divelab/Sys2Bench huggingface dataset:
Question: A car travels uphill at 30 km/hr and downhill at 80 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
Options:
A)38kmph
B)33kmph
C)34kmph
D)35kmph
E)36kmph
Rationale: avg speed=total distance/total time.
total distance traveled=100+50=150km;
time taken for uphill journey=100/30=10/3;
time taken for down hill journey=50/80=5/8;
avg speed=150/(10/3+5/8)=38kmph
ANSWER:A
Answer: A
Question: The number of arrangements that can be made with the letters of the word WORDS so that the vowels occupy the even places?
Options:
A)14
B)32
C)777
D)24
E)221
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 1 = 24.
Answer:D
Answer: D
Question: There are 50 students in a class. If 14% are absent on a particular day, find the number of students present in the class.
Options:
A)43
B)36
C)28
D)129
E)11
Rationale: Number of students absent on a particular day = 14 % of 50
i.e., 14/100 × 50 = 7
Therefore, the number of students present = 50 - 7 = 43 students.
Answer:A
Answer: A
Question: A train running at the speed of 27 km/hr crosses a post in 20 seconds. What is the length of the train?
Options:
A)200
B)150
C)300
D)175
E)250
Rationale: Speed=(27x5/18)=7.5 m/sec.
Length of the train=(Speed x Time).
Length of the train=7.5 x20	m = 150 m.
Answer: B
Answer: B
Question: The inverse ratio of 3: 2: 1 is?
Options:
A)2:3:7
B)2:3:9
C)2:3:2
D)2:3:6
E)2:3:1
Rationale: 1/3: 1/2: 1/1 = 2:3:6
Answer:D
Answer: D
Question: Luke travelled 12 2/3 miles in 1 hours and 40 minutes. What was his average rate of speed in miles per hour?
Options:
A)7
B)7 3/5
C)8 1/5
D)9
E)9 2/5
Rationale: D = 12(2/3) = 38/3
T = 1(2/3) = 5/3
S = D/T = 7 3/5
Answer = B
Answer: B
Question: If x = 7 and y = −2, what is the value of (x − 2y)^y?
Options:
A)−100
B)0.001
C)0.25
D)4
E)8
Rationale: Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
by inversing and squaring 0.001
Answer: B
Answer: B
Question: The sum of 4 hours 45 minutes and 5 hours 55 minutes is approximately what percent of a day?
Options:
A)32%
B)36%
C)40%
D)44%
E)48%
Rationale: Since the question is asking for an approximate percentage
4:45+5:55 ~ 11 hours
% of day = 11*100/24 ~ 11*100/25= 44%
Answer is D.
Answer: D
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)10 km/hr
C)12.5 km/hr
D)9 km/hr
E)None of these
Rationale: Explanation:
Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 15 - 2.5 = 12.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 12.5 - 2.5 = 10 km/hr
ANSWER IS B
Answer: B
Question: 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 20% of the total school population of x students, what is x?
Options:
A)125
B)150
C)212
D)250
E)500
Rationale: 90=x/100*20/100*x=>x^2 = 9*10000/2 = > x =212
C
Answer: C
Question: If z + | z | = 0, which of the following must be true?
Options:
A)z > 0
B)z≥0
C)z< 0
D)z≤0
E)z = 0
Rationale: Manipulate the equations:
z + | z | = 0
|z| = -y
-z > 0 OR -z = 0
This means z could be 0 or z is less than 0.
D. z≤0
E. z=0
Answer: D
Answer: D
Question: If 20% of s = t, then t% of 20 is the same as
Options:
A)10% of s
B)4% of s
C)20% of s
D)None
E)30% of s
Rationale: Explanation :
20% of s = t
=> t = 20/100s
Then,
t% of 20 = (t/100)*20=((20/100)*s)*20/100
=(2020s)/(100100) =4s/100 = 4% of s
Answer : B
Answer: B
Question: What is the minimum value of z for which z^2 + z - 3/6 > 0 is not true?
Options:
A) -5/2
B) -3/2
C) -1
D) 1/4
E) 1/2
Rationale: I think C -1 is the best ans...
Answer: C
Question: One side if a square is doubled. If the parameter is now 12x. What was the length of one of the sides before it was doubled?
Options:
A)12x/4
B)12x/2
C)6x/2
D)12x/6
E)4x/1
Rationale: If the parameter is now 12x, the each side is 12x/4. To get the original each side is divided by 2. One side is represented by 1 since it's a square. 1/2 is 0.5, which when times by 4 is 2. Thus the answer is 12x/2. Answer option B.
Answer: B
Question: How many of the following numbers are divisible by 22 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: By using your calculator you can calculate that the following numbers are divisible by 22 : 264, 396, 462, 792, 968, 2178, 6336.
Required number of number = 7.
E
Answer: E
Question: A lady builds 10cm length, 13cm width, and 5cm height box using 5cubic cm cubes. What is the minimum number of cubes required to build the box?
Options:
A)107
B)108
C)130
D)150
E)145
Rationale: Number of cubes required = Volume of box/Volume of cube
= 10*13*5/5
=130 cubes
ANSWER:C
Answer: C
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+3 and 7*+7, inclusive ?
Options:
A)4
B)1
C)2
D)3
E)0
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 7* + 3 = 7! + 2 and 7* + 7 = 7! + 7.
Now, notice that we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 3 and 7! +7, inclusive. Which means that there are no primes in this range.
Answer: E
Answer: E
Question: Find the smallest number of 6 digits which is exactly divisible by 111?
Options:
A)12000
B)15550
C)100011
D)158993
E)100010
Rationale: Smallest number of 6 digits is 100000.
On dividing 100000 by 111, we get 100 as remainder.
Number to be added = (111 - 100) - 11.
Hence, required number = 100011
Answer B
Answer: B
Question: If m is a positive integer and m^2 is divisible by 24, then the largest positive integer that must divide m is?
Options:
A) 3
B) 6
C) 8
D) 12
E) 16
Rationale: M^2 is divisible by 48 so M^2 must be multiple of 48.
If the value of M is Multiples of 8 then it will satisfy the condition. If we If M is 12 or 24 or 36 then it ans is C but if M = 48 then answer should be 16.
Is the question right? Or am i missing some thing?
C
Answer: C
Question: A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options:
A)17.5%
B)24%
C)30%
D)35%
E)38%
Rationale: Suppose enrollment in 1991 was 100
Then enrollment in 1992 will be 120
And enrollment in 1993 will be 120*1.15=138
Increase in 1993 from 1991 = 138-100= 38
Answer : E
Answer: E
Question: a person travels from his house to office from 11:10am to 11:50 am and covers a distence of 13.4km. find the average speed of the person.
Options:
A)20.1km/h
B)20.5km/h
C)21.1km/h
D)22.1km/h
E)20.9km/h
Rationale: time=11:50-11:10=40min=2/3hour
distance=13.4km
speed=13.4*3/2=20.1km/h
ANSWER:A
Answer: A
Question: 3/x + 3x = 3(x-9)
Options:
A)-9
B)-1/6
C)-1/9
D)1/9
E)9
Rationale: We can solve - expand the right side, multiply by x on both sides and then subtract away the 3x^2 terms:
(3/X) + 3x = 3(x-9)
(3/x) + 3x = 3x - 18
3 + 3x^2 = 3x^2 - 18x
3 = -18x
-1/6 = x
and to confirm, you can plug that answer back into the original equation to see that it makes the left and right sides equal.
B
Answer: B
Question: A bowl of fruit contains 14 apples and 21 oranges. How many oranges must be removed so that 70% of the pieces of fruit in the bowl will be apples?
Options:
A) 3
B) 15
C) 14
D) 17
E) 20
Rationale: Number of apples = 14
number of oranges = 23
let number of oranges that must be removed so that 70% of pieces of fruit in bowl will be apples = x
Total number of fruits after x oranges are removed = 14+(21-x) = 35-x
14/(35-x) = 7/10
=>20 = 35-x
=>x= 15
Answer B
Answer: B
Question: A train 210 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 120 meters long is?
Options:
A)29
B)22
C)48
D)99
E)11
Rationale: D = 210 + 120 = 330
S = 54 * 5/18 = 15 mps
T = 330/15 = 22 sec
Answer: B
Answer: B
Question: An air conditioner can coo the hall in 15 minutes while another takes 20 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?
Options:
A)about 5 minutes
B)about 7 minutes
C)about 15 minutes
D)about 19 minutes
E)about 9 minutes
Rationale: Take LCM of 15 and 20 = 60
15*4=60/ 20*3=60.
So if both are switched on together , room cooled in 60/(4+3)=60/7=8.57 minutes
8.57 can be round to 9 minutes , so about 9 minutes
ANSWER: E
Answer: E
Question: At the store opening, Larry's Grocery had 50 Lemons and 60 Oranges. By closing, the store at 20 Lemons and 40 Oranges left. By approximately what percent did the ratio of Lemons to Orange decrease from opening to closing.
Options:
A)50.0%
B)40.0%
C)30.0%
D)20.0%
E)10.0%
Rationale: Opening: Lemons/Oranges = 50/60 =100/120
Closing: Lemons/Oranges = 20/40 =60/120
ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.
So, our ratio went from 100/120 to 60/120
Ignoring the denominators, we went from 100 to 60
The percent change = 100(difference in values)/(original value)
= (100)(100-60)/100
= (100)(40)/100)
= 40
Answer: B
Answer: B
Question: .
On dividing a number by 357, we get 40 as remainder. On dividing the same number 17, what will be the remainder ?
Options:
A)6
B)3
C)5
D)8
E)11
Rationale: Let x be the number and y be the quotient. Then,
x = 357 x y + 40
= (17 x 21 x y) + (17 x 2) + 6
= 17 x (21y + 2) + 6)
Required remainder = 6.
Answer: Option A
Answer: A
Question: A number x is 7 times another number y. The percentage that y is less than x is
Options:
A)12.5%
B)85.7%
C)80%
D)11%
E)1%
Rationale: Say y=1 and x=7.
Then y=1 is less than x=7 by (7-1)/7*100=6/7*100=85.7%.
Answer: B.
Answer: B
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is
Options:
A)100
B)110
C)120
D)140
E)150
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer: A
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
Options:
A)1.2
B)3.78
C)16.5
D)5.84
E)7.62
Rationale: Explanation:
Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Correct Option : C
Answer: C
Question: From a group of 7 men and 6 women, 4 persons are to be selected to form a committee so that at most 2 men are there in the committee. In how many ways can it be done?
Options:
A)480
B)520
C)760
D)470
E)464
Rationale: Total Men = 7
Total Women = 6
Persons in committee = 4
No. of ways to select at most 2 men = 6C4 + 7C1 * 6C3 + 7C2*6C2
= 470
Ans -D
Answer: D
Question: 14, 35, 56, 91, 126
In the sequence above, each term is related with the others. Which of the following could not be a term in the sequence?
Options:
A)407
B)259
C)322
D)686
E)847
Rationale: Simplifying the question into easier words we just need to find which of the numbers is not divisible by 7
clearly the answer is 407 because if we divide 407 by 4 we get a remainder of 1
Correct answer - A
Answer: A
Question: Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. Find out his new time compared with the old time.
Options:
A)twice as much
B)three times as much
C)the same
D)half as much
E)a third as much
Rationale: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
Answer is A.
Answer: A
Question: When x is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < x< 200, what is the greatest possible value of x?
Options:
A)5
B)19
C)61
D)74
E)110
Rationale: Answer is E.
I started with E.110 and it fits the bill . 105 is divisible by 7 and 104 is divisible by 13. so its E.
Modular approach would be the proper way, but this worked at first attempt. E
Answer: E
Question: The age of Ritu's mother is 6 times that of Ritu's age. After 6 years it will be 3 times that of Ritu's age. what is Ritu's mother present age?
Options:
A)24 years
B)26 years
C)28 years
D)10 years
E)None of the above
Rationale: Let present age of Ritu=x
then, present age of ritu's mother=6x
A/c
after 6 years
=>6x+6=3(6+x)
x=4
so, Ritu mother present age is 24 years
ANSWER:A
Answer: A
Question: Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "RAT"?
Options:
A)108
B)111
C)114
D)117
E)120
Rationale: "RAT" = (18+1+20)*3=117.
The answer is D.
Answer: D
Question: For any non-zero a and b that satisfy |ab| = -ab and |a| = a, a^2+b^2+2|ab| =?
Options:
A)ab-4
B)(a+b)^2
C)(a-b)^2
D)a^2-|ab+ab^2|
E)4-ab
Rationale: Given: |ab| = -ab and |a| = a
Question: a^2+b^2+2|ab| =?
**** Looking at |ab| = -ab tells us that a and b are either positive or negative
**** Looking at |a| = a tells us that a must be positive
**** Combine two observations: a is positive, b is negative
so a^2+b^2+2|ab| = a^2+b^2-2ab.
as we know : (a-b)^2= a^2+b^2-2ab.
hence option c is correct.
Answer: C
Question: A boat crossed a lake from West to South at the speed of 8 km/h, entered a river and covered twice as much distance going upstream at 7 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?
Options:
A)4
B)5
C)6
D)7
E)9
Rationale: One way of solving this is:
Speed of boat on still water (lake)=8kmph
Speed upstream = 7kmph = speed in still water - speed of river => speed of river = 1kmph
=>Speed downstream = speed in still water + speed of river = 8+1 =9kmph
Ans is E
Answer: E
Question: A train speeds past a pole in 15 seconds and a platform 100 meter long in 25 seconds. What is length of the train ?
Options:
A)140 meter
B)145 meter
C)150 meter
D)155 meter
E)None of these
Rationale: Explanation:
Let the length of the train is x meter and Speed of the train is y meter/second
Then x/y = 15 [because distance/speed = time]
=> y = 15/x
=>x+100/25=x/15
x=150 meters
So length of the train is 150 meters
Option C
Answer: C
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1: 96.
B)1: 99
C)1: 94
D)1: 93
E)1: 72
Rationale: Explanation:
Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer: Option A
Answer: A
Question: A sequence of positive and negative numbers contain q numbers. If the sequence begins with a negative number and q is an odd number how many positive numbers are in it.
Options:
A)q/(2+1)
B)(q+1)/2
C)(q-1)/2
D)q/(2-1)
E)q/(2+2)
Rationale: Lets put values for x, say q=7 since it's odd
and first number is neg so sequence will be {neg,pos,neg,pos,neg,pos,pos} we can see that it has 3 positive terms
so putting q=7 in the options,
option C = (q-1)/2 => 7-1/2 = 3 , the number of positive integers
So, C is the answer
Answer: C
Question: There are 8 executives, including the CEO and CFO, that are asked to form a small team of 5 members. However, the CEO and CFO may not both be assigned to the team. Given this constraint, how many ways are there to form the team?
Options:
A)34
B)35
C)36
D)37
E)38
Rationale: The total number of ways to form a team of 5 is 8C5=56.
We need to subtract the number of teams that have both the CEO and the CFO.
The number of teams with both the CEO and CFO is 6C3=20.
The number of ways to form an acceptable team is 56-20=36.
The answer is C.
Answer: C
Question: A car covers a distance of 720 km in 6 ½ hours. Find its speed?
Options:
A)104 kmph
B)187 kmph
C)120 kmph
D)175 kmph
E)106 kmph
Rationale: 720/6
= 120 kmph
Answer: C
Answer: C
Question: The parameter of a square is equal to the perimeter of a rectangle of length 8 cm and breadth 6 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square.
Options:
A)23.56
B)23.59
C)23.55
D)23.53
E)11.0
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(8 + 6) = 28 cm Parameter of the square = 28 cm
i.e. 4a = 28
A = 7
Diameter of the semicircle = 7 cm
Circimference of the semicircle
= 1/2(âˆ)7
= 1/2(22/7)(7) = 11 cm
Answer:E
Answer: E
Question: A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)2
B)1.4
C)1.1
D)1.5
E)1.9
Rationale: M = 6
S = x
6 + x = (4.5 - x)2
6 + x = 12 -2x
3x = 6
x = 2
Answer:A
Answer: A
Question: A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is πr during the first 30 seconds, πr/2 during next one minute, πr/4 during next 2 minutes, πr/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?
Options:
A)4
B)8
C)16
D)32
E)36
Rationale: Explanation :
There is more than 1 way to approach the solution; however, I will detail the easiest way to go about it here.
We want to find the ratio of time taken for nth round : time taken for (n-1)th round
It will be same as finding the ratio of time taken for 2nd round : Time taken for 1st round.
1 round = Circumference of the circle = 2πr
1st round :
Speed = πr for 30 seconds. So, total distance travelled = πr/2.
Speed = πr/2 for 1 minute. So, total distance travelled = πr/2.
Speed = πr/4 for 2 minutes. So, total distance travelled = πr/2.
Speed = πr/8 for 4 minutes. So, total distance travelled = πr/2.
So, for a distance of 2πr, time taken is 7.5 minutes.
2nd round:
Speed = πr/16 for 8 minutes. So, total distance travelled = πr/2.
Speed = πr/32 for 16 minutes. So, total distance travelled = πr/2.
Speed = πr/64 for 32 minutes. So, total distance travelled = πr/2.
Speed = πr/128 for 64 minutes. So, total distance travelled = πr/2.
So, for a distance of 2πr, time taken is 120 minutes.
Ratio is 120:7.5 = 16:1.
Answer : C
Answer: C
Question: Anand and Deepak started a business investing Rs. 4,500 and Rs. 6,000 respectively. Out of a total profit of Rs. 420. Deepak's share is?
Options:
A)s. 280
B)s. 310
C)s. 240
D)s. 840
E)s. 400
Rationale: Ratio of their shares = 4500 : 6000 = 3 : 4
Deepak's share = Rs. (420 * 4/7) = Rs. 240 ANSWER "C
Answer: C
Question: Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61
Options:
A)4
B)6
C)8
D)2
E)10
Rationale: Given Expression = a(power 2) - b(power 2) / a-b
= (a + b)(a - b) / (a-b)
= (a + b) = (2.39 + 1.61) = 4.
Answer is A.
Answer: A
Question: The average of first 16 even numbers is?
Options:
A)10
B)11
C)17
D)13
E)14
Rationale: Sum of 16 even numbers = 16 * 17 = 272
Average = 272/16 = 17
ANSWER:C
Answer: C
Question: A basket contains 9 marbles. 4 are red and 5 are blue marbles If two marbles are drawn at random what is the probability that at least one ball is red.
Options:
A)19/18
B)17/18
C)11/18
D)13/18
E)15/18
Rationale: Total probability=9C2=36
4C2 +4C1*5C1=6+20=26
therefore the probability that at least one of the red ball will be selected= 26/36=13/18
answer is D
Answer: D
Question: The average age of 38 students in a group is 14 years. When teacherâ€™s age is included to it, the average increases by one. What is the teacherâ€™s age in years?
Options:
A)31
B)36
C)53
D)58
E)None
Rationale: Sol.
Age of the teacher = ( 39 Ã— 15 â€“ 38 Ã— 14 ) years = 53 years.
Answer C
Answer: C
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-7, 1), (1, 1), (1, -6) and (-7, -6)?
Options:
A)112
B)64
C)42
D)24
E)56
Rationale: Length of side 1= 7+1=8
Length of side 2= 6+1= 7
Area of rectangle= 7*8= 56
E is the answer
Answer: E
Question: How many three digit numbers N are divisible by 78 or 91?
Options:
A)17
B)19
C)20
D)21
E)22
Rationale: The answer will be 19.
Explanation:
78= 2*3*13 now multiples of 78, 156 ....780, now 1000-780 = 220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are 9+2=11
91= 13*7--Total number of three digit multiples --9
No remember we have a common multiples as well N-- 13*7*6=91*6=546
So total number of multiples--11+9 -1 =19.
Hence Answer is 19.B
Answer: B
Question: In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 50% average total marks, it is necessary for him in third yearly examination to secure marks :
Options:
A)300
B)250
C)400
D)450
E)500
Rationale: total marks:1500 for three exams
50% of 1500=750
first exam marks=45% of 500=225
second exam marks=55% of 500=275
let X be the third exam marks
225 + 275 + X =750
X=250
ANSWER:B
Answer: B
Question: When divided by 5, x has a remainder of 3 and y has a remainder of 2. Which of the following could be the remainder when x + y is divided by 10?
Options:
A)6
B)7
C)8
D)9
E)0
Rationale: x = 5k+3 and y = 5j+2
x+y = 5(j+k) + 5
When divided by 10, the remainder is either 5 or 0.
The answer is E.
Answer: E
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Options:
A)18%
B)16%
C)17%
D)78%
E)28%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer:A
Answer: A
Question: Two circular signs are to be painted. If the diameter of the larger sign is six times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: Let R be the radius of the smaller sign.
Then the diameter of the smaller sign is 2R, the diameter of the larger sign is 12R, and the radius of the larger sign is 6R.
The area A of the smaller sign is A = piR^2.
The area of the larger sign is pi(6R)^2=36piR^2=36A.
Since the area is 36 times larger, we need 36 times more paint for the larger sign.
The answer is D.
Answer: D
Question: A cube of edge 5cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 10cm * 5cm , find the rise in water level?
Options:
A)2.5cm
B)3.6cm
C)5cm
D)6.43cm
E)7.56cm
Rationale: Increase in volume = volume of the cube = 5*5*5 cm^3
Rise in water level = volume / area = 5*5*5/10*5 = 2.5cm
Answer is A
Answer: A