divelab/Sys2Bench huggingface dataset:
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned?
Options:
A)19828.29
B)19828.2
C)19828.8
D)19828.88
E)19828.21
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P
= 2828.80 / (0.08)(2.08)
= 1360/0.08 = 17000 Principal + Interest
= Rs.19828.80
Answer:C
Answer: C
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.
Options:
A)200
B)300
C)400
D)Cannot be determined
E)600
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: Option D
Answer: D
Question: How many numbers from 10 to 10000 are exactly divisible by 9?
Options:
A)900
B)1000
C)1110
D)1200
E)1400
Rationale: 10/9 = 1 and 10000/9 = 1111 ==> 1111 - 1 = 1110. Therefore 1110
Answer : C
Answer: C
Question: IF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
Options:
A)x(x+1)(x+2)
B)3x^3
C)9x^2
D)x-1
E)9x/3
Rationale: *any number multiplied by 3, will be divided by 3
for option D if we put value x=8, 8-1=7 is not divisible by 3
Answer : E
Answer: E
Question: If two numbers are in the ratio 7:2. If 5 is subtracted to both of the numbers then the ratio becomes 2:3then find the largest number?
Options:
A)26/17
B)37/17
C)35/17
D)25/17
E)24/17
Rationale: 7:2
7x - 5: 2x - 5 =2 : 3
3[7x - 5] =2[2x- 5]
21x - 15= 4x - 10
21x - 4x = 15 - 10
17x = 5, then x=5/17
Then the first number is = 7
7x = 35/17
Option C
Answer: C
Question: Panya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
Options:
A)1/24
B)1/8
C)1/4
D)1/3
E)3/8
Rationale: Total Panya# of ways - 4! = 24.
Desired:
A-Mapped to the only correct address----------x 1 way only
B-Mapped to other two incorrect addresses - x 2 ways
C-Mapped to other two incorrect addresses - x 2 ways
D-Mapped to other two incorrect addresses - x 2 ways
Therefore, 1*2*2*2/24 = 1/3.?
Answer: D
Question: saran professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
Options:
A)67 6/9%
B)54 1/2%
C)33 3/8%
D)11 1/9%
E)87 7/9%
Rationale: D
900 --- 100
100 --- ? => 11 1/9%
Answer: D
Question: 47% of the students in a class of 44 students has glasses or contacts. How many students in the class have either glasses or contacts?
Options:
A)15
B)16
C)17
D)18
E)21
Rationale: a=r⋅b
47%=0.47a
=0.47⋅34
a≈21
Option E is correct.
Answer: E
Question: There are 324,437 chicks in a farm. Jack wants to distribute these evenly across 9 different retail shops, how many chicks would remain with him.
Options:
A)1 chicks
B)2 chicks
C)3 chicks
D)4 chicks
E)5 chicks
Rationale: This is equivalent to finding the first number that is divisible by 9 that occurs before 324,437.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 324,437 = 23 and 18 is divisible by 9.
Hence, we need to remove 5 to this number for it to be divisible by 9
Correct Option: E
Answer: E
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)30/16 hours
B)80/13 hours
C)30/73 hours
D)30/13 hours
E)50/13 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream
= d/s = 60/26
= 30/13 hours.
Answer:D
Answer: D
Question: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 28 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
Options:
A)6 2/3
B)15
C)20
D)25
E)30
Rationale: Here is how I did it:
The cyclist travels 28 miles in 60 mins, so in 5 mins he will travel [(28*5)/60] miles, which equals 7/3 miles in 5 mins.
Now the hiker travels 4 miles in 60 mins. To travel 7/3 miles, he will take [(60*7/3)/4] = 35 mins.
hence 35-5 =30 mins
E
Answer: E
Question: Ella and Frank race around a running track. Ella runs at a constant rate of one lap every 3 minutes and Frank runs at a constant rate of one lap every 5 minutes. If they both start at the same time, how many minutes will it take for Ella to get exactly one lap ahead of Frank?
Options:
A)5.5
B)6.5
C)7.5
D)8.5
E)9.5
Rationale: Let x be the number of minutes it takes for Ella to get one lap ahead.
Then Ella ran x/3 laps and Frank ran x/5 laps.
x/3 = 1+x/5
5x=15+3x
2x=15
x=7.5
The answer is C.
Answer: C
Question: A person spent Rs. 6,040 from his salary on food and 5,000 on house rent. After that he was left with 80% of his monthly salary. What is his monthly salary ?
Options:
A)55,200
B)65,200
C)75,200
D)85,200
E)95,200
Rationale: Total money spent on food and house rent = 6,040+5,000 = 11,040
Which is 100 - 80 = 20% of his monthly salary
∴ His salary = 11040x100/20 = 55200
Answer : A
Answer: A
Question: What is the smallest no. which must be added to 25268 so as to obtain a sum which is divisible by 11?
Options:
A)5
B)10
C)11
D)20
E)30
Rationale: For divisibility by 11, the difference of sums of digits at even and odd places must be either zero or divisible by 11.
For 25268, Difference =(2+2+8) -(5+6)=12-11=1.
The units digit is at odd place. So we add 10 to the number
=> 25268 +10= 25278
Now , (2+2+8) -(5+7)=12-12=0=>25268 is also divisible by 11
B
Answer: B
Question: 15 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
Options:
A)190
B)200
C)210
D)220
E)225
Rationale: Though 2*(15C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.
The first guy has to play 2 matches with the rest of 14, so he'll play 28 matches.
Similarly, second guy has to play with the rest of 13 as his 2 games with the first guy are already played. So he plays 26 matches.
This continues like this and the total matches are 28+26+24...+2
28+26+...+2 = 2(14+13+...+1) = 2((14*15)/2) = 14*15 = 210.
ANSWER:C
Answer: C
Question: In measuring the sides of a rectangle, one side is taken 10% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.
Options:
A)3.5%
B)2.4%
C)3%
D)4.5%
E)2.6%
Rationale: Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.
Now, the area obtained with wrong measurements would be 110*95=10,450, which is 4.5% greater than the actual area.
Answer: D.
Answer: D
Question: 10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 3240, how much was it in the beginning?
Options:
A)A)3800
B)B)4200
C)C)4400
D)D)4500
E)E)4600
Rationale: X * (90/100) * (80/100) = 3240
X = 4500
ANSWER:D
Answer: D
Question: The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 460 kms in 4 hours, then the speed of the first train is:
Options:
A)100.6 km/hr.
B)37.25 km/hr.
C)90.25 km/hr.
D)94.25 km/hr.
E)96.25 km/hr.
Rationale: Let the speed of two bullet trains be 7x and 8x km/hr.
Then, 8x = (460/4) = 115
x = (115/8) = 14.375
Hence, speed of first bullet train = (7 x 14.375) km/hr = 100.6 km/hr.
A
Answer: A
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively. If they cross each other in 23 seconds, what is the ratio of their speeds?
Options:
A)1:2
B)3:2
C)3:1
D)1:3
E)1:4
Rationale: Speed =x and y resp
length of first = 27x
length of second train = 17y
related speed = x + y
time taken to cross each other = 23 s
27x+17y/x+y = 23
27x+17y = 23(x+y)
4x=6y
x/y=6/4=3/2
ANSWER B
Answer: B
Question: On the Richter scale, which measures the total amount of energy released during an earthquake, a reading of x-1 indicates one-tenth the released energy as is indicated by a reading of x. On that scale, the frequency corresponding to a reading of 9 is how many times as great as the frequency corresponding to a reading of 3?
Options:
A)40
B)50
C)10^4
D)10^5
E)10^6
Rationale: If Richter scale reading goes from X-1 to X it will be 10
if Richter scale reading goes from 3 to 4 it will be 10
if Richter scale reading goes from 4 to 5 it will be 10
if Richter scale reading goes from 5 to 6 it will be 10
Similarly if Richter scale reading goes from 6 to 7 it will be 10
and if Richter scale reading goes from 7 to 8 it will be 10
and if Richter scale reading goes from 8 to 9 it will be 10
so it will from 3 to 9 i.e 4,5,6,7,8,9 = 10*10*10*10*10*10 = 10^6
Answer is E
Answer: E
Question: In how many ways can 5 white and 2 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
Options:
A)120
B)60
C)10
D)240
E)30
Rationale: 5 white chess pieces can be arranged in 5! ways and 2 black pieces can be arranged in 2 ! ways.
W_W_W_W
Number of ways = 5!*2! = 120 * 2 = 240
Answer D
Answer: D
Question: When Jack picks olives for two hours at three times his regular speed, he picks 10 pounds of olives more than Mac working for five hours at 80% of his regular speed. Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 85% of his regular speed, then
Options:
A)Jack picks double the amount of olives Mac picks
B)Mac picks 10 pounds more than Jack
C)Jack picks 10 pounds more than Mac
D)Mac picks 5 more pounds than Jack
E)Jack picks 5 more pounds than Mac
Rationale: Let's say Jack's regular speed is J olives/hr and Mac's regular speed is M olives/hr
Given:
2*3J = 10 + 5*(4/5)M
3J = 5 + 2M
Question:if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed
Mac picks 2M and Jack picks 4*(3/4)J = 3J
They are asking you for the relation between 3J and 2M. You already know 3J = 5 + 2M
So Jack picks 5 pounds more olives than Mac.
E
Answer: E
Question: A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Options:
A)A)150
B)B)140
C)C)130
D)D)120
E)E)110
Rationale: A+B+C = 400
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 400
----------------
C = 150
Answer:A
Answer: A
Question: Three positive integers a, b, and c are such that their average is 28 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?
Options:
A)31
B)32
C)33
D)34
E)35
Rationale: Solution
Given Data
3 positive integers
Average of a, b, and c = 28.
So, a+b+c3a+b+c3 = 84 or a + b + c = 84
a ≤ b ≤ c
Median = (a + 13)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 13
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 13) + (a + 13) = 84 (b and c are equal and b, the median, is a + 13)
Or 3a = 58 or a = 19.33
So, b = c = 19.33+ 13= 32.33
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 13) + (a + 14) = 84
Or 3a = 57or a=19 The value of the numbers is an integer.
If a = 19, b = 32 and c = 33.
The least value for c that satisfies all these conditions is 33
Correct answer is choice C.
Answer: C
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)35
B)34
C)36
D)32
E)31
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: C
Answer: C
Question: A store reduced the price of all items in the store by 8% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place?
Options:
A)80.0
B)80.9
C)81.0
D)81.1
E)82.8
Rationale: consider price of the all items as $100
after a initial reduction of 8% price becomes = 0.92 *100 = $ 92
after the final reduction of 10% price becomes = 0.9* 92 = $ 82.8
price of all items on second day is 82.8% of price on first day
correct answer option E
Answer: E
Question: Noelle walks from point A to point B at an average speed of 5 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 8 kilometers per hour?
Options:
A)6.75
B)7
C)7.25
D)7.5
E)20
Rationale: Let's suppose that speed while returning was xkm/h
Since the distance is same, we can apply the formula of avg speed
Avg speed= 2S1S2/S1+S2
8= 2*5*x/5+x
x= 20
E is the answer
Answer: E
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
Options:
A)156
B)159
C)166
D)170
E)180
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: C
Question: JAMES school has 2000 GIRLS and 5000 BOYS. What is the percentage increase from GIRLS to total attendance and BOYS to total attendance?
Options:
A)40%
B)10%
C).4%
D)50%
E)12%
Rationale: Ratio of GIRLS to total attendance (2/7)
Ratio of BOYS to total attendance (5/7)
percentage increase is (difference/initial quantity)*100
(2/7)/(5/7 )* 100= 40%
Correct answer is A
Answer: A
Question: A train passes a platform in 22 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
Options:
A)40
B)50
C)60
D)30
E)20
Rationale: Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 12
=> 300+L = 15×22 = 330
=> L =330-300 = 30 meter
Answer is D.
Answer: D
Question: A box contains twelve bulbs out of which seven are defective. If seven bulbs are chosen at random, find the probability that all the four bulbs are defective?
Options:
A)1/127
B)1/792
C)1/789
D)1/689
E)1/126
Rationale: Out of twelve, five are good and seven are defective. Required probability
= 7C7/12C7
= 1/792
Answer: B
Answer: B
Question: The remainder obtained when a prime number greater than 3 is divided by 3 is
Options:
A)a) 1 or 3
B)b) 2 or 4
C)c) 3 or 5
D)d) 4 or 5
E)e) 5
Rationale: The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 3, i.e. 7 and 5:
7/3 = 1 + remainder of 4
5/3 = 1 + remainder of 2
This is already sufficient to see that answer choice b) is correct.
B
Answer: B
Question: The number of livestock in a farm at the beginning of year 2015 was 100,000. During the year, the number increased by p%. During the next year 2016, there was a famine and the number decreased by q%. A census at the end of year 2016 revealed that the number of livestock in the farm was 100,000. Which of the following expressions is correct?
Options:
A)q > p
B)p > q
C)p = q
D)With the exception of 1 instance, p will be equal to q
E)There is no relation between p and q
Rationale: Number plugging in will be best strategy for this question.
Let p = 5%,
Per the question 100000(1.05)(1-q/100) = 100000 ---> q = 4.7%. Thus p > q and hence B is the correct answer.
Answer: B
Question: The average of 3 consecutive odd numbers is 30. What is the difference between the highest and lowest numbers?
Options:
A)5
B)6
C)8
D)4
E)3
Rationale: Let the numbers be x, x+2, x+4
Then, (x+ x+2+ x+4)/3 = 30
x = 28
Required answer is = 28+4-28 = 4
Answer is D
Answer: D
Question: x and y are positive integers of Q. If 1/x + 1/y < 2, which of the following must be true?
Options:
A) x + y > 4
B) xy>1
C) x/y + y/x < 1
D) (x - y)^2 > 0
E) None of the above
Rationale: Answer is B:
1/X + 1/Y < 2
The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.
So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.
Another way of putting it is:
X*Y>1.B
Answer: B
Question: Which one of the following is a prime number?
Options:
A)55
B)2
C)74
D)25
E)21
Rationale: 2 is divisible by 1 and itself So, it is a prime number.
B
Answer: B
Question: If p^2 – 13p + 40 = a, and p is a positive integer between 1 and 10, inclusive, what is the probability that a < 0?
Options:
A)1/10
B)1/5
C)2/5
D)3/5
E)3/10
Rationale: p2 – 13p + 40 = a
so (p – 8)(p – 5) = a
For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.
The correct answer is B.
Answer: B
Question: What is the remainder when 47*50 is divided by 8?
Options:
A) 1
B) 3
C) 13
D) 5
E) 14
Rationale: we can make use of the rule :
Remainder of { (a * b)/n}} = Remainder of (a/n) * Remainder of (b/n)
Here
Remainder of { 47 * 50)/8}} = Remainder of (47/8) * Remainder of (50/8) = 7 * 2 = 14
Answer :E
Answer: E
Question: Two numbers are in the ratio of 6 : 8. If 10 is subtracted from each, the new numbers are in the ratio 16 : 32. Find the smaller number.
Options:
A)22
B)12
C)38
D)15
E)17
Rationale: Explanation:
Let the number be 6x and 8x.
Then, (6x – 10) / (8x – 10) = 1 / 2
2 (6x – 10) = (8x – 10)
12x – 20 = 8x – 10
4x = 10
x = 2.5
The smaller number = (6 x 2.5) = 15
ANSWER D
Answer: D
Question: There are 6 ball in bag out of them 4 green and 2 red, randomly picked two boll one by one so find the probabilty atleast one picked boll will be red?
Options:
A)1/5
B)2/5
C)3/5
D)4/5
E)6/5
Rationale: probality of selecting 1 red + probality of selecting 2 red =((2c1*4c1)/6c2)+((2c2)/(6c2))=3/5
ANSWER:C
Answer: C
Question: A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is
Options:
A)400 kg
B)560 kg
C)600 kg
D)640 kg
E)None
Rationale: Solution
ratio of 1st and 2nd parts = 4 : 6 = 2 : 3.
Quantity of 2nd kind = (3/5 x 1000)kg = 600 kg.
Answer C
Answer: C
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $29. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Options:
A)180xy
B)261/(xy)
C)20xy
D)20xy/9
E)xy/180
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 29 / (xy/9) = 261/(xy).
The answer is B.
Answer: B
Question: Michael cashed a check for $1,170 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?
Options:
A) $830
B) $800
C) $770
D) $730
E) $700
Rationale: 1. 15 bills spent
2. Number of $10 bills is one more or one less than number of $50 bills.
So, 2 choices
1. 7*10 + 8*50 = $470
2. 8*10 + 7*50 = $430
Least money lost implies most money spent. i.e $470
Therefore, lost money = 1170 - 470 = 700.
Answer E
Answer: E
Question: An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the same amount of time. What is the rate of the plane in still air ?
Options:
A)803km/hr
B)805km/hr
C)809km/hr
D)807km/hr
E)806km/hr
Rationale: Let the speed of the air plane in still air be x km/hr
And the speed of the wind be y km/hr.
Then speed of the airplane going with the wind = (x + y) km/hr
and speed of the airplane going against the wind = (x - y) km/hr.
We know that,
Distance = Speed × Time
or, Speed = Distance
Time
According to the problem,
An airplane travels 4362 km against the wind in 6 hours
x - y = 4362/6
or, x - y = 727 ----------- (1)
Again, the airplane travels 5322 km with the wind in the same amount of time i.e. 6 hours
x + y = 5322/6
or, x + y = 887 ----------- (2)
Now add (1) and (2) we get,
x - y = 727
x + y = 887
2x = 1614
or, 2x/2 = 1614/2, (Divide both sides by 2)
or, x = 807
Now substitute the value of value of x = 807 in equation (2) we get,
807 + y = 887
-807 -807, (Subtract 407 from both sides)
y = 80
Answer: Rate of the plane in still air = 807 km/hr
correct answer D)807 km/hr
Answer: D
Question: A train covers a distance of 12 km in 10 min. If it takes 8 sec to pass a telegraph post, then the length of the train is?
Options:
A)100
B)110
C)160
D)130
E)140
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 8 = 160 m.
Answer: Option C
Answer: C
Question: You get 1 & -0.25 for each right and wrong answer. Answring 72 ques u get 47. How many ans were wrong?
Options:
A)10
B)20
C)25
D)30
E)35
Rationale: let x be cort,thn 72-x are wrong.
x(1)+(72-x)(-1/4)=47
x=52,72-52=20.
so,20 are wrong.
ANSWER:B
Answer: B
Question: How many numbers are divisible by 4 between 1 and 100.
Options:
A)24
B)23
C)22
D)21
E)25
Rationale: Numbers divisible by 4 till 100=(100/4)=25
But we should not consider 100 as we are asked to find the number between 1 to 100 which are divisible by 4.
So answer is 24 numbers.
Option:A
Answer: A
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 215 m long?
Options:
A)40
B)46
C)88
D)77
E)21
Rationale: :
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 215 = 575 m
Required time = 575 * 2/25 = 46 sec
Answer:B
Answer: B
Question: How many times are the hands of a clock at right angle in a day?
Options:
A)45
B)84
C)55
D)22
E)44
Rationale: Explanation:
In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Answer is E
Answer: E
Question: You have been given a physical balance and 7 weights of 43, 45, 30, 33, 28, 37 and 55 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 145 kgs.
Options:
A)145
B)143
C)147
D)141
E)142
Rationale: 55 + 43 + 45 = 143
Answer: B
Answer: B
Question: If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 2?
Options:
A)-1
B)0
C)1
D)2
E)3
Rationale: Answer
x = 1 + √2
∴ x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 2
= x2(x - 2)2 +2
= (1 + √2)2(1 + √2 - 2)2 + 2
=(√2 + 1)2 (√2 - 1)2 + 2
=[(√2)2 - (1)2]2 + 2
=(2 - 1)2 =1 + 2=3
Correct Option: E
Answer: E
Question: Four children have small toys. The first child has 1/10 of the toys, the second child has 12 more toys than the first, the third child has one more toy of what the first child has and the fourth child has double the third child. How many toys are there?
Options:
A)20 toys
B)30 toys
C)40 toys
D)60 toys
E)50 toys
Rationale: x : the total number of toys
x/10 : the number of toys for first child
x/10 + 12 : the number of toys for second child
x/10 + 1 : the number of toys for the third child
2(x/10 + 1) : the number of toys for the fourth child
x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x
x = 30 toys : solve for x
correct answer B
Answer: B