 7/17
(B) 7/12
(C) 7/19
(D) 7/11
(E) 7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂
= 7/15
Answer:E
Answer: (E) 7/15
Question: The standard serial numbers for medical licence are 3 letters followed by 5 digits. How many different medical licenses are possible if letters and digits can be repeated?
(A) 26 × × 3 × 5
(B) 26³ × 10 000
(C) 26³ x 100 000
(D) 26 × 25 × 24 × 10 × 9 × 8 × 7
(E) 26³ × 10 000 x 15
Rationale: OFFICIAL SOLUTION:
(C) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 × 26 options for the three letters, and 10 × 10 × 10 × 10 x 10 for the five digits. The number of different Medical license is 26 × 26 × 26 × 10 × 10 × 10 × 10 x 10= 26³ × 100 000.
The correct answer is choice (C).
Answer: (C) 26³ x 100 000
Question: Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7740 km and comes back to the starting point. The total time taken by him is:
(A) 914.2 hours
(B) 900 hours
(C) 915 hours
(D) 982.9 hours
(E) 915 hours
Rationale: Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 7740/18 + 7740/14 = 430 + 552.9 = 982.9 hours
Answer: Option D
Answer: (D) 982.9 hours
Question: The average of 10 numbers was calculated as 18. It is discovered later on that while calculating the average, one number, namely 66, was incorrectly read as 26. What is the correct average?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: 10*18 - 26 + 66 = 220
220 / 10 = 22
The answer is C.
Answer: (C) 22
Question: How many positive integers less than 90 are multiples of 6 but NOT multiples of 9?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: The LCM of 6 and 9 is 18.
If x <90 and x is divisible by 6 not by 9 --> x is NOT divisible by 18.
From 1--> 90, we have 5 numbers which is divisible by 18: 18, 36, 54, 72, 90.
From 1-->90, we have (90-6)/6 +1 = 15 numbers divisible by 6.
Therefore, our answer is 15-5 = 10 numbers.
D
Answer: (D) 10
Question: If |z|/w = 4,which of the following must be true?
(A) z = -4w
(B) z = 4w
(C) z^2 = 16w^2
(D) z^2 = 16w^3
(E) z^3 = 64w^3
Rationale: |z|/w = 4.
|z| = 4w.
Then z = 4w or -4w and so z^2 = 16w^2.
The answer is C.
Answer: (C) z^2 = 16w^2
Question: A total of 50 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]
(A) 1/4
(B) 7/12
(C) 2/3
(D) 7/8
(E) 8/7
Rationale: Let' take the Number of geese to be 100.
Male = 50. Female = 50.
Now the second part of the Q, Let's take the Number migrated to be 20.
So we have 20 geese that migrated and out of that 20% are male i.e 20/100 *20 = 4 Geese (Males)
And now we know out of the total 20 geese , 4 are male , then 16 have to be female.
Now the ratio part , Male Geese Ratios = 4/50 = 2/25. - A
Female Geese Ratios =16/50=8/25 - B
Cross Multiply Equations A and B and you get =1/4 .
Ans A
Answer: (A) 1/4