divelab/Sys2Bench huggingface dataset:
Question: What is the units digit of (52^5)(37^3)(71^9)?
Options:
A)3
B)4
C)6
D)7
E)8
Rationale: The units digit of 52^5 is the units digit of 2^5 which is 2.
The units digit of 37^3 is the units digit of 7^3 which is 3.
The units digit of 71^9 is the units digit of 1^9 which is 1.
The units digit of 2*3*1 is 6.
The answer is C.
Answer: C
Question: In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?
Options:
A)3990
B)1540
C)1995
D)3672
E)2314
Rationale: We must place all these books as under:
XEXEX….XEX
There are 21 books on English, 19 books on Hindi
19 places out of 22 can be chosen 22C19=22C3=1540 ways
ANSWER B 1540
Answer: B
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 20 with him, what was the average amount with the group before his joining the group?
Options:
A)s.17
B)s.12
C)s.15
D)s.29
E)s.20
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 20. So, the amount with remaining 6 people = 140 - 20 = Rs. 20
The average amount with them = 120/6
= Rs.20.
Answer:E
Answer: E
Question: If 1 tic equals 4 tacs and 5 tacs equal 8 tocs, what is the ratio of one tic to one toc?
Options:
A)15/2
B)6/5
C)5/6
D)32/5
E)1/15
Rationale: Tic=4*Tac and 5*Tac=8*Toc;
5*Tic=20*Tac and 20*Tac=32*Toc --> 5*Tic=32*Toc --> Tic/Toc=32/5.
Answer: D.
Answer: D
Question: In a class there are 20 boys and 30 girls. In how many ways can a boy and a girl be selected?
Options:
A)400
B)500
C)600
D)530
E)630
Rationale: Explanation:
We can select one boy from 20 boys in 20 ways.
We select one girl from 30 girls in 30 ways
We select a boy and girl in 20 * 30 ways i.e., = 600 ways.
Answer: Option C
Answer: C
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)22
B)10 minutes
C)88
D)566
E)222
Rationale: 4/12 + x/15 = 1
x = 10.Answer: B
Answer: B
Question: Man1 alone can do a piece of work in 6 days and Man2 alone in 8 days. Man1 and Man2 undertook to do it for Rs. 3200. With the help of Man3, they completed the work in 3 days. How much is to be paid to Man3?
Options:
A)400
B)200
C)100
D)150
E)500
Rationale: Man3 1 day work = 1/3-(1/6+1/8) = 1/3-7/24 = 1/24
Man1 : Man2: Man3 = 1/6:1/8:1/24 ==>4:3:1
Man3 share = 3*1/24*3200 = Rs 400
ANSWER A
Answer: A
Question: A ratio between two numbers is 7:9 and their L.C.M. is 189. The Second number is
Options:
A)35
B)25
C)20
D)27
E)None
Rationale: Sol.
Let the required numbers be 7x and 9x. Then, their L.C.M. is 63x.
∴ 63x = 189⇔ x = 3. Hence, the Second number is 27.
Answer D
Answer: D
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?
Options:
A)11
B)50
C)88
D)65
E)22
Rationale: 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:B
Answer: B
Question: 1.12.91 is the first Sunday. Which is the fourth Tuesday of December 91?
Options:
A)20.12.91
B)22.12.91
C)24.12.91
D)25.12.91
E)None of these
Rationale: Explanation :
Given that 1.12.91 is the first Sunday
Hence we can assume that 3.12.91 is the first Tuesday
If we add 7 days to 3.12.91, we will get second Tuesday
If we add 14 days to 3.12.91, we will get third Tuesday
If we add 21 days to 3.12.91, we will get fourth Tuesday
=> fourth Tuesday = (3.12.91 + 21 days) = 24.12.91. Answer : Option C
Answer: C
Question: A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet?
Options:
A)124 sq.ft.
B)120 sq.ft.
C)126 sq.ft.
D)129 sq.ft.
E)132 sq.ft.
Rationale: Let l = 9 ft.
Then l + 2b = 37
=> 2b = 37 - l = 37 - 9 = 28
=> b = 28/2 = 14 ft
Area = lb = 9 × 14 = 126 sq. ft.
Answer is C.
Answer: C
Question: Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction Q of the work will be done by Adam?
Options:
A) 1/4
B) 12/47
C) 1/3
D) 5/12
E) 20/47
Rationale: Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.
adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work
Q>( 60/47 *12)/60 =12/47
Answer B
Answer: B
Question: The average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew, who weighs 53 kg is replaced by a new man. Find the weight of the new man.
Options:
A)69
B)72
C)75
D)71
E)None of them
Rationale: Total weight increased =(1.8 x 10) kg =18 kg.
:. Weight of the new man =(53 + 18) kg =71 kg.
Answer is D
Answer: D
Question: Which number, when found in the denominator of any given fraction, gives a terminating decimal?
Options:
A)2^3 * 3^4
B)5^2 * 7^3
C)2^4 * 11^3
D)5^3 * 11^2
E)2^4 * 5^3
Rationale: All the other choices except Option E have numbers other than 2 or 5.
Option E.
Answer: E
Question: A man sold 18 toys for Rs. 21000, gaining thereby the cost price of 3 toy find the cost price of a toy
Options:
A)s. 600
B)s. 800
C)s.500
D)s.900
E)s. 1000
Rationale: Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 21000.
Gain = SP â€“ CP
3X = 21000 â€“ 18X
21X = 21000
X = Rs. 1000.
ANSWER : OPTION E
Answer: E
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 45 more than n. What is y in terms of x ?
Options:
A)x+5
B)x+3
C)x+4
D)x-3
E)x-4
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 45 more than 10x+y
10x+y+45=10y+x
10x-x+45=10y-y
9x+45=9y
x+5=y
OR
y=x+5
Answer : A
Answer: A
Question: A man has Rs. 630 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)45
B)60
C)75
D)90
E)118.125
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 630
16x = 630
x = 39.375.
Hence, total number of notes = 3x = 118.125.
Answer = E
Answer: E
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,90,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)80000
B)60000
C)50000
D)76000
E)90000
Rationale: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (190000 - x) respectively. Then,
=1/3 x = 1/2 (190000 - x)
=x/3 + x/2 = 95000
=5x/6 = 95000
=x = 95000 x 6 /5	= 114000
Savings in Public Provident Fund = Rs. (190000 - 114000) = Rs. 76000
Answer is D
Answer: D
Question: A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 5 a rupee. Find his net profit or loss percent?
Options:
A)33 1/8 %
B)33 7/3 %
C)33 1/3 %
D)33 5/8 %
E)20 %
Rationale: The total number of mangoes bought by the shopkeeper be 30.
If he buys 6 a rupee, his CP = 5
He selling at 5 a rupee, his SP = 6
Profit = SP - CP = 6 - 5 = 1
Profit Percent = 1/5 * 100 = 20 %
Answer: E
Answer: E
Question: In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons?
Options:
A)A)160
B)B)6720
C)C)6570
D)D)210
E)E)230
Rationale: 8p2 =8 x 7 × 6 × 5 x4 =6720
Option 'B'
Answer: B
Question: The list price of an article is Rs.66. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)3.45%
B)4.45%
C)5.45%
D)6.45%
E)7.45%
Rationale: 66*(90/100)*((100-x)/100) = 56.16
x = 5.45%
ANSWER:C
Answer: C
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 30% profit on the first article and 30% loss on second article. Find the net profit or loss percent?
Options:
A)200
B)768
C)276
D)300
E)279
Rationale: Profit on first article = 30% of 1000 = 300.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: D
Answer: D
Question: Excluding the stoppages, the speed of a bus is 12 km/hr and including the stoppages the speed of the bus is 6 km/hr. For how many minutes does the bus stop per hour?
Options:
A)15 min
B)30 min
C)12 min
D)20 min
E)18 min
Rationale: Speed of the bus without stoppage=12 km/hr
Speed of the bus with stoppage=6 km/hr
Difference in speed=6 km/hr
so,the time taken in the stoppages = time taken to cover 6 km=(6/12)hr = 1/2 hr =30 min
ANSWER:B
Answer: B
Question: A square is of side 1 km. A man travels first 2 sides with the 30 mph and third side with 60 kmph. What is the speed that man has to travel the fourth side if the average speed is 60 kmph
Options:
A)100 Kmph
B)110 Kmph
C)120 Kmph
D)130 Kmph
E)140 Kmph
Rationale: 1 Mile= 1.6 Km
Total time taken to travel 3 sides =(1/48)+(1/48)+(1/60)= 7/120 hr
time taken to travel 4 sides at avg speed= 1/15 hr
So, reqred speed for fourth side= 1/{(1/15)-(7/120)}= 120 Kmph
ANSWER:C
Answer: C
Question: A library has an average of 510 visitors on Sunday and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is
Options:
A)250
B)276
C)280
D)285
E)None
Rationale: Sol.
Since the month begins with a Sunday, so there will be five Sundays in the month.
∴ Required average = [510 x 5 + 240 x 25 / 30] = 8550 / 30 = 285
Answer D
Answer: D
Question: If a store adds 100 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 10%, what will the new inventory of chairs be?
Options:
A)40
B)60
C)100
D)140
E)220
Rationale: Explanation:
Letâ€™s say t = total current inventory of chairs. The first sentence states that 100 + t = (3/2)t. First solve for the current inventory:
100 + t = (3/2)t
100 = (3/2)t âˆ’ t
100 = (1/2)t
200 = t
The manager wants to increase this by 10%.
10% of 200 is 20, so the new inventory will be 220
Answer: E
Answer: E
Question: A can do a work in 24 days and B can do it in 12 days. In how many days A and B can do the work?
Options:
A)20 days
B)10 days
C)6 days
D)5 days
E)8 days
Rationale: Explanation:
A's 1day's work = 1/24
B's 1day's work = 1/12
They work together = 1/24 + 1/12 = 3/24 = 24/3 = 8 days
Answer: Option E
Answer: E
Question: How many prime numbers between 1 and 100 are factors of 143?
Options:
A)6
B)5
C)4
D)2
E)3
Rationale: factor of 143= 11*13--- 2 prime numbers
D
Answer: D
Question: Solve below question
y : 6y - 27 + 3y = 4 + 9 - y
Options:
A)2
B)4
C)6
D)7
E)8
Rationale: 9 y + y = 13 + 27
10 y = 40 => y = 4
B
Answer: B
Question: In the fifth grade at Parkway elementary school there are 420 students. 296 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
Options:
A)69.
B)73.
C)81
D)91
E)89
Rationale: Total students = 420
Boys = 296, Girls = 124
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 124 - 35 = 89.
Correct option: E
Answer: E
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
Options:
A)29
B)10
C)28
D)20
E)11
Rationale: 7*5: 5*x = 7:10
x = 10
Answer: B
Answer: B
Question: what is the area of a circle having the same perimeter as that of a square whose area is 121.
Options:
A)306
B)307
C)308
D)309
E)310
Rationale: side of the square=sqrt(12)=11
perimeter of the square=44
2*pie*r=44
r=44/2*pie
area of the circle=pie*r^2=308
ANSWER:C
Answer: C
Question: A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
Options:
A)A)1/32
B)B)1/16
C)C)1/8
D)D)2/5
E)E)1/2
Rationale: Favorable outcomes will be obtained by making Password using {0, 2, 3, 5, 7} i.e. 5 digits
Total Such Passwords = 5*5*5*5*5 = 5^5
Total Possible Password = 10*10*10*10*10 = 10^5
Probability = (5^5) / (10^5) = 1/2^5 = 1/32
Answer: option A
Answer: A
Question: A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
Options:
A)8 1/6 sec
B)8 1/9 sec
C)8 2/2 sec
D)8 1/2 sec
E)2 1/2 sec
Rationale: D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 1/2 sec
Answer: D
Answer: D
Question: Erik's mother gave him $86 to go to the store. Erik bought 3 loaves of bread and 3 cartons of orange juice. Each loaf of bread cost $3 and each carton of orange juice cost $6. How much money does Erik have left?
Options:
A)$24
B)$27
C)$59
D)$75
E)$35
Rationale: Step 1: Find the cost of the loaves of bread.
3 × $3 = $9
Step 2: Find the cost of the orange juice.
3 × $6 = $18
Step 3: Find the total cost of the groceries.
$9 + $18 = $27
Step 4: Find the amount of money left.
$86 – $27 = $59
Erik has $59 left.
Answer is C.
Answer: C
Question: A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
Options:
A)9 1/5 days
B)9 2/5 days
C)9 3/5 days
D)10
E)15
Rationale: Explanation:
(A + B + C)'s 1 day's work =	1/4
A's 1 day's work =	1/16
B's 1 day's work =	1/12
C's 1 day's work =	1/4-(1/16+1/12)=5/48
So, C alone can do the work in	48/5=9 3/5 days
ANSWER IS C
Answer: C
Question: If x and y are integers such that |y + 3| ≤ 3 and 2y – 3x + 6 = 0, what is the least possible value E of the product xy?
Options:
A)	-12
B)	-3
C)	0
D)	2
E)	None of the above
Rationale: How to deal with inequalities involving absolute values? First example shows us the so callednumber case
In this case we have |y + 3| ≤ 3 which is generalized |something| ≤ some number. First we solve as if there were no absolute value brackets:
y + 3 ≤ 3
y ≤ 0
So y is 0 or negative
Second scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:
y + 3 >= -3
y >= -6
Therefore we have a possible range for y: -6=<y<=0
Ok, so far so good, we're half way through. What about x?
Here's the formula: 2y – 3x + 6 = 0, rewrite it as 2y + 6 = 3x.
You can say that 2y + 6 is a multiple of 3 (=3x). So all values which must be integer must also satisfy this constraint. I'm just saying that, so it's easier to evaluate all the possible numbers (-6, -3, 0). If you plug in y = 0, x will be 2 and xy = 0 as the lowest possible value E.
Hence, Answer Choice C is the one to go.
Answer: C
Question: Look at this series 8, 22, 8, 28, 8, ... What number should come next?
Options:
A)34
B)8
C)12
D)44
E)30
Rationale: simple addition series with a random number, 8 - interpolated as every other number. In the series, 6 is added to each number except 8, to arrive at the next number.
ANSWER A
Answer: A
Question: 2+2+2²+2³ ... +2^11
Options:
A)2^9
B)2^10
C)2^16
D)2^12
E)2^37
Rationale: 2+2=2^2
2^2+2^2=(2^2)*(1+1)=2^3
2^3+2^3=(2^3)*(1+1)=2^4
so you can notice the pattern... in the end you will have 2^11+2^11, which will give you 2^12
Answer D
Answer: D
Question: One fourth of one third of two fifth of a number is 30. What will be40% of that number
Options:
A)A)360
B)B)150
C)C)180
D)D)200
E)E)220
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 30
then x = 30 * 30 = 900
40% of 900 = 360
Answer: Option A
Answer: A
Question: 30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq.m. Find the length of each stone slab?
Options:
A)150cm
B)767cm
C)88cm
D)666cm
E)776cm
Rationale: Area of each slab
=67.5/30m2=2.25m2
Length of each slab √2.25=1.5m=150cm
Answer: A
Question: If a = 105 and a^3= 21 * 25 * 15 * b, what is the value of b?
Options:
A)35
B)42
C)45
D)147
E)54
Rationale: First step will be to break down all the numbers into their prime factors.
105 = 3 * 5 * 7
21 = 7 * 3
25 = 5 * 5
15 = 3 * 5
so, (105)^3 = 3 * 7 * 5 * 5 *3 *5 *b
Therefore (3 * 5 * 7) ^ 3 = 3^2 * 5^3 * 7 *b
Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^2 * 5 ^3 * 7
b = 3*7^2 =3* 49=147
Correct answer D.
Answer: D
Question: Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk. If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.
Options:
A)21 liters
B)22 liters
C)20 liters
D)14 liters
E)28 liters
Rationale: Lets start with option:
Vessel capacity be 20litre:
8litre water removed and milk added: W=12litre, M=8litre
8litre mixture removed, (removed proportionately) : W= 12-4.8 = 7.2litre, M= 8-3.2 = 4.8 litre
8litre milk added ; W=7.2 litre, M=12.8 litre
Ratio will be 72/128 = 18/32 = 9/16
As we can see that milk is less so we have to select the ratio even less than 20,
Vessel capcity be 14 litre
8litre water removed and milk added: W=6 litre, M=8 litre
8litre mixture removed, (removed proportionately) : W= 6-3.4 = 2.6 litre, M= 8-4.6 = 3.4 litre
8litre milk added ; W=2.6 litre, M=11.4 litre
Ratio will be 26/114 = 8.66/38 (approx) very close to 9/40
So correct option is D
Answer: D
Question: A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 640 m?
Options:
A)120 sec
B)99 sec
C)89 sec
D)80 sec
E)88 sec
Rationale: Explanation:
v = 240/24 (where v is the speed of the train) = 10 m/s
t = (240+640)/10 = 88 seconds
Answer: Option E
Answer: E
Question: P, Q and R can do a work in 5 , 7 and 10 days respectively. They completed the work and got Rs.310. What is the share of Q and R respectively?
Options:
A)100 and 80
B)100 and 90
C)100 and 110
D)70 and 100
E)100 and 70
Rationale: The ratio of their working rates = 1/5 : 1/7 : 1/10 = 14 : 10 : 7.
Since, they work together, the share of Q
= 10/31 * 310 = Rs.100
the share of R = 7/31 * 310 = Rs.70
the share of Q and R respectively is Rs. 100 and Rs.70
Answer: E
Answer: E
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
Options:
A)156 m
B)189 m
C)175 m
D)134 m
E)972 m
Rationale: RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m
Answer:C
Answer: C
Question: The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?
Options:
A) 1/8
B) 1/2
C) 3/4
D) 7/8
E) 15/16
Rationale: P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.
Answer: D.
Answer: D
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140
B)156
C)175
D)214
E)None of these
Rationale: Explanation:
Given that the area of the square = 1225 sq.units
=> Side of square = âˆš1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
ANSWER IS A
Answer: A
Question: Jennifer works 20 days a month at d dollars per day for m months out of the year. Which of the following represents her yearly pay?
Options:
A)m/(20d)
B)20d
C)10md/6
D)20d/m
E)20md
Rationale: Total income of Jennifer in a year = d*20*m dollars. = 20dm Answer E
Answer: E
Question: In how many ways W can the crew of a ten oared boat be arranged ,when of the ten persons available, 2 of whom can row only on the bow side and 3 of whom can row only on the stroke side?
Options:
A)1. 10!/(2! * 3!)
B)2. 10!/(8! * 7!)
C)3. 5!/(3! * 2!)
D)4. (5!)^3/(3! * 2!)
E)5. 5!/(8! * 7!)
Rationale: Ans is D.
Going by the assumtion that both the Bow side and Stroke side will have 5 person each.
Five(3+2) of them had allready been selected(according to their preference), so from the remaining 5 we have to select 2 for the stroke side or 3 for the bow side.
and the 5 crew of each side can be arranged in 5! ways=W
Hence answer is 5C3 * 5! * 5!= (5!)^3/ 3!2!.D
Answer: D
Question: A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 10.00 a.m., at what time will he first touch a flag at 120 feet from the ground?
Options:
A)4 p.m.
B)5 p.m.
C)6 p.m.
D)8 p.m.
E)None of these
Rationale: Explanation:
Net ascent of the monkey in 1 hour = (30 - 20) feet = 10 feet.
So, the monkey ascends 90 feet in 9 hours i.e. till 7 p.m.
Clearly, in the next 1 hour i.e. till 8 p.m. the monkey ascends remaining 30 feet to touch the flag.
Answer:D
Answer: D
Question: A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is:
Options:
A)260
B)262
C)270
D)272
E)None of these
Rationale: Explanation:
Volume will be length * breadth * height, but in this case two heights are given so we will take average,
Volume=(12∗9∗(1+4 /2))m312∗9∗2.5m3=270m3
Option C
Answer: C
Question: In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
Options:
A)5
B)6
C)7
D)8
E)10
Rationale: Let us write the fraction for each group of students
Group A: younger than 10: 50% = 50/100 = 1/2
Group B: 10 years old: 1/20
Group C: older that 10 but younger than 12: 1/10
Group D: 12 years or older: 70 students
The fraction for group A, B and C together is given by
1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator
= 13 / 20 , add numerators
The fraction for group D is given by
20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students
If X is the total number of students, then
7 / 20 of X = 70
or (7 / 20) × X = 70
Solve for X
X = 70 × (20 / 7) = 200
Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to
(1 / 20) of 200 = 10 students
correct answer is E)10
Answer: E
Question: What is the smallest prime number?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Explanation :
smallest prime number is 2.
0 and 1 are neither prime numbers nor composite numbers. Answer : Option C
Answer: C
Question: If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly twice in 2 consecutive flips ?
Options:
A)0.125
B)0.225
C)0.25
D)0.5
E)0.666
Rationale: Total number of ways in which H or T can appear in 3 tosses of coin is
= 2 * 2 = 4 ways
For 2 H
HH,
Thus probability is
= P(HH)
= 1/4
= .25
Answer : C
Answer: C
Question: What will come in place of the x in the following Number series? 6, 12, 21, 33 , x
Options:
A)33
B)35
C)39
D)48
E)42
Rationale: The pattern is + 6, + 9, + 12, +15 â€¦â€¦â€¦..
So the missing term is = 33 + 15 = 48
Answer : D
Answer: D