divelab/Sys2Bench huggingface dataset:
Question: B @ K I 9 D Â© 5 2 T $ M 4 E J # U R 1 A Î´ K 5 W 6 % F Q 7 H P 8 Z
Which of the following should come in place of the question mark(?) in the following series based on the elements in the above arrangement?
K9D 2$M JUR ?
Options:
A)Î´KW
B)Î´K5
C)Î´56
D)Î´W6
E)None of these
Rationale: Explanation:
K +6 2 +6 J +6 Î´
9 +6 S +6 U +6 5
D +6 M +6 R +6 W
ANSWER IS E
Answer: E
Question: For any positive integer Y, the sum of the first Y positive integers equals Y(Y+1)/2 . If X and Y are positive integers and X > Y, what is the sum of all the integers between X and Y, inclusive?
Options:
A) X(X+1)/2 + Y(Y+1)/2
B) X(X+1)/2 - Y(Y-1)/2
C) X(X+1)/2 - Y(Y+1)/2
D) X(X+1)/2 + Y(Y-1)/2
E) X(Y+1)/2 - Y(X-1)/2
Rationale: The sum of all the integers between X and Y,inclusiveis the sum of the first X positive integersminusthe sum of the first Y-1 positive integers.
The sum of the first X positive integers is X(X+1)/2;
The sum of the first Y-1 positive integers is (Y-1)Y/2;
Therefore the answer is X(X+1)/2 - (Y-1)Y/2.
Answer: B.
Answer: B
Question: Rectangular tile each of size 60cm by 56cm must be laid horizontally on a rectangular floor of size 560cm by 240cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
Options:
A)50
B)54
C)47
D)40
E)45
Rationale: Area of tile = 60*56 = 3360
Area of floor = 560*240 = 134400
No of tiles = 134400/3360 = 40
So, the no of tile = 40
ANSWER:D
Answer: D
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
Options:
A)100
B)110
C)120
D)130
E)140
Rationale: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Answer: C
Question: Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-8) = 0, then f(x) crosses the y-axis at what y-coordinate?
Options:
A)-8
B)-1
C)0
D)1
E)8
Rationale: When x = 1 and when x = -8, the expression f(x) = x² + bx + c equals 0.
Then f(x) = (x-1)(x+8)
f(0) = -8
The answer is A.
Answer: A
Question: A man can swim in still water at 1.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.7
B)0.5
C)1.1
D)1.5
E)1.9
Rationale: M = 1.5
S = x
DS = 1.5 + x
US = 1.5 + x
1.5 + x = (1.5 - x)2
1.5 + x = 3 -2x
3x = 1.5
x = 0.5
Answer:B
Answer: B
Question: In the xy-coordinate system, what is the slope of the line that goes through point (2, 4) and is equidistant from the two points P = (9, 3) and Q = (5, 9)?
Options:
A)0.1
B)0.2
C)0.3
D)0.4
E)0.5
Rationale: First, get the middle coordinate between (9,3) and (5,9).
x = 9 + (5-9)/2 = 7
y = 3 + (9-3)/2 = 6
Second, get the slope of (7,6) and (2,4). m = 6-4 / 7-2 = 2/5 = 0.4
Answer: D
Answer: D
Question: A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in?
Options:
A)1/65
B)1/62
C)1/63
D)1/60
E)1/61
Rationale: A = 140 days
B = 105 days
1/140 + 1/105 = 7/420 = 1/60
=>60 days
Answer: D
Answer: D
Question: 45 men can complete a work in 16days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?
Options:
A)6
B)10
C)15
D)7
E)8
Rationale: 45*16 men can complete the work in 1 day
1 man's 1 day work = 1/720
45 men 6days work = 6*1/16 = 3/8
remaining work = 1-3/8 = 5/8
75 men's 1 day's work = 75/720 = 5/48
5/8 work is done by them in 48/5 * 5/8 = 6days
Answer is A
Answer: A
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)28
B)68
C)25
D)23
E)11
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Answer: B
Question: A large box contains 17 small boxes and each small box contains 26 chocolate bars. How many chocolate bars are in the large box?
Options:
A)A)442
B)B)490
C)C)380
D)D)450
E)E)690
Rationale: the only thing you have to do is a simple multiply
we have:
17*26
=442
correct answer is:
A) 442
Answer: A
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 34.9%. What would have been the percentage of profit earned if no discount had been offered?
Options:
A)28.5
B)27.675
C)30
D)Data inadequate
E)42
Rationale: Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100.
Then printed price = 100Ã—(100+34.9)/(100âˆ’5)=142
Hence, required % Profit = 142 â€“ 100 = 42%
Answer E
Answer: E
Question: The ages of Raju and Biju are in the ratio 3:1. Fifteen years hence, the ratio will be 2:1. Their present ages are:
Options:
A)30yrs, 10yrs
B)45 yrs, 15yrs
C)21 yrs, 7 yrs
D)60yrs, 20yrs
E)40yrs, 20yrs
Rationale: Let the ages of raju and Biju is 3x and x years respectively.
Then, (3x +15)/ (x+15) = 2/1;
-> 2x + 30 = 3x + 15 -> x = 15
So Raju’s age = 3*15 = 45 and Biju’s age = 15 years
ANSWER:B
Answer: B
Question: The sum of money will be thrice itself in 15 years and simple interest find rate of interest?
Options:
A)A)12.33%
B)B)13.33%
C)C)14.33%
D)D)15.33%
E)E)16.33%
Rationale: T = 15 years
P= principle amount = x
A = total amount = 3x
SI = simple interest = A-P = 3x-x = 2x
R = 100SI/PT = 100.2x/15x =13.33%
Answer is B
Answer: B
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)657
B)280
C)438
D)289
E)427
Rationale: x*(85/100)
= (480 - x)119/100
x = 280
Answer:B
Answer: B
Question: A certain junior class has 1000 students and a certain senior class has 600 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
Options:
A)3/40000
B)1/1000
C)9/2000
D)1/60
E)1/15
Rationale: Let's see
Pick 60/1000 first
Then we can only pick 1 other pair from the 800
So total will be 60 / 600 *1000
Simplify and you get 1/10000
Answer is B
Answer: B
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Answer: A
Answer: A
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.560, find the number of 50 paise coins ?
Options:
A)498
B)488
C)428
D)528
E)600
Rationale: 50*3k + 20*4k + 10*5k = 56000
280k = 56000 => k = 200
50p coins = 3k = 3*200 = 600
ANSWER:E
Answer: E
Question: A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more thanC. Out of a total profit of Rs. 35,000, A receives :
Options:
A)14700
B)14703
C)37798
D)13777
E)14778
Rationale: Explanation:
Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. (35000 * 21/50 ) = Rs. 14,700.
Answer: A) 14700
Answer: A
Question: One hour after Matthew started waking from w to y, a distance of 45km, Johnny started walking along the same road from y to w. Matthew's walking rate was 3 km per hour and Johnny's was 4km per hour, how many km had Johnny walked when they met?
Options:
A)24
B)23
C)22
D)21
E)19.5
Rationale: Just an alternative method...
After the first hour the distance w is 42 km (45-3). Now the problem can be treated as if bothof them started at the same time. Since the speeds are in the ratio 3 : 4, the distances will also be in the same ratio. Splitting 42 in that ratio we get 18 : 24. So answer is 24.
Hence A.
Answer: A
Question: What will be the difference between simple and compound interest at 6% per annum on a sum of Rs. 1000 after 4 years?
Options:
A)24.19
B)24.12
C)22.1
D)24.1
E)22.5
Rationale: S.I. = (1000 * 6 * 4)/100 = Rs. 240
C.I. = [1000 * (1 + 6/100)4 - 1000] = Rs. 262.5 Difference = (262.5 - 240) = Rs. 22.5
Answer: E
Answer: E
Question: If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $71, how much does one shirt cost?
Options:
A)$10
B)$12
C)$13.20
D)$15
E)$16.80
Rationale: 3J + 2S = 69
2J + 3S = 71
----------------
5J + 5S = 140 ----(divide by 5)---> J + S = 28
3J + 2S = J + 2(J + S) = J + 56 = 69 ---> J = 13
3*13 + 2S = 69
39 + 2S = 69
2S = 30
S = 15
Answer: D
Answer: D
Question: A baseball team won 50 percent of the first 80 games it played. How many of the remaining 82 games will the team have to win in order to have won exactly 50 percent of all the games it played?
Options:
A)36
B)41
C)50
D)55
E)81
Rationale: Games won out of first 80 questions = (50/100)*80 = 40
Total Games = 80+82 = 162
Games to be won = (50/100)*162 = 81
Remaining games to be won = 81-40 = 41
Answer: Option B
Answer: B
Question: If l and g are distinct prime numbers less than 10, which of the following cannot be the product of l and g?
Options:
A)6
B)9
C)10
D)14
E)15
Rationale: If l and g are distinct prime numbers less than 10, prime numbers less than 10 are 2, 3, 5, 7
all except 9 is product of any two numbers picked from above set.
Ans: B
Answer: B
Question: Susan is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of bap. The pattern repeats after she leaves the morsel of rye. If Susan drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
Options:
A)wheat − wheat − white
B)bap − wheat − wheat
C)white − bap − wheat
D)white − white − white
E)white − white − bap
Rationale: In a single round Susan drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options A, C, D and E can be eliminated
Answer: B
Answer: B
Question: FOG + FOG + FOG + FOG = 1468.
If F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ?
Options:
A)11
B)12
C)13
D)14
E)16
Rationale: given,FOG + FOG + FOG + FOG = 1468
4(FOG)=1468
=>FOG=367
Face value of F is:3
Face value of O is:6
Face value of G is:7
so F+O+G=3+6+7=16
ANSWER:E
Answer: E
Question: The ration of the father’s age to his son’s age is 7:3.The product of their ages is 756.The ratio of their ages after 6 years will be :
Options:
A)5:2
B)2:1
C)11:7
D)13:9
E)None of these
Rationale: Solution
Let the present ages of the father and son be 7x and 3x years respectively.
Then,7x 3x =756 ⇔ 21x2=756 ⇔ x2=36 ⇔ x=6.
∴ Required ratio =(7x +6) :(3x +6)=48:24=2:1. Answer B
Answer: B
Question: If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 25 degrees?
Options:
A)π
B)3π/2
C)2π
D)5π/9
E)8π
Rationale: Area = 16π
Radius = 4
Circumference = 2 x 4 x π = 8π
Angle forming the arc = 25 degrees. 25/360 = 5/72.
Therefore length of arc = 5/72 * 8π = 5π/9 - Answer choice D.
Answer: D
Question: A palindrome is a number that reads the same forward and backward, such as 242. How many even seven-digit numbers are palindromes?
Options:
A)40
B)4000
C)500
D)5,000
E)100,000
Rationale: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 2221222,4441444.
The middle number in the seven-digit could be 0-9 ( 10 ways), e.g 2225222, 2228222
The 2nd and fourth numbers could must also be same i.e 0-9( 10 ways) e.g 2234322, 2856582
The 3rd and fifth numbers could must also be same i.e 0-9( 10 ways) e.g 2234322, 2856582
we thus have, 4 *10**10*10 = 4000.B
Answer: B
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 200 girls, the total number of
students in the college is
Options:
A)420
B)520
C)620
D)620
E)None of these
Rationale: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 200
=> x = 40
Total students = 8x+5x = 13x = 13(40) = 520
Answer: B
Answer: B
Question: If 76 is divided into four parts proportional to 7,5,3,4, then the smallest part is :
Options:
A)12
B)15
C)16
D)19
E)20
Rationale: Solution
Given ratio = 7 : 5 : 3 : 4,Sum of ratio terms = 19.
∴ Smallest part =(76x3/19) = 12.
Answer A
Answer: A
Question: If x and y are both odd prime numbers and x < y, how many distinct positive integer E factors does 2xy have?
Options:
A)3
B)4
C)6
D)8
E)12
Rationale: Since 2xy prime E factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.
Answer: D
Question: If -2 and -3 are negative integers, then -2*-3 + 2 is
Options:
A)-5
B)8
C)-6
D)-3
E)-8
Rationale: Answer : B
Answer: B
Question: Find the average of all the numbers between 4 and 32 which are divisible by 5.
Options:
A)17.5
B)20
C)24
D)30
E)32
Rationale: Solution
Average	= (5+10+15+20+25+30)/6)
= 105 / 6
= 17.5.
Answer A
Answer: A
Question: Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations W of classes are available?
Options:
A)3
B)6
C)W=7
D)W=9
E)W=12
Rationale: I think it should be E only.
No where it is given that he attends different classes on each day.
Experts please provide your views.
--- EDITED my Response. It was a typo. I meant 12 is the answer.
If only Day 1 : 3 options
If Day 1 and Day 2 : 3*3 = 9 Options
So, Total = 3+9= 12.
Answer: D
Question: Find the perimeter and area of a square of side 9 cm.
Options:
A)36
B)49
C)64
D)81
E)100
Rationale: We know that the perimeter of square = 4 Ã— side
Side= 9 cm
Therefore, perimeter = 4 Ã— 9 cm = 36 cm
Now, area of the square = (side Ã— side) sq. units
= 9 Ã— 9 cmÂ²
= 81 cmÂ²
ANSWER : D
Answer: D
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)399
B)77
C)500
D)77
E)221
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: C
Answer: C
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46 meters. How many times did the ball bounce?
Options:
A)4
B)6
C)7
D)8
E)9
Rationale: Division of total distance traveled will be 16+16+8+4+2
Ans: A
Answer: A
Question: In the following question, various terms of an alphanumerical series are given with one or more terms missing as shown by (?).Choose the missing terms out of the given alternatives. 2Z5, 7Y7, 14X9, 23W11, 34V13, ?
Options:
A)47U77
B)47U79
C)47U71
D)47U72
E)47U99
Rationale: Explanation:
The first numbers increase by 5, 7, 9, 11....
The letters move one step backward.
The last numbers are consecutive odd numbers.
Answer: A) 47U77
Answer: A
Question: A number consists of 3 digit whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
Options:
A)145
B)253
C)370
D)352
E)452
Rationale: Let the middle digit be x. Then, 2x = 10 or x = 5.
So, the number is either 253 or 352. Since the number increases on reversing the digits, so the hundred's digit is smaller than the unit's digit. Hence, required number = 253.
ANSWER:B
Answer: B
Question: In a group of ducks and cows, the total number of legs are 30 more than twice the number of heads. Find the total number of cows.
Options:
A)12
B)15
C)16
D)18
E)20
Rationale: Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 28 more than twice the number of heads
=> 2(d + 2c) = 30 + 2(c + d)
=> d + 2c = 15 + c + d
=> 2c = 15 + c
=> c = 15
i.e., total number of cows = 15
Answer is B.
Answer: B
Question: Louie takes out a three-month loan of $4000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
Options:
A)A)333
B)B)383
C)C)1608
D)D)433
E)E)483
Rationale: Here's the calculation for that case, assume monthly payment is X.
After 1st month: (4000)(1.1)-X = 4400-X
After 2nd month: (4400-X)(1.1)-X = 4840-2.21X
After 3rd month: (4840-2.21X)(1.1)-X = 5324-3.31X
Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:
5324-3.31X = 0
X = 5324/3.31 = 1608.45
Answer C
Answer: C
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 70, what is the value of c − a?
Options:
A)25
B)50
C)90
D)140
E)It cannot be determined from the information given
Rationale: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=140 --2
subtracting 1 from 2 we have
c-a=50;
ANSWER:B
Answer: B
Question: Machine–X produces 50% of the total output and Machine-Y produces 75% of the total output. An average of nine units out of a thousand goods manufactured by Machine-X and two unit of 500 units produced by Machine-X prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
Options:
A)0.008
B)0.1
C)0.12
D)0.006
E)0.007
Rationale: Suppose machine X produce 1000 units
total defective = 9
Machine Y then produces=1500 units
total defective=6
probability=15/2500
=0.006
Answer : D
Answer: D
Question: The length of a rectangle is 4 times its width. If the width of the rectangle is 5 inches, what is the rectangle's area, in square inches?
Options:
A)30 square inches
B)75 square inches
C)100 square inches
D)89 square inches
E)92 square inches
Rationale: If the width is 5 in and the length is 4 times the width, then the length is
4 * 5 = 20 in
The area is given by
5 * 20 = 100 square inches
correct answer C
Answer: C
Question: Find the odd man out
7, 8, 18, 57, 228, 1165, 6996
Options:
A)8
B)18
C)57
D)228
E)258
Rationale: 7
7*1+1 = 8
8*2+2 = 18
18*3+3 = 57
57*4+4 = 232
232*5+5 = 1165 and so on
ANSWER:D
Answer: D
Question: Find the sum of all 3 digit natural numbers, which are divisible by 8.
Options:
A)61376
B)54411
C)612314
D)64170
E)64171
Rationale: The three digit natural numbers divisible by 8 are
104, 112, 120, …. 992.
Let Sndenote their sum. That is, Sn = 104 112 120 128 , 992 g + + + + + .
Now, the sequence 104, 112, 120, g, 992 forms an A.P.
a=104, d=8, l=992
n=l-a/d
n=112
S112=n/2(a+l)=61376
Option A
Answer: A
Question: A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 4km/hr. Total time of travel is 6 hours. What is the maximum distance he
can cover?
Options:
A)20km
B)40km
C)60km
D)80km
E)26.6km
Rationale: t=d/s, so
6=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr)
6=x(18/80)
x=26.6km
ANSWER:E
Answer: E
Question: The average of five consecutive odd numbers is 55. What is the difference between the highest and lowest numbers?
Options:
A)2
B)5
C)8
D)9
E)10
Rationale: Explanation :
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then, (x + (x + 2) + (x + 4) + (x + 6) + (x + 8))/5 = 55
5x + 20 = 275
x = 255/5 = 51.
So, required difference = (51 + 8) 51 = 8
Answer : C
Answer: C
Question: According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 4 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 120 six-ounce servings of orange juice?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: 1 X 12 ounce can of concentrate + 4 X 12 ounce cans of water = 60 ounces of the mixture.
60 ounces of mixture gives (60 / 6 ) = 10 servings.
Thus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture.
To make 120 servings of the mixture, we need 120 / 10 = 12 cans of the concentrate.
The answer is B.
Answer: B
Question: If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
Options:
A)11 1/8%
B)11 1/7%
C)11 1/9%
D)61 1/9%
E)21 1/9%
Rationale: 100 – 10 = 90
90------10
100------? => 11 1/9%
Answer: C
Answer: C
Question: If k^2 = t^2, which of the following must be true?
Options:
A)|k| = |t|
B)k = -m
C)k = |m|
D)k = -|m|
E)k = m
Rationale: Solution:
We are given that k^2 = t^2, and we can start by simplifying the equation by taking the square root of both sides.
√k^2 = √t^2
When we take the square root of a variable squared, the result is the absolute value of that variable. Thus:
√k^2 = √t^2 is |k| = |t|
Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.
Answer: A
Answer: A
Question: The ratio of the radius of two circles is 1: 9, and then the ratio of their areas is?
Options:
A)1: 8
B)1: 6
C)1: 9
D)1: 3
E)1: 81
Rationale: r1: r2 = 1: 9
Πr12: Πr22
r12: r22 = 1: 81
Answer:E
Answer: E
Question: Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4?
Options:
A)a) 1/12
B)b) 1/36
C)c) 1/6
D)d) 5/12
E)e) 1/3
Rationale: We can have 6 different outcomes on a dice.
Total outcomes on two dices = 6*6
We need only the cases where total sum of the numbers on the dices is 4
They can be {1, 3}, {2, 2}, {3, 1}
A total of 3 outcomes
Probability = favorable outcomes/ total outcomes = 3/36 = 1/12.
Option A
Answer: A
Question: (17)5.25 x (17)? = 178
Options:
A)2.29
B)2.75
C)4.25
D)4.5
E)None of these
Rationale: Solution
let (17)5.25 * (17)x = 178. then, (17)5.25 + x = (17)8.
∴ 5.25 + x = 8 ⇔ x = (8 - 5.25) ⇔ x = 2.75
Answer B
Answer: B
Question: A can do a piece of work in 8 days. B can do it in 16 days. With the assistance of C they completed the work in 4 days. Find in how many days can C alone do it?
Options:
A)87 days
B)20 days
C)26 days
D)19 days
E)16 days
Rationale: C = 1/4 - 1/8 - 1/16 = 1/16
=> 16 days
Answer:E
Answer: E
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 5 different boat to go and 2 flight to return. In how many ways, can the boy perform his journey?
Options:
A)10
B)20
C)45
D)60
E)70
Rationale: Ans.(A)
Sol. Number of choices to go by ship = 5 Number of choices to return by airline = 2 From, fundamental principle, total number of ways of performing the journey = 5 x 2 = 10 ways
Answer: A
Question: John makes $40 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
Options:
A)16%
B)16.66%
C)76.69%
D)76.98%
E)75%
Rationale: Increase = (30/40)*100 = (3/4)*100 = 75%.
E
Answer: E
Question: The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)766 m
B)156 m
C)245 m
D)156 m
E)235 m
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2
==> 2(140 + X) = 750 ==> X
= 235 m.
Answer: E
Answer: E
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 2 on it exactly once?
Options:
A)9/100
B)1/10
C)18/100
D)19/100
E)1/5
Rationale: Probability = No of balls with exactly one 2 / total number of balls
= {2,12,20,21,23 to 29, 32,42,52,62,72,82,92}/100
= 18/100
Answer is C
Answer: C