divelab/Sys2Bench huggingface dataset:
Question: Two trains 120 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9
B)10.7
C)10.3
D)10.08
E)10.2
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 120 + 160 = 280 m.
Required time = 280 * 9/250 = 252/25 = 10.08 sec.
'Answer: D
Answer: D
Question: A faucet, partially on, fills a bucket with water at a rate of r buckets per minute. If the faucet is turned up it will fill the same bucket at a rate r + 2 buckets per minute, and the same bucket would fill in 2/3 minute less. What is the value of r?
Options:
A)5
B)4
C)3
D)2
E)1
Rationale: Equation: 1/r = 1/(r + 2) + 2/3
Plug options into the equation:
E fits: 1/1 = 1/(1 + 2) + 2/3
Answer: E
Answer: E
Question: An automobile manufacturer offers a station wagon with either a 10-cylinder engine or a 8-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 10-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?
Options:
A) 18
B) 24
C) 30
D) 34
E) 36
Rationale: 10-cylinder engine wagons = 2*2*2*2 = 16(manual or automatic, with or without trailer);
8-cylinder engine wagons = 2*2*2 = 8(manual or automatic).
Total = 16 + 8 = 24.
Answer: B.
Answer: B
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)76 2/3%
B)86 2/3%
C)66 2/3%
D)16 2/3%
E)26 2/3%
Rationale: Explanation:
600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: D
Question: What is the 124th digit to the right of the decimal point in the decimal form of 24/44?
Options:
A)8
B)9
C)6
D)4
E)2
Rationale: To solve this question, we first have to use some long division. This long division allows us to get 24/44 in decimal form, which is 0.545454… where “54” is repeating.
We can see that the 1st, 3rd, 5th digit to the right of the decimal point is a 5 and that the 2nd, 4th, 6th digit to the right of the decimal point is a 4. In other words, each odd-positioned digit is a 5, and each even-positioned digit is a 4.
Then the 124 digit to the right of the decimal point and we see that 124 is even, we know that the 124th digit is a 4.
Answer D.
Answer: D
Question: Two pipes can fill a tank in 18 minutes and 6 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Options:
A)1/15
B)1/6
C)1/11
D)1/10
E)1/12
Rationale: Part of the filled by all the three pipes in one minute
= 1/18 + 1/6 - 1/45 = 1/6
So, the tank becomes full in 6 minutes.
Answer:B
Answer: B
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
Options:
A)33
B)77
C)24
D)55
E)71
Rationale: 2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer:C
Answer: C
Question: The average age of a group of 18 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
Options:
A)22 years
B)30 years
C)40 years
D)32 years
E)None of these
Rationale: Answer
The average age of a group of 18 students is 20.
Therefore, the sum of the ages of all 18 of them = 18 * 20 = 360
When two new students join the group, the average age increases by 2. New average = 22.
Now, there are 20 students.
Therefore, the sum of the ages of all 20 of them = 20* 22 = 440
Therefore, the sum of the ages of the two new students who joined = 440 - 360 = 80
And the average age of each of the two new students = 80/2 = 40 years.
Answer C
Answer: C
Question: A person spent Rs. 7,540 from his salary on food and 5,690 on house rent. After that he was left with 60% of his monthly salary. What is his monthly salary ?
Options:
A)73,075
B)34,075
C)23,075
D)33,075
E)32,075
Rationale: Total money spent on food and house rent = 7,540+5,690 = 13,230
Which is 100 - 60 = 40% of his monthly salary
∴ His salary = 13230x100/40 = 33075
Answer : D
Answer: D
Question: The ratio between the length and the breadth of a rectangular park is 3 : 1. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
Options:
A)124545 m
B)134561 m
C)156787 m
D)15450 m
E)120000 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 1x metres.
Then, 2(3x + 1x) = 1600 or x = 200.
Length = 600 m and Breadth = 200 m.
Area = (600 x 200) m2 = 120000 m
E
Answer: E
Question: A man’s speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is :
Options:
A)8.5 km/hr
B)8.5 km/hr
C)10 km/hr
D)12.5 km/hr
E)None of these
Rationale: Solution
Man's rate in still water = (15-2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5-2.5) km/hr = 10 km/hr Answer C
Answer: C
Question: 22 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?
Options:
A)33
B)32
C)60
D)Data inadequate
E)None of these
Rationale: Capacity of the tank = 22 Ã— 13.5= 297 litres
When the capacity of each bucket = 9 litres, then the required no. of buckets
= 297â„9 = 33
Answer A
Answer: A
Question: Set A consists of all the prime numbers between 6 and 42. What is the range of set A?
Options:
A)16
B)34
C)16.6
D)17
E)23
Rationale: The range of a set of data is the difference between the highest and lowest values in the set
In this set,
Highest number = 41
Lowest number = 7
Range = Highest - Lowest = 41 - 7 = 34
Option B
Answer: B
Question: Excluding stoppages, the speed of a bus is 86 kmph and including stoppages, it is 76 kmph. For how many minutes does the bus stop per hour?
Options:
A)7.5 min
B)16 min
C)20 min
D)7 min
E)40 min
Rationale: D
7 min
Due to stoppages, it covers 10 km less.
Time taken to cover 10 km = (10/86 x 60) min = 7 min
Answer: D
Question: A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
Options:
A)2.5π
B)3π
C)5π
D)4π
E)10π
Rationale: If a rectangle is inscribed in a circle, then the diagonal of the rectangle = diameter of the circle.
In this case, diagonal = (9 + 16)^(1/2) = 5
Hence the radius = 2.5
Circumference = 2πr = 2π*2.5 = 5π
Correct Option: C
Answer: C
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
Options:
A)10.30 p.m
B)10.20 p.m
C)10.50 p.m
D)10.38 p.m
E)10.40 p.m
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer:C
Answer: C
Question: 189. The inside dimensions of a rectangular wooden box
are 2 inches by 4 inches by 6 inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume?
Options:
A) 2
B) 4
C) 5
D) 6
E) 8
Rationale: Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 6x4 width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 4, so the radius will be 2.
A
Answer: A
Question: A man can row upstream at 25 kmph and downstream at 55 kmph, and then find the speed of the man in still water?
Options:
A)65
B)40
C)30
D)78
E)38
Rationale: US = 25
DS = 55
M = (55 + 25)/2
= 40
Answer: B
Answer: B
Question: Several people are sitting around a round table playing a card game with a deck of 56 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?
Options:
A)4
B)6
C)7
D)11
E)13
Rationale: Let n be the number of people at the table.
If Martin gets the first and the last card, it means Martin got one more card than the others.
Thus 56/n has a remainder of 1 and so 56-1 = 55 is a multiple of n.
The answer is D.
Answer: D
Question: 8 points are marked on a straight line and another 7 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
Options:
A)264
B)91
C)168
D)196
E)264
Rationale: Solution: select 2 from 8 and one from 7 + select 2 from 7 and 1 from 8
8C2*7C1 + 7C2*8C1
= 196+ 168 = 364
Answer : A
Answer: A
Question: In a partnership between A, B and C. A's capital is Rs.7000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)23676
B)19766
C)29172
D)16450
E)11267
Rationale: Explanation:
200 + 130 = 330
800 - 330 = 470
200 ---- 7000
470 ---- ? => 16450
Answer:D
Answer: D
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 700 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
Options:
A)2880.
B)4860.
C)5780
D)5040
E)6380.
Rationale: Normal Day = 700 kw/h
Stormy Day = 700*1.2=840 kw/h
3 windmills for 2 hours on stormy day
840*3*2=5040
Answer: D
Answer: D
Question: Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 4-cent stamps she could have bought ?
Options:
A) 5
B) 10
C) 3.75
D) 20
E) 25
Rationale: 2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.04y
=> 2.65 = 0.30x + 0.20x + 0.04y
=> 265 = 50x + 4y
So Max value of 50x < 265 = 250
Hence y = 3.75
Answer - C
Answer: C
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 9 sec. What is the length of the platform?
Options:
A)389 m
B)350 m
C)289 m
D)799 m
E)1000 m
Rationale: Speed = 300/9 = 100/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 100/3
=> x = 1000 m.
Answer:E
Answer: E
Question: A certain club has 10 members, including Tarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Tarry will be either the member chose to be secretary or the member chose to be treasurer?
Options:
A)1/720
B)1/80
C)1/10
D)1/9
E)1/5
Rationale: In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9
Probability to become a secretary = (9/10 * 1/9) = 1/10
Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8
probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10
Since, the problem is saying Tarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E
Answer: E
Question: At what time between 4 & 5 will the hands of a watch point in opposite directions?
Options:
A)50 min past 4
B)42 5/11 min past 4
C)43 min past 4
D)40 min past 4
E)50 4/11 min past 4
Rationale: At 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30min. spaces apart.
Minute hand will have to gain 5 min. spaces.
55min spaces are gained in 60 min.
5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min.
Required time = 54 6/11 min. past 4.
Answer is E
Answer: E
Question: If the sum of two numbers is 22 and the sum of their squares is 386, then the product of the numbers is
Options:
A)40
B)49
C)80
D)88
E)90
Rationale: Sol.
Let the numbers be x and y.
Then, (x+y) = 22 and x2 + y2 = 386.
Now, 2xy = (x+y)2 - (x2 + y2)
= (22)2 - 386= 484 - 386= 98
xy = 49.
Answer B
Answer: B
Question: What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
Options:
A)Rs. 31
B)Rs. 32.10
C)Rs. 40.40
D)Rs. 64.10
E)Rs. 74.10
Rationale: S.I. = (1000 * 10 * 4)/100 = Rs. 400
C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10
ANSWER:D
Answer: D
Question: Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
Options:
A)23
B)14
C)31
D)35
E)45
Rationale: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation
larger number – smaller number = 7
which is equivalent to
Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.
C
Answer: C
Question: The length of the side of a square is represented by x+2. The length of the side of an equilateral triangle is 2x. If the square and the equilateral triangle have equal perimeter,then the value of x is ?
Options:
A)5
B)7
C)4
D)8
E)6
Rationale: Since the side of the square is x + 2, its perimeter = 4 (x + 2) = 4x + 8
Since the side of the equilateral triangle is 2x, its perimeter = 3 * 2x = 6x
Also, the perimeters of both are equal.
(i.e.) 4x + 8 = 6x
(i.e.) 2x = 8 è x = 4.
Answer:C
Answer: C
Question: The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability S that Tommy CANNOT form a triangle from the 3 sticks?
Options:
A)11/32
B)13/32
C)15/32
D)17/32
E)19/32
Rationale: In order to form a triangle, the sum of two sides must be greater than the third side.
So we can choose the combination of numbers which will NOT result in a triangle.
Favorable outcomes:
1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or
1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!
1,3,4 (4=1+3): 6 ways of arriving at this
2,2,4 (4=2+2): 3 ways of arriving at this
1,1,3 (3>1+1): 3 ways of arriving at this
1,2,3 (3=1+2): 6 ways of arriving at this
1,1,2 (2+1+1): 3 ways of arriving at this
Overall favourable outcomes: 30
Total outcomes: 4*4*4 = 64 (4 ways of choosing a stick from each of the 3 bags)
Probability S that a triangle is not formed = 30/64 = 15/32
C is the correct option here.
Answer: C
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number W?
Options:
A)126
B)1386
C)3108
D)308
E)13986
Rationale: As we are using digits 1,5, 8 and digits are allowed to repeat. Each of the unit, tenth and hundredth digit can be used by each of three digits.
So,Total possible numbers with these digits=3 X 3 X 3 =27.
First, As we have 27 three digit number, Sum will be for sure more than 2700..Eliminate options A,B,D
Second, If you imagine numbers W with the given digits 1,5,8. We have numbers like 888,885,855,858,851. Sum is for sure more than 4000.Eliminate option C.
You are left withanswer E.
Answer: E
Question: List I: 2, 6, 8, 19
List II: x, 2, 6, 8, 19
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(6+8)/2=7.
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 7, then x=7.
Answer: A.
Answer: A
Question: David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
Options:
A)19
B)28
C)30
D)37
E)47
Rationale: Suppose their paths cross after x minutes. Then, 11 + 57x = 51 - 63x => 120x = 40
x=1/3
Number of floors covered by David in (1/3) min. = (1/3)*57= 19
So, their paths cross at (11 +19) i.e., 30th floor.
ANSWER:C
Answer: C
Question: By selling a book for 200, 20% profit was earned. What is the cost price of the book?
Options:
A)A)215
B)B)166
C)C)230
D)D)235
E)E)240
Rationale: SP = 120% of CP; :. CP = 200 × 100/120 = 166
Option 'B'
Answer: B
Question: What will come in place of the x in the following Number series? 5,28,57
Options:
A)156
B)159
C)166
D)170
E)88
Rationale: 28=23+5
57=29+28
88=31+57
=88
E
Answer: E
Question: What is the average of four tenths and six thousandths
Options:
A)0.2022
B)0.3325
C)0.203
D)0.2012
E)0.2114
Rationale: Explanation:
Four tenths = 0.4
Six thousandths = 0.006
The average is (0.4 + 0.006)/2 = 0.2030
Answer: C
Answer: C
Question: A Purse contains a total of 93 coins in the form of one rupee and 50 paise coins. If the total value of coins in the Purse is Rs.56, find the number of 50 paise coins in the Purse?
Options:
A)59
B)30
C)60
D)74
E)80
Rationale: D
74
Let the number of one rupee coins in the Purse be x.
Number of 50 paise coins in the Purse is 93 - x.
Total value of coins
[100x + 50(93 - x)]paise = 5600 paise
=> x = 74
Answer: D
Question: By selling a watch for Rs.400/-, a man loses 20% what is that watch cost price?
Options:
A)s. 600/-
B)s. 700/-
C)s. 800/-
D)s. 500/-
E)s. 900/-
Rationale: 80 % ------> 400 (80 * 5 = 400)
100 % ------>500 (100 * 5 = 500)
Cost price = Rs. 500/-
D)
Answer: D
Question: If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element?
Options:
A)27 grams
B)21 grams
C)29 grams
D)31 grams
E)32 grams
Rationale: Let original mass be 100
The final mass of that element will be 7
So whatever option we have it will be divisible by 7
Check for the options the one that doesn't produce non terminating decimal is our answer
A. 27 grams
27/7 = 3.857...
B. 21 grams
21/7 = 3
C. 29 grams
29/7 = 4.142.......
D. 31 grams
31/7 = 4.428.....
E. 32 grams
32/7 = 4.571....
Hence our answer will be (B)
Answer: B
Question: At exactly what time past 5:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
Options:
A)20 13/21 minutes past 7:00
B)20 13/17 minutes past 7:00
C)21 3/23 minutes past 7:00
D)21 9/11 minutes past 7:00
E)22 4/9 minutes past 5:00
Rationale: A1 = hour angle
A2 = minute angle
A1-A2 = 90
Assume the minutes = M
A1 = (5*60+M)/12*60 )*360
A2 = M*360/60
Solving all three equation , results in the answer E
Answer: E
Question: Which of the following is greatest?
Options:
A)1/10
B)1/100
C)1/1000
D)1/10^9
E)1/5
Rationale: Simply we eliminate B,C,D. 1/5 > 1/10
Answer : E
Answer: E
Question: P, Q, R enter into a partnership. P initially invests 25 lakh & adds another 10 lakhs after one year. Q initially invests 35 lakh & withdrawal 10 lakh after 2 years and R invests Rs 30 Lakhs . In what ratio should the profit be divided at the end of 3 years?
Options:
A)18:19:19
B)18:18:19
C)19:19:18
D)18:19:19
E)None of these
Rationale: Explanation :
P:Q:R = (25*1+35*2) : (35*2 : 25*1) : (30*3)
= 95 : 95 : 90
= 19 : 19: 18. Answer : Option C
Answer: C
Question: The admission charge in a water park is $1 by adult and $0.75 by child accompanying an adult.
How much was there of child with an adult who paid in quite $3.25 to have access to the water park?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: a = # of adults Price for on adult = $1.00
e = # of kids Price for on kid (accompanying an adult) = $0.75
t = total ($) $3.25
t = Price for an adult*a + Price for on kid * e
3.25 = $1*a + $0.75*e
3.25 = a + $0.75*e
Because the kids have to be accompanying by an adult, a = 1
$3.25 = 1 + $0.75*e
$3.25 - 1 = 1 - 1 + $0.75*e
$2.25 = $0.75*e
$2.25 / $0.75 = ($0.75*e) / $0.75
3 = e = number of kids accompanying an adult.
Correct option: C) 3 kids
Answer: C
Question: A five digit number is to be formed using each of the digits 1, 2, 3, 4 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?
Options:
A)12
B) 36
C) 72
D) 60
E) 120
Rationale: Reqd ways = (Total No. of ways - cases when both 1 and 2 are together)
4 numbers can be arranged in 4 places in 4! ways. Now tie 1 and 2 together so effectively there are 4 nos. they can be arranged in 3! ways. 1 and 2 can be arranged within themselves in 2!ways.
Reqd. Answer = 4! - 3!2! = 24 - (6*2) = 12
Answer: A
Answer: A
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
Options:
A)680
B)700
C)720
D)740
E)760
Rationale: 720
C
Answer: C
Question: 5 and 20 are the first two terms in a geometric sequence. What is the arithmetic difference between the 10th term and the 12th term?
Options:
A)3*5^2
B)5* 3^13 - 5 * 3^11
C)75*4^10
D)40 * 3^10
E)3^12 - 3^10
Rationale: Common ratio = 20/5 =4
12th term = 5*4^12
10th term = 5*4^10
5 * (4^12 - 4^10) = 5 * 4^10*(4^2 - 1)
= 5 * 4^10 * 15
= 75 * 4^10....
C
Answer: C
Question: Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?
Options:
A)4.2
B)4.4
C)4.7
D)5.1
E)1.2
Rationale: Answer: Option C
In this simple addition series, each number increases by 0.8.
Answer: C
Question: David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, mathematics, physics, chemistry and biology. What are his average marks?
Options:
A)65
B)69
C)75
D)None of these
E)Cannot be determined
Rationale: Solution:
Average= (76+65+82+67+85)/5 =375/5 =75.
Hence, average =75.
Answer: Option C
Answer: C
Question: A certain class of students is being divided into teams. The class can either be divided into 12 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
Options:
A)24
B)36
C)48
D)60
E)72
Rationale: Let total no of students in the class be N
So, we are told that N is divisible by both 12 24
So, Lets find the least common multiple of 12 24 , ie 24
So our answer is (A) 24
Answer: A
Question: Find all rational zeros of P(x) = x3 - 7x + 6.
Options:
A)x=1,2,-3
B)x=2,2,-5
C)x=7,4,-8
D)x=6,6,-9
E)x=2,1,-3
Rationale: P(x) = x3 - 7x + 6 : given
leading coefficient 1 and its factors are : +1,-1
constant term is 6 and its factors are : +1,-1,+2,-2,+3,-3,+6,-6
possible rational zeros : +1,-1,+2,-2,+3,-3,+6,-6
test : P(1) = 0, P(2) = 0 and P(-3) = 0
x = 1, x = 2 and x = -3 are the zeros of P(x).
correct answer A
Answer: A
Question: What is the remainder when 3^29 is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1}
29 has the form 4k+1, so the units digit of 3^29 is 3.
The remainder when dividing by 5 is 3.
The answer is D.
Answer: D
Question: Find out the square of a number which when doubled exceeds its one nineth by 17 ?
Options:
A)16
B)25
C)81
D)26
E)17
Rationale: Let the number be p, then the square will be p^2
According to question:
2p = (p/9) + 17
=> 18p = p + 153
=> p = 9
p^2 =9^2 = 81
Answer : C
Answer: C
Question: The probability of Sam passing the exam is 1/2. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test?
Options:
A)1/24.
B)1/2.
C)1/3.
D)2/3.
E)2/5
Rationale: 1/2 *1/m= 1/6 , 1/m = 1/3
Answer C
Answer: C
Question: Mr. Wayne bungee jumps from the top of a building straight to the ground at a constant speed. 3 seconds after he starts plummeting he passes the 20th floor. 15 seconds after he starts plummeting he passes the 5th floor. Each floor is 3.8 meters high. What is Mr. Wayne's speed in meters per second?
Options:
A)3
B)4.75
C)4
D)4.25
E)5
Rationale: IMO: B
15 Floors * 3.8 Meter/Floor = 57 Meters
Time= 12 sec
Rate * 12 = 57
Rate= 57/12
=4.75
Answer B
Answer: B