divelab/Sys2Bench huggingface dataset:
Question: How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?
Options:
A)2160
B)2162
C)2161
D)2163
E)2134
Rationale: In the given word, we treat the vowels IEO as one letter.
Thus, we have DRCTR (IEO).
This group has 6 letters of which R occurs 2 times and others are different.
Number of ways of arranging these letters = 6!/2! = 360.
Now 3 vowels can be arranged among themselves in 3! = 6 ways.
Required number of ways = (360x6) = 2160.
Answer A.
Answer: A
Question: At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses R at the restaurant? (Assume that all boxes are filled to capacity.)
Options:
A)96
B)240
C)R=256
D)R=384
E)R=480
Rationale: Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....
We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.
This means, at the minimum, we have...
1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....
The difference in the number of boxes MUST be 16 though, so we could have....
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes
etc.
With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....
396+28 = 424
424+28 = 452
452+28 = 480
Final Answer:
E
Answer: E
Question: There are 9 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?
Options:
A)15
B)16
C)28
D)56
E)72
Rationale: Every team plays with 8 teams...so total no of matches = 9 x 8 = 72.
Now, each match is played twice => 72 x 2
But 2 teams play a match => 72 x 2 /2 = 72.
Answer: E
Answer: E
Question: A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 25 hours, 50 percent worked 40 hours, and the rest worked 50 hours?
Options:
A) $180,000
B) $185,000
C) $180,000
D) $200,000
E) $192,500
Rationale: 30% of 1000 = 300 worked for 20 hours
Payment @ 5/hr
Total Payment = 300*25*5 = 37500
50 % of 1000 = 500 worked for 40 hours
Payment @ 5/hr
Total payment = 500*40*5 = 100000
Remaining 200 worked for 50 Hours
Payment for first 40 Hours @ 5 /hr
Payment = 200*40*5 = 40000
Payment for next 10 hr @ 7.5/hr
Payment = 200 * 10 * 7.5 = 15000
Total Payment = 37500+100000 + 40000 +15000 = 192500
Hence , answer is E
Answer: E
Question: The instructions state that Deepthi needs 4/17 square yards of one type of material and 3/10 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 9/30 square yards left that she did not use. What is the total amount of square yards of material Deepthi used?
Options:
A)1/12
B)4/17
C)2/3
D)1 1/9
E)2 1/9
Rationale: Total bought = 4/17+3/10
left part 9/30--->3/10
so used part 4/17+3/10-3/10=4/17
ANSWER:B
Answer: B
Question: A dishonest dealer uses a scale of 85 cm instead of a metre scale and claims to sell at cost price. His profit is
Options:
A)17.65%
B)10%
C)12%
D)None of these
E)Cannot be determined
Rationale: Solution
Gain%	= (15 / 85 x 100)%
= 17.65%
Answer A
Answer: A
Question: If 42.12 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?
Options:
A)5
B)7
C)8
D)9
E)10
Rationale: 42.12 = 14K + Km/50...we can rewrite the number as follows:
42+ 0.12= 14K + Km/50........Since K is integer, then 42=14K..........K=3
0.12=Km/50......12/100=3m/50......m=2
k+m=3+2=5
Answer: A
Answer: A
Question: (68-a)(68-b)(68-c)(68-d)(68-e)=725.wat is the value of a+b+c+d?
Options:
A)230
B)231
C)232
D)233
E)234
Rationale: factors of 725= 5,5 29
so (68-63)=5 ,(68-63)=5,(68-39)=29, (68-67)=1 ,(69-67)=1
so a+b+c+d= 232
ANSWER:C
Answer: C
Question: If the integer n has exactly four positive divisors, including 1 and n, how many positive divisors does n^2 have?
Options:
A)4
B)5
C)6
D)8
E)9
Rationale: take the example of 6...
it has 4 positive divisors (1,2,3,4)
Now, take the example of 36...
it has only 9 divisors..
so E is the ans
Answer: E
Question: A placed three sheets with two carbons to get two extra copies of the original. Then he decided to get more carbon copies and folded the paper in such a way that the upper half of the sheets were on top of the lower half. Then he typed. How many carbon copies did he get?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Explanation:
Since the number of carbons is 2, only two copies can be obtained.
Answer: B
Answer: B
Question: Two fair die with sides numbered 1 to 6 are tossed. What is the probability that the sum of the exposed faces on the die is a prime number?
Options:
A)5/11
B)5/12
C)5/21
D)2/9
E)5/36
Rationale: Two dices are thrown ! So we may get 1+1 or 1+2 ... or 1+6.. or 2+6 or 3+6 etc
Therefore the total different sum values we can get are :2,3,4,5,6,7,8,9,10,11,12[Sample space] ----------------(1)
Out of these values, 5 numbers are primes i.e.2,3,5,7,11[Favorable events] --------------------(2)
From (1)(2)
The answer is5/11!!
Option A
Answer: A
Question: 1,345
1,354
1,435
.....
....
+5,431
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,3,4,5 exactly once in each integer. What is the sum of these 24 integers?
Options:
A)78,690
B)82,240
C)86,658
D)90,240
E)94,426
Rationale: In each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.
Then the sum equals 6(1111)+6(3333)+6(4444)+6(5555) = 86,658
The answer is C.
Answer: C
Question: A batsman makes a score of 65 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
Options:
A)17
B)39
C)42
D)45
E)None of the above
Rationale: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
∴ 16(x – 3) + 65 = 17x or x = (65 – 48) = 17.
Answer A
Answer: A
Question: The actual price of an article was Rs. 6000/- the successive discount on 10% and 20% then Finds the selling price
Options:
A)Rs.3240/-
B)Rs. 4320/-
C)Rs.4230/-
D)Rs.4200/-
E)None of these
Rationale: Explanation:
Note: Selling price = MRP * (100 - d1)/100 * (100 - d2)/100 * -------------
MRP = 6000/- , d1 = 10, d2 = 20
Selling price = 6000 * (100 - 10)/100 * (100-20)/100 ==> 6000 * 90/100 * 80/100
=> 48 * 90 = Rs. 4320/-
Answer: Option B
Answer: B
Question: If a(a + 5) = 6 and b(b + 5) = 6, where a ≠ b, then a + b =
Options:
A) −5
B) −2
C) 2
D) 46
E) 48
Rationale: a(a + 5) = 6 and b(b + 5) = 6
=> a, b must be integers and if a is -6 or 1, b will be 1 and -6 respectively
=> a+b = -5
Ans: A
Answer: A
Question: John and Peter are among the eight players a volleyball coach can choose from to field a six-player team. If all six players are chosen at random, what is the probability of choosing a team that includes John and Peter?
Options:
A)7/15
B)11/20
C)14/25
D)15/28
E)16/35
Rationale: The total possible ways of selecting a 6-member team is 8C6 = 28
The possible ways which include John and Peter is 6C4 = 15
The probability of choosing both John and Peter is 15/28
The answer is D.
Answer: D
Question: If 15 Horses eat 15 bags of gram in 15 days, in how many days will one horse eat one bag of Grain?
Options:
A)15 days
B)1/15 days
C)1 day
D)30 days
E)225 days
Rationale: Horse*days=bags
15*15=15 and 1*days=1
(15*15)/(1*days)=15/1
Days=15
ANSWER:A
Answer: A
Question: An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability P that the sum of the 2 numbers on the balls will be even?
Options:
A)25%
B)37.5%
C)50%
D)62.5%
E)75%
Rationale: Correct Answer: C
Since there are 5 even numbered balls and 5 odd numbered balls, the probability of selecting either an even or an odd is 5/10= 1/2. In order for the sum of the numbers on the two balls to be even, either both numbers must be even or both numbers must be odd; one even and one odd number would add to an odd number. The probability of selecting two even numbers is:
1/2 * 1/2= 1/4
The probability of selecting two odd numbers is also:
1/2 * 1/2= 1/4
Adding both probabilities gives P=1/4+1/4= 1/2 , or 50%, as the probability that the sum of the numbers will be even. Thus, the correct answer is (C).
Answer: C
Question: The speed of a boat in still water is 60kmph and the speed of the current is 10kmph. Find the speed downstream and upstream?
Options:
A)87 kmph
B)40 kmph
C)50 kmph
D)15 kmph
E)18 kmph kmph
Rationale: Speed downstream = 60 + 10
= 70 kmph
Speed upstream = 60 - 10
= 50 kmph
Answer:C
Answer: C
Question: A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.
Options:
A)1/6
B)1/7
C)1/11
D)1/13
E)1/15
Rationale: The sample space has 216 outcomes.
Now X =
(1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)
(3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)
(5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)
Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}
and X n Y = {(6,5,4)}.
Now P(Y) = 6/216
and P (X n Y) = 1/216
Then P(X|Y) = (1/216)/(6/216) = 1/6
A)
Answer: A
Question: In a pet shop there are 120 eyes and 172 legs. How many birds and puppies are included in these?
Options:
A)Birds=34 , Puppies=26
B)Birds=36 , Puppies=26
C)Birds=34 , Puppies=20
D)Birds=32 , Puppies=24
E)Birds=38 , Puppies=24
Rationale: Let there are x birds and y puppies.
Each bird and puppy has 2 eyes. Each bird has 2 legs and each puppy has 4 legs.
Then
2x+2y = 120 => x+y = 60----------(1)
2x+4y = 172 => x+2y = 86-----------(2)
Solving (i) and (ii) we get
y = 26 & x = 34
So birds are 34 and puppies are 26. Answer : A
Answer: A
Question: Two boats are heading towards each other at constant speeds of 4 miles/hr and 20 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
Options:
A)1/12
B)6/15
C)1/6
D)1/3
E)1/5
Rationale: The question asks: how far apart will they be 1 minute=1/60 hours before they collide?
Since the combined rate of the boats is 4+20=25 mph then 1/60 hours before they collide they'll be rate*time=distance --> 24*1/60=6/15miles apart.
Answer: B.
Answer: B
Question: 0.009/x=0.03. find the value of X
Options:
A)0.0003
B)0.03
C)0.3
D)3
E)30
Rationale: x=0.009/0.03=0.3
ANSWER:C
Answer: C
Question: In a room with 6 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
Options:
A)5/21
B)3/7
C)4/7
D)5/7
E)16/15
Rationale: (4/6)(5/5) + (3/6)(4/5) if you choose one of the 4 with one other friend, then you have a 5/5 chance of not picking their friend 2nd. If you choose one of the 3 with 2 friends, you have a 4/5 chance of not picking one of their friends second. Add them up.
20/30 + 12/30
32/30 = 16/15
E. 16/15
Answer: E
Question: A box contains TWELVE bulbs out of which 3 are defective. If THREE bulbs are chosen at random, find the probability that atleast one bulb is good?
Options:
A)250/251
B)265/265
C)241/242
D)256/257
E)219/220
Rationale: Required probability=1-3C3/12C3= 1 - 1/220= 219/220Answer:E
Answer: E
Question: Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day D on which the buses leave at the same time.
Options:
A)D=Tuesday
B)D=Wednesday
C)Thursday
D)Sunday
E)D=The busses will never leave at the same time
Rationale: The answer is E.
I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.
Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E
Answer: E
Question: find the ratio of 8th and 4th term of sequence 3.1, 6.2, 12.4, .....?
Options:
A)16
B)12
C)4
D)8
E)20
Rationale: a= first term = 3.1
r = common ratio = 6.2/3.1 = 2 ====> 4th term = a * r^(4-1) = 3.1 * (2)^3 = 24.8 and 8th term = 3.1 * (2)^7 = 396.8
Ratio of a8/a4 = 396.8/24.8 = 16 ------Ans- A
Answer: A
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
Options:
A)70 cm2
B)30 cm2
C)66 cm2
D)55 cm2
E)54 cm2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2
Answer: B
Answer: B
Question: Eight friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $680. If one of the friends had a coupon for 12% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
Options:
A)$90
B)$74
C)$45
D)$37
E)$35
Rationale: 680 * 0,12 = 81
680 - 81 = 599
599 / 8 = 74
Answer B
Answer: B
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150
B)2787
C)277
D)279
E)271
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: A
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
Options:
A)1:8
B)1:6
C)2:1
D)1:1
E)1:7
Rationale: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1:1
Answer:D
Answer: D
Question: If the area of circle is 520 sq cm then its circumference?
Options:
A)11
B)81
C)99
D)266
E)12
Rationale: 22/7 r2 = 520 => r = 12.9
2 * 22/7 * 12.9 = 81 Answer: B
Answer: B
Question: CP of two houses are Rs.1.995 lakhs each. On one gains 5% and on the other, loses 5%. What is the gain or loss percent in the whole transaction?
Options:
A).23%
B).25%
C).30%
D).50%
E)1%
Rationale: If a person sells two items at the same price; one at a gain of x % and another at a
loss of x %, then the seller always incurs a loss expressed as
Loss%=(Common Loss and Gain%10)2=(x10)2So in this case, he will have a loss. Loss%=(510)2=(12)2=(14)=.25%
B
Answer: B
Question: Rs.1070 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Options:
A)Rs.190
B)Rs.260
C)Rs.493
D)Rs.393
E)Rs.593
Rationale: A+B+C = 1070
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1070 = Rs.493
ANSWER:C
Answer: C
Question: If an object travels at six feet per second, how many feet does it travel in one hour?
Options:
A)30
B)21600
C)720
D)1800
E)18000
Rationale: Speed = 6 feet per second.
1 Hour= 60X60 Seconds = 3600 Seconds.
Total no of feet traveled in 1 hour = 3600X6 = 2160X10 =21600
Answer B
Answer: B
Question: Three friends Alice, Bond and Charlie divide $1260 amongs them in such a way that if $10, $20 and $30 are removed from the sums that Alice, Bond and Charlie received respectively, then the share of the sums that they got will be in the ratio of 10 : 20 : 30. How much did Charlie receive?
Options:
A)$490
B)$630
C)$500
D)$510
E)$520
Rationale: A+B+C = 1260
Given ratio 10:20:30
Let us say the shares of A,B,C deducting 10,20,30 be a,b,c
a+b+c = 1260-60= 1200 = 60K
c share = (1200X30)/60 = 600
C = charlie share = 600+30 = 630
Option B
Answer: B
Question: In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability Q at least one of the shirts he draws will be blue?
Options:
A)25/153
B)28/153
C)5/17
D)4/9
E)Q=12/17
Rationale: P(at least one blue) = 1- P(0 blue) = 1 - 10/18*9/17 =Q= 12/17.
Answer: E.
Answer: E
Question: A walks at 4 kmph and 4 hours after his start, B cycles after him at 10 kmph. How far from the start does B catch up with A?
Options:
A)62.6 km
B)26.7 km
C)22.8 km
D)19.5 km
E)None
Rationale: Sol.
Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 4 hours.
∴ x/4 - x/10 = 4 or x = 26.7 km.
Answer B
Answer: B
Question: What least value must be assigned to * so that th number 197*5462 is divisible by 9?
Options:
A)2
B)4
C)6
D)1
E)3
Rationale: Let the missing digit be x
Sum of digits = (1+9+7+x+5+4+6+2)=34+x
For 34+x to be divisible by 9 , x must be replaced by 2
The digit in place of x must be 2.
ANSWER A 2
Answer: A
Question: Find the value of x from this equation? 7(x - 1) = 21
Options:
A)2
B)3
C)4
D)6
E)7
Rationale: 1. Divide both sides by 7:
2. Simplify both sides:
x - 1 = 3
3. Add 1 to both sides:
x - 1 + 1 = 3 + 1
4. Simplify both sides:
x = 4
C
Answer: C
Question: What is his percentage profit made by Felix if he purchased 21 dozen t-shirts at Rs. 12 per dozen. He sold 7 dozens at 15% profit and the remaining 14 dozens with 18% profit?
Options:
A)18%
B)17%
C)15%
D)13%
E)14%
Rationale: Explanation :
C.P of 21 dozen = Rs.(12 x 21) = Rs.252
C.P of 7 dozen = Rs. (12 x7) = Rs. 84.
C.P of 14 dozen =Rs. (12 x14) = Rs. 168
profit on 7 dozen at 15% = 15/100*84 = 12.6
profit on 14 remaining dozen at 18% = 18/100*168 = 30.24
total profit = 12.6 + 30.24 = 42.84
% profit = ?/100*252 = 42.84
= 17%
Answer : B
Answer: B
Question: A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 15 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
Options:
A)1/10
B)3/10
C)1/4
D)7/10
E)9/10
Rationale: C+M+B-CM-MB-CB-2CMB = 100
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-15-2CMB = 100
B-CB-MB-2CMB = 25
hence the probability = 25/100 = 1/4.
C
Answer: C
Question: In an island, there are four men for every three women and five children for every three men. How many children are there in the island if it has 531 women ?
Options:
A)454
B)1180
C)1070
D)389
E)983
Rationale: The ratio of Women : Men = 3 : 4
Men : Children = 3 : 5
The combined ratio,
Women : Men : Children = 9 : 12 : 20
In this ratio, 9 ==> 531 Women
Thus, 20 ==> 1180 Children
ANSWER:B
Answer: B
Question: A chopper flies along the four sides of a square at the speeds of 100,200,300 and 400 km/hr. Find the average speed of the plane around the field?
Options:
A)100km/hr
B)192km/hr
C)154km/hr
D)212km/hr
E)168km/hr
Rationale: Let each side of the square be x
Let the average speed of the chopper be y km/hr
x/100 + x/200 + x/300 + x/400 = 4x/y
25x/1200 = 4x/y
y = 1200*4/25 = 192km/hr
Answer is B
Answer: B
Question: How many number of 3 digits can be formed with the digits 1,2,3,4,5 if repetition of digits is not allowed?
Options:
A)60
B)120
C)30
D)240
E)48
Rationale: n = number of digits = 5
r = number of places to be filled up = 3
Required number = 5P3 = 5!/2! = 60
Answer is A
Answer: A
Question: A father is 30 years older than his son however he will be only thrice as old as the son after 5 years what is father's present age ?
Options:
A)40 yrs
B)30 yrs
C)50 yrs
D)60 yrs
E)none of these
Rationale: Son's age: x
Father's age: x + 30
In 5 years:
Son's age: x + 5
Father's age: x + 35
In 5 years the father is thrice as old as his son so:
3(x + 5) = x + 35
x = 10
Current father's age is 40.
ANSWER:A
Answer: A
Question: If t and b are positive numbers, and t^3 + b^3 = 75, then the greatest possible value of t is between:
Options:
A)0 and 3
B)3 and 5
C)4 and 5
D)5 and 7
E)6 and 9
Rationale: Yes the question is ambiguous, and the answer is certainly not C between 4 and 5 .
The question stated: t and b are positive numbers but not positive integers.
so fractions are allowed to be a part of calculation.
So if the answer is C then the value 4.5 = 9/2 must comply the equation.
(9/2)^3 + b^3 = 75
so, b^3 = -129/8 , which is not possible according to the question.
Moreover the question didn't mentioninclusive or not, so we can't assume that b is 4 .
hi asif,
question is correct IMO.
Sincemaximumvalues areuniqueso you cant take any value and make it satisfy with equation
question is asking that maximum value ofa(means that unique value ofa) is between...
its not saying all value of that range will satisfy.
Answer: C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)78
B)89
C)36
D)34
E)23
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: Option C
Answer: C
Question: The area of a square is 4900 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is same the side of the square and breadth is 20 cm less than the side of the square?
Options:
A)5:8
B)5:10
C)5:13
D)5:7
E)5:16
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4900
a = (4900)^1/2 = 70
l = a and b = a - 20
b : l = a - 20 : a = 50 : 70 = 5:7
Answer: D
Answer: D
Question: What percent of a day is ten hours?
Options:
A)41.67%
B)16x1/2%
C)18x2/3%
D)22x1/2%
E)None of these
Rationale: Explanation :
Required percentage = (10/24100)%.
= 41.67%.
Answer : A
Answer: A
Question: What is the difference between the place value of 4 in the numeral 7449?
Options:
A)150
B)360
C)180
D)190
E)210
Rationale: 400 - 40 = 360
B
Answer: B
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
Options:
A)22
B)50
C)88
D)25
E)12
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph.
Answer: B
Answer: B