mathewhe/aqua_rat huggingface dataset:
Question: In how many ways 8 different tickets R can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.
(A) From 2 to 6 inclusive.
(B) From 98 to 102 inclusive.
(C) From 122 to 126 inclusive.
(D) From 128 to 132 inclusive.
(E) From 196 to 200 inclusive.
Rationale: Possibilities
J 8 6 4 2 0
B 0 2 4 6 8
# of ways 8C8 8C6 8C4 8C2 8C0
R=1+28+70+28+1 = 128 Answer is D.
Answer: (D) From 128 to 132 inclusive.
Question: Three numbers are in the ratio 3:4:5 and their L.C.M. is 1200. Their H.C.F is?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let the numbers be 3x,4x and 5x
their L.C.M. = 60x
60x = 1200
x = 20
The numbers are 3*20 , 4*20 , 5*20
Hence required H.C.F. = 20
Answer is A
Answer: (A) 20
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
(A) 4208
(B) 4202
(C) 4209
(D) 4200
(E) 42012
Rationale: 15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
Answer: D
Answer: (D) 4200
Question: Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 3w widgets.
(A) 4
(B) 6
(C) 18
(D) 10
(E) 12
Rationale: I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets. So, he will take 18 days to doing 3w widgets.
Answer : C
Answer: (C) 18
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
(A) 17 km/hr
(B) 88 km/hr
(C) 36 km/hr
(D) 99 km/hr
(E) 45 km/hr
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: C
Answer: (C) 36 km/hr
Question: An event manager has ten patterns of chairs and eight patterns of tables. In how many chairs can he make a pair of table and chair?
(A) 100
(B) 120
(C) 60
(D) 80
(E) 90
Rationale: He has 10 patterns of chairs and 8 patterns of tables.
Hence,A chair can be arranged in 10 ways
A table can be arranged in 8 ways
Hence one chair and one table can be arranged=10*8 ways
=80 ways
Option D
Answer: (D) 80
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 120 marks, the no of questions he attempts correctly is :
(A) 35
(B) 36
(C) 40
(D) 42
(E) 44
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 120
=> 5x = 180
=> x = 36
Answer: B
Answer: (B) 36
Question: There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts W needed to confirm that each of the 5 keys matches each of the 5 locks?
(A) 5,15
(B) 4,15
(C) 5,10
(D) 4,10
(E) 5,20
Rationale: Assume you have locks 1-5 and keys A-E.
Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.
Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of W= 4 + 3 + 2 + 1 = 10 attempts.D
Answer: (D) 4,10
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 17000, then find the annual income of A?
(A) Rs. 571200
(B) Rs. 180000
(C) Rs. 201600
(D) Rs. 504000
(E) None of these
Rationale: B's monthly income = 17000 * 112/100 = Rs. 19040
B's monthly income = 2 parts ----> Rs. 19040
A's monthly income = 5 parts = 5/2 * 19040 = Rs. 47600
A's annual income = Rs. 47600 * 12 = Rs. 571200
ANSWER:A
Answer: (A) Rs. 571200
Question: Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it?
(A) 700
(B) 710
(C) 720
(D) 740
(E) 750
Rationale: We have to arrange 6 books.
The number of permutations of n objects isn!=n.(n−1).(n−2)...2.1n!=n.(n−1).(n−2)...2.1
Here n=6n=6 and therefore, number of permutations is 6.5.4.3.2.1=6.5.4.3.2.1= 720
Option is C
Answer: (C) 720
Question: After the recall of defective by Telvin inc 2 years ago, its share price has since lost 12%. However, after the launch of its new product 1 year ago its stock price has appreciated by 6%, bringing its share price to $25. What was its share price 2 years ago?
(A) 28
(B) 26.8
(C) 56.6
(D) 27.2
(E) 25.7
Rationale: -12+6-(12*6)/100=-6.72% net decrease
let initial price be Y
Y(1-6.72/100)=25
Y=25/0.9328 = ~26.8
Ans is B)
Answer: (B) 26.8
Question: A "word" is defined as a sequence of three dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: there are two ways of possibilities..
1) all three same colour- YYY or BBB- 2 ways
2) two of one colour and one of different colour- 3!/2!-3ways..
now two /one could be Y/B or B/Y.... so 3*2=6..
total 6+2=8 ans D
Answer: (D) 8
Question: Which of the following is the lowest positive integer that is divisible by the first 8 positive integer multiples of 3?
(A) 1720
(B) 2120
(C) 2520
(D) 2920
(E) 3320
Rationale: The number must be divisible by 3, 2*3, 3^2, 2^2*3, 5*3, 2*3^2, 7*3, and 2^3*3.
The lowest such number is 2^3*3^2*5*7 = 2520.
The answer is C.
Answer: (C) 2520
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 1000
(B) 2998
(C) 2778
(D) 2788
(E) 2991
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer:A
Answer: (A) 1000
Question: A pupil's marks were wrongly entered as 83 instead of 53. Due to the average marks for the class got increased by half. The number of pupils in the class is?
(A) 18
(B) 82
(C) 60
(D) 27
(E) 29
Rationale: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (83 - 53) => x/2
= 30 => x = 60.
Answer: C
Answer: (C) 60
Question: What comes next in the sequence?
4, 2, 4, 8, 6, 8, 16
(A) 14
(B) 16
(C) 4
(D) 18
(E) 8
Rationale: (4,8,16)
(2,6,18)
(4,8,16)
series is 4,2,4,8,6,8,16,18,16
ANSWER:D
Answer: (D) 18
Question: Shelly rows 4m kilometers downstream at 6x kilometers per hour. Then she turns around and rows m/6 kilometers upstream at 2x kilometers per hour. What is Shelly's average rowing speed in kilometers per hour during the entire journey?
(A) 50x/9
(B) 50x/(9m)
(C) 50/9
(D) 50m/9
(E) 50mx/9
Rationale: Total distance covered = 4m + m/6 = 25m/6
Total time taken = 4m/6000x + (m/6)/2000x = 9m/12000x = 3m/4000x
Average speed = Total distance/Total Time taken = (25m/6)/(3m/4000x)
= 50,000x/9 mt/hr
= 50x/9 km/hr
Option A.
Answer: (A) 50x/9
Question: 2 pipes can separately fill a tank in 20hrs and 30hrs respectively. Both the pipes are opened tofill the tank, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
(A) 10 hrs
(B) 12 hrs
(C) 16 hrs
(D) 18 hrs
(E) 20 hrs
Rationale: 1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
C
Answer: (C) 16 hrs
Question: A truck covers a distance of 392 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 70 km more than that travelled by the truck ?
(A) 6 hours
(B) 5 hours
(C) 7 hours
(D) 8 hours
(E) None
Rationale: Explanation :
Speed of the truck = Distance/time = 392/8 = 49 kmph
Now, speed of car = (speed of truck + 18) kmph = (48 + 18) = 66 kmph
Distance travelled by car = 392 + 70 = 462 km
Time taken by car = Distance/Speed = 462/66 = 7 hours.
Answer – C
Answer: (C) 7 hours
Question: If k^2 = n^2, which of the following must be true?
(A) k = m
(B) k = -m
(C) |k| = |n|
(D) k = -|m|
(E) k = |m|
Rationale: Solution:
We are given that k^2 = n^2, and we can start by simplifying the equation by taking the square root of both sides.
√k^2 = √n^2
When we take the square root of a variable squared, the result is the absolute value of that variable. Thus:
√k^2 = √n^2 is |k| = |n|
Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.
Answer: C
Answer: (C) |k| = |n|
Question: 36 people attend a party. 7 men are single and the rest are there with their wives. There are no children in the party. In all 22 women are present. Then the number of married men at the party is ?
(A) 7
(B) 6
(C) 5
(D) 8
(E) 9
Rationale: Total people = number of men + number of women
36 = 7 + number of married men + 22
number of married men = 36- 22-7 = 7 men
ANSWER:A
Answer: (A) 7
Question: A train 250 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) 95
(B) 50
(C) 12
(D) 13
(E) 67
Rationale: Speed of the train relative to man = (250/10) m/sec = (25) m/sec. [(25) * (18/5)] km/hr = 90 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr.
Answer: Option A
Answer: (A) 95
Question: Townville has 100 residents, and 30 of them are females. If half of Townville’s male residents are smokers, and 1/3 of the female residents are smokers, which of the following represents the total number of Townville’s residents who are NOT smokers?
(A) 55
(B) 65
(C) 25
(D) 22
(E) 21
Rationale: Number of people =100
Females = 30
men = 100-30=70
Half of the men are smoker70/2=35, that means the remaining men 70-35=35 are non smokers.
1/3 females are smoker. i.e 1/3*30 = 10.
30-10=20 females are non smokers
So, total number of non smokers in the town are 35+20 =55
Answer : A
Answer: (A) 55
Question: The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments.
(A) 2:3:6
(B) 3:5:6
(C) 3:2:4
(D) 2:4:3
(E) 2:5:3
Rationale: The ratio of investments of A, B and C is 5:6:7.
The ratio of shares of A, B and C is 5:9:21.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6.
ANSWER:A
Answer: (A) 2:3:6
Question: 23 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
(A) 22
(B) 23
(C) 44
(D) 45
(E) 46
Rationale: n for cyclic hand shake and n-1 for linear handshake.
so here no of hand shake is 23.
ANSWER:B
Answer: (B) 23
Question: Jaime earned enough money by selling seashells at 35 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?
(A) 5
(B) 11
(C) 17
(D) 22
(E) 30
Rationale: Let's TEST Answer D: 22 seashells....
With 22 seashells, Jamie would have 22(35) = 770 cents. This would allow him to buy 14 books for 770 cents total, with no money left over. This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
[Reveal]Spoiler:D
Answer: (D) 22
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 28
(B) 27
(C) 12
(D) 99
(E) 14
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5
= 12 seconds.
Answer:C
Answer: (C) 12
Question: How many ways are there to award a gold, silver and bronze medal to 12 contending teams?
(A) 12 x 11 x 10
(B) 10!/(3!7!)
(C) 10!/3!
(D) 360
(E) 300
Rationale: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 12 ways
if gold medal is given to 1 of the teams then only possible 11 teams can be considered for silver medal. we can do selection in 11 ways
similarly if gold and silver medals are awarded then only remaining 10 teams can be considered for a bronze medal. we can do the selection in 10 ways
Total number of ways to select the 3 possible medal winners = 12 * 11 * 10
Correct answer - A
Answer: (A) 12 x 11 x 10
Question: Points M(5,2) and N(5,8) lie on the xy - plane. What is the midpoint of line segment MN?
(A) (5,0)
(B) (0,5)
(C) (0, (136^(1/2))/2)
(D) (3/2,0)
(E) (5,5)
Rationale: The midpoint of a segment is exactly halfway between its endpoints and it's location can be found using the Midpoint Theorem, which states:
• The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints.
• Likewise, the y-coordinate is the average of the y-coordinates of the endpoints.
So, x=(5+5)/2=5 and y=(2+8)/2=5 --> coordinates of the midpoint are (5, 5).
Answer: E.
Answer: (E) (5,5)
Question: Half of 5 percent written as decimal is
(A) 5
(B) 0.025
(C) 0.015
(D) 0.005
(E) None of these
Rationale: Explanation:
It will be 1/2(5%) = 1/2(5/100) = 5/200 = 0.025
Option B
Answer: (B) 0.025
Question: If 21,394 + x is a multiple of 3, which of the following could be the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
Rationale: Sum of the digits of 21,394 is 2+1+3+9+4 = 19
Now 19 is not a multiple of 3, the next multiple of 3 close to 19 is 21, which is 2 added to 19.
So the least number to be added to 21,394 is 2
B
Answer: (B) 2
Question: Emily has a cylindrical water bottle that can hold 1000π cubic centimeters of water. Right now,
the bottle is holding 100π cubic centimeters of water, and the height of the water is 1 centimeter.
Compute the radius of the water bottle.
(A) 8
(B) 10
(C) 15
(D) 22
(E) 13
Rationale: if the height of the water is 1 centimeter when there are 100π cubic centimeters
of water, then the height of the water would be 10 centimeters when the water bottle is full.
Therefore,πr2 * 10 = 1000π and r2 = 100, so r = 10 .
correct answer B
Answer: (B) 10
Question: A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?
(A) 95%
(B) 90%
(C) 80%
(D) 75%
(E) 60%
Rationale: According to the matrix the probability of selecting a colorblind person is 0.6 and the probability of NOT selecting a colorblind person is 0.4.
{The probability of selecting a colorblind person in three tries} = 1 - {the probability of NOT selecting a colorblind person in three tries} = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936 = 93.6%.
We are asked to find the approximate probability, so the answer is 95%.
Answer: A.
Answer: (A) 95%
Question: The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
(A) 4.2
(B) 4.4
(C) 4.6
(D) 5.6
(E) 5.7
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
C
Answer: (C) 4.6
Question: For which of the following values of n is (200+n)/n NOT an integer?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: Solution:
This problem is easiest solved by plugging in each answer choice.
A) (200 + 1)/1 = 101/1 = 201
Answer choice A yields an integer.
B) (200 + 2)/2 = 202/2 = 101
Answer choice B yields an integer.
C) (200 + 3)/3 = 203/3 = 67, remainder 2
Answer choice C DOES NOT yield an integer.
Although we believe answer choice C is correct, we should still test the other answer choices.
D) (200 + 4)/4 = 204/4 = 51
Answer choice D yields an integer.
E) (200 + 5)/5 = 205/5 = 41
Answer choice E yields an integer.
Thus, the correct answer is answer choice C.
Answer: (C)  3
Question: If x is negative and y is positive, which of the following cannot be positive?
(A) -x/y
(B) x/-y
(C) -xy
(D) x*(-y)
(E) x^3*y
Rationale: -*-*-= -
x^3*y is negative.
Answer : E
Answer: (E) x^3*y
Question: What is the smallest number which when increased by 3 is divisible by 12, 15, 35, and 40?
(A) 837
(B) 947
(C) 1027
(D) 1155
(E) 1231
Rationale: Factor each of the numbers 8, 15, 35, and 40 into primes:
12=2*2*3; 15=3*5; 35=5*7; 40=2*2*2*5
The smallest number divisible by all of them is thus 2*2*2*3*5*7 = 840
837 + 3 = 840
A
Answer: (A) 837
Question: The fourth proportional to 12, 14 and 18 is?
(A) 21
(B) 66
(C) 77
(D) 88
(E) 99
Rationale: (14*18)/12 = 21
Answer: A
Answer: (A) 21
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 30 seconds. Its length is?
(A) 188 m
(B) 876 m
(C) 251 m
(D) 200 m
(E) 145 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 30= x / 15
x = 200 m.
Answer: D
Answer: (D) 200 m
Question: A car drives 60 miles on local roads at 20 mph, and 195 miles on the highway at 65 mph, what is the average speed of the entire trip?
(A) 36 mph
(B) 40 mph
(C) 44 mph
(D) 43 mph
(E) 58 mph
Rationale: So The Answer is Plainly D....
we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance)
for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20*t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles
in the same way we should divide 195 to 65 to find the needed time to cover 195 miles ,so t= 3 hours
so the total time for covering total distance would be 3+3 = 6 hours and total distance is 60+195= 255 miles
Final stage : average speed is total distance divide to total time : 255/6 = 42.5 miles per hour rounded up to 43 MPH....
Answer: (D) 43 mph
Question: A certain airline's fleet consisted of 100 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Let x be the number of years.
4x > 100 - 3x
7x > 100
x > 14 + 2/7
The answer is B.
Answer: (B) 15
Question: Find the next number in the Sequence
5, 16, 49, 104, ?
(A) 111
(B) 224
(C) 133
(D) 181
(E) 231
Rationale: D
181
+11 =>16
+33 =>49
+55 =>104
+77 =>181
Answer: (D) 181
Question: In the xy-plane, a line has slope 3 and x-intercept 5. What is the y-intercept of the line?
(A) -15
(B) -3
(C) 0
(D) 3
(E) 9
Rationale: Let the line be represented by a general equation y=mx+b, where m = slope (3) and b=y intercept. We are also given the value of x-intercept 5.
Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.
Putting these values in the equation : 0 = 3*5 + b => b = -15. Hence A.
Answer: (A) -15
Question: 100 identical coins, each with probability P of showing 'heads' are tossed once. If 0<P<1 and the probability of 'heads' showing on 50 coins is equal to that of 'heads' showing on 50 coins, then find the value of P.
(A) 51/101.
(B) 51/100
(C) 32/81
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Let X be the number of coins showing 'heads', then X follows a binomial distribution with parameters n = 100 and P.
As given, P(X=50) = P(X=51)
=> 100C50P50(1-P)50 = 100C51P51(1-P)49 .
=> 51/50 = P / (1-P)
=> p = 51/101.
Hence, the value of p is 51/101.
Answer : A
Answer: (A) 51/101.
Question: At what rate percent on simple interest will a sum of money double itself in 30 years?
(A) 3 1/3%
(B) 3 1/9%
(C) 3 9/3%
(D) 3 2/3%
(E) 3 6/3%
Rationale: P = (P*30*R)/100
R = 3 1/3%
Answer: A
Answer: (A) 3 1/3%
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)?
(A) 28 years
(B) 29 years
(C) 20 years
(D) 26 years
(E) 21 years
Rationale: Present total age of the members = 26(5) = 130 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 130 -10 = 120 years
Their average age at the time of the birth of the youngest member = [120 - (4 * 10)] / 4
= 30 - 10 = 20 years.
Answer:C
Answer: (C) 20 years
Question: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 50 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
(A) 105
(B) 120
(C) 140
(D) 147
(E) 98
Rationale: Car Y began travelling after 72 minutes or 1.2 hours.
Let t be the time for which car Y travelled before it stopped.
Both cars stop when they have travelled the same distance.
So,
35(t+1.2) = 50t
t=2.8
Distance travelled by car X from the time car Y began traveling until both cars stopped is
35 x 2.8
= 98 miles
Answer:- E
Answer: (E) 98
Question: A boat goes 100 km downstream in 10 hours, and 75 Km upstream in 25 hours. The speed of the stream is?
(A) 22 1/9
(B) 6
(C) 5
(D) 3.5
(E) 4.5
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 25 US = 3
? ----- 1 S = (10 - 3)/2
= 3.5 kmph.
Answer:D
Answer: (D) 3.5
Question: If (y - 4)(z - 8) + 9(z - 8) = 0, then which of the following must be true?
(A)  y = -4 and z = -3
(B)  y = -4 or z = 8
(C)  y = -4 or z = 3
(D)  y = 1 and z = 3
(E)  y = 1 or z = 3
Rationale: factor out:
(z-8)(y-4+9)=0
(z-8) (y+5) = 0
So by checking options we get ,
B.
Answer: (B)  y = -4 or z = 8
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is
(A) 25/42
(B) 25/40
(C) 25/49
(D) 25/47
(E) 25/44
Rationale: Explanation:
Total fruits = 9
Since there must be at least two apples,
= 25/42.
Answer: A
Answer: (A) 25/42
Question: How many distinct integer values of n satisfy the inequality||n-3| + 4| ≤ 15?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 13
Rationale: so i can write this as In-3I+4<=15
or In-3I<=11
so n can have -8 to 14 = 13 true values....
E
Answer: (E) 13
Question: The area of a square is 4356 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
(A) 5:28
(B) 5:19
(C) 7:12
(D) 5:13
(E) 7:22
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4356
a = 66
L = 2a and b = a - 24
b : l = a - 24 : 2a = 42 : 132
= 7:22
Answer:E
Answer: (E) 7:22
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 1000 revolutions. How many revolutions does the second wheel make in covering d feet?
(A) 1000xy
(B) 1000x/y
(C) 1000x - y
(D) 1000y/x
(E) 1000y - x
Rationale: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
1000 = d/(x*pi)
d = 1000 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (1000 * x * pi) / (y*pi) = 1000x/y
Answer (B)
Answer: (B) 1000x/y