divelab/Sys2Bench huggingface dataset:
Question: Let y=1+1/2+1/3+1/2+......, what is the value of y ?
Options:
A)(√11 + 3 ) / 2
B)(√11 - 3 ) / 2
C)(√15 + 3 ) / 2
D)(√15 - 3 ) / 2
E)None of these
Rationale: Explanation :
=> y = 1 / (2 + 1 / ( 3 + y) ).
=> y = (3 + y) / (7 + 2y).
=> 2y2 + 6y - 3 = 0.
=> y = −6±36+24/√4
=> −6±60/√4= −3±15/√2.
Since 'y' is a +ve number, therefore:
y = ( √15 - 3 ) / 2.
Answer : D
Answer: D
Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
Options:
A)1
B)2
C)4
D)6
E)7
Rationale: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
B
Answer: B
Question: A person says that their speed while going to a city was 10mph however while
returning as there is no much traffic they came with a speed of 15mph. what is their
average speed?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: Avg speed= 2xy/x+y
Hence Ans: 12
ANSWER:A
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
A)150 m
B)145 m
C)140 m
D)135 m
E)155 m
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
ANSWER:A
Answer: A
Question: Rahim bought 65 books for Rs.1160 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ?
Options:
A)Rs.18.28
B)Rs.20
C)Rs.18.08
D)Rs.28.08
E)Rs.38.08
Rationale: Average price per book = (1160 + 920) / (65 + 50) = 2080 / 115 = Rs.18.08
ANSWER:C
Answer: C
Question: If an object travels 70 feet in 2 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
Options:
A)15.95
B)17.28
C)19.54
D)21.73
E)23.86
Rationale: 70 feet/2 seconds = 35 feet/second
(35 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 23.86 miles/hour (approximately)
The answer is E.
Answer: E
Question: Meena wrote all the numbers from 1 to 29,999 inclusive. How many digits did she write in total?
Options:
A)118,889
B)138,889
C)159,889
D)188,789
E)188,989
Rationale: 1-9=>1*9 digits
10-99=>2*90=180 (numbers between 10-99 is 90 where each has 2 digits)
100-999=>3*900=2700
1000-9999=>4*9000 = 36,000
10000-29999=>5*20,000 = 100,000
The answer is 138,889
The answer is B.
Answer: B
Question: Two taps can separately fill a cistern 5 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Options:
A)A)7
B)B)6
C)C)8
D)D)9
E)E)4.74
Rationale: 1/5 + 1/15 - 1/x = 1/18
x = 4.74
Answer:E
Answer: E
Question: Evaluate: 50 - 12*3*2 = ?
Options:
A)62
B)52
C)32
D)12
E)42
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
50 - 12*3*2 = 50 - 8 = 42
correct answer E
Answer: E
Question: In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are marketing majors?
Options:
A)3
B)5
C)7
D)11
E)17
Rationale: pqrs = 1365 = 3 * 5 * 7 * 13
Since 1< p < q < r < s, the number of students who are marketing majors is r = 7.
The answer is C.
Answer: C
Question: What is the probability of getting a sum 9 from two throws of dice
Options:
A)1/3
B)1/9
C)1/12
D)2/9
E)None of these
Rationale: Explanation:
Total number of cases = 6*6 = 36
Favoured cases = [(3,6), (4,5), (6,3), (5,4)] = 4
So probability = 4/36 = 1/9
Answer: B
Answer: B
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Options:
A)3901
B)3909
C)3929
D)3900
E)3912
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer: D
Answer: D
Question: In an examination, a student scores 4 marks for every correct answer and loses I mark for every wrong answer. If he attempts in all 60 questions and secures 130 marks, the number of questions he attempts correctly, is:
Options:
A)35
B)38
C)40
D)42
E)45
Rationale: = 4x – (60 – x) = 130
= 5x = 190 x = 38
Answer: Option B
Answer: B
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 25 percent on food, and 25 percent on other items. If Jill paid a 10 percent tax on the clothing, no tax on the food, and an 20 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: Assume she has $200 to spend.
TAX
Clothing = 50% = $100= $10.00
Food = 25% = $ 50 = $0.00
Items = 25% = $ 50 = $ 10.00
Total tax = $20.00
% of total amount = 20/200 * 100 = 10%
Answer B
Answer: B
Question: When x - p is divided by p , the quotient is n and there is no remainder. Which of the following must be the value of x?
Options:
A)p(n + 1)
B)n(p + 1)
C)p(n + 1) + 2n
D)p(n - 1) + 2n
E)n(p + 1) (p − 1)
Rationale: Given in question (x-p)/p= n
=> x-p= np
=>x= np+p
Now we are good to check the options
x= p(n+1)
Answer A
Answer: A
Question: Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 8% greater than any other employee, what is the lowest possible salary that any one employee earned?
Options:
A) $40,000
B) $41,667
C) $42,000
D) $46,460.17
E) $60,000
Rationale: Employee 1 earned $x(say)
Employee 2 will not earn more than $1.08x
Therfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 20 employees
(1.08x*20)+x=1,050,000
Solving for x=$46,460.17
Answer D
Answer: D
Question: 2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost?
Options:
A)26
B)56
C)110
D)28
E)54
Rationale: Let the cost of 1 chair = x, let the cost of 1 table = y
2x + y = 110
y = 110 - 2x
Again,
4x + y = 166
4x + (110 - 2x) = 166
4x + 110 - 2x = 166
2x + 110 = 166
2x = 56
x = 28
Answer: D
Answer: D
Question: Find a sum for first 4 prime no's from number series?
Options:
A)24
B)28
C)30
D)17
E)36
Rationale: Required sum = (2 + 3 + 5 + 7 ) = 17
Note: 1 is not a prime number
Option D
Answer: D
Question: After giving a discount of rs.45 the shopkeeper gets a loss of 10%,if the cost price is rs.180.find the markup %?
Options:
A)0.21
B)0.2
C)0.17
D)0.21
E)0.15
Rationale: cost price=180
s.p=180*90/100=162
disc=45
so...mark price=162+45=207......
mark up%=207-180/180=81/180=.15 or 15%
ANSWER:E
Answer: E
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 12%. What is the selling price of the cycle?
Options:
A)s. 1090
B)s. 1160
C)s. 1232
D)s. 1202
E)s. 1204
Rationale: since,c.p=1400
loss%=(c.p-s.p)/c.p*100
12=(1400-s.p)/1400*100
so,after solving answer=1232.
ANSWER:C
Answer: C
Question: The cost of painting the four walls of a room is Rs.350. The cost of painting a room three times in length, breadth and height will be :
Options:
A)Rs.1050
B)Rs.1400
C)Rs.3150
D)Rs.4200
E)None
Rationale: Explanation:
Area of 4 walls of the room = [2(l+b)×h]m2
Area of 4 walls of new room = [2(3l+3b)×3h]m2 = 9[2(l+b)×h]m2
Cost of painting the 4 walls of new room = Rs.(9×350)=Rs.3150
Correct Option: C
Answer: C
Question: The average of 13 numbers is 59. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Options:
A)59
B)83
C)45
D)53
E)64
Rationale: Sum of all the 13 numbers = 13 * 59 = 767
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 767 = 59.
Answer:A
Answer: A
Question: An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 24 metre of cloth ?
Options:
A)175 seconds
B)195 seconds
C)155 seconds
D)188 seconds
E)115 seconds
Rationale: Explanation:
Let the time required by x seconds.
Then, More cloth means More time (Direct Proportion)
So,
0.128 : 1 :: 24 : x => x = {\color{Blue} \frac{24\times 1}{0.128}}
=> x = 187.5
So time will be approx 188 seconds
Answer: D
Answer: D
Question: An investor bought a 1-year $7,000 certificate of deposit that paid interest at an annual rate of 10 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
Options:
A)$350
B)$367.25
C)$700
D)$717.50
E)$1400
Rationale: 1.05*1.05*7000 = $7717.50
The answer is D.
Answer: D
Question: A sum of Rs.2200 has been divided among A, B and C such that A gets 1/4 of what B gets and B gets 1/5 of what C gets. What is B's share?
Options:
A)342
B)352
C)322
D)332
E)362
Rationale: Let C's share = Rs. x
Then B's share = x/5
A's share = x/5×1/4=x/20
Hence, x+x/5+x/20=2200
⇒x(1+1/5+1/20)=2200
⇒x(25/20)=2200
⇒x(5/4)=2200
⇒x=2200×4/5=440×4=Rs.1760
B's share = x/5=1760/5=Rs.352
Answer is B.
Answer: B
Question: 1,3,5,7,9,..50 find term of sequnce
Options:
A)1230
B)1300
C)1500
D)1679
E)2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500 .
E
Answer: E
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
Options:
A)157
B)169
C)197
D)280
E)176
Rationale: 80* 7: x* 3
= 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Answer: D
Question: A pet store owner has 12 cats and 20 dogs. They want to have 20% more cats than dogs. How many dogs do they have to sell to achieve their goal of having 20% more cats than dogs assuming they do not sell any cats in this time.
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: You can use basic arithmetic to solve the answer by testing each of the possible answers.
Lets test C:
if they sold 10 dogs they would have 12 cats and 10 dogs and a total of 22 pets
12/22= 54.5%
10/22= 45.5%
for a difference of 9%
lets test D:
if they sold 12 dogs they would have 12 cats and 8 dogs and a total of 20 pets
12/20=60%
8/20=40%
for a difference of 20%
The answer is D
Answer: D
Question: A inlet pipe can fill a tank in 12 hours and an outlet pipe can empty the tank in 16 hours. If both the pipes are opened simultaneously, find the time taken to fill the tank.
Options:
A)36 hours
B)12 hours
C)4 hours
D)48 hours
E)58 hours
Rationale: Explanation:
As the inlet can fill the tank in 12 hours, in one hour it will fill 1/12th of the tank.
Similarly, the outlet pipe in one hour can empty 1/16th part of the tank.
If both are opened simultaneously, the part of the tank filled in one hour is:
1/12 - 1/16 = 1/48
Hence, the tank gets filled in 48 hours.
ANSWER D
Answer: D
Question: If the average of 20 digits is 500 and the average of 14 of them is 390, calculate the average of the remaining 6 numbers?
Options:
A)756.7
B)751.7
C)753.7
D)752.7
E)722.7
Rationale: Explanation:
Total of the 20 digits - 20 * 500= 10000
Total of the 14 digits - 14*390 = 5460
Total of the remaining 6 digits - 10000-5460 = 4540
average of the remaining 6 numbers = 4540/6 = 756.7
ANSWER: A
Answer: A
Question: The instructions state that Cheryl needs 4/9 square yards of one type of material and 2/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 6/12 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
Options:
A)1/12
B)1/9
C)2/3
D)1 1/9
E)11/18
Rationale: total bought = 4/9+2/3
left part 6/12--->1/2
so used part 4/9+2/3-1/2=11/18
Ans E
Answer: E
Question: A woodworker normally makes a certain number of parts in 24 days. But he was able to increase his productivity by 5 parts per day, and so he not only finished the job in only 22 days but also he made 80 extra parts. How many parts does the woodworker normally makes per day and how many pieces does he make in 24 days?
Options:
A)240
B)420
C)560
D)190
E)360
Rationale: Let x be the number of parts the woodworker normally makes daily. In 24 days he makes 24⋅x pieces. His new daily production rate is x+5 pieces and in 22 days he made 22⋅(x+5) parts. This is 80 more than 24⋅x Therefore the equation is:
24⋅x+80=22(x+5)
30=2x
x=15
Normally he makes 15 parts a day and in 24 days he makes 15⋅24=360 parts.
Answer: E
Question: An investment of y dollars at p percent simple interest yields $600 interest over a 3-year period. In terms of y, what dollar amount invested at the same rate will yield the same amount of interest over a 2-year period?
Options:
A)2/3 y
B)3/4 y
C)3/2 y
D)2y
E)3y
Rationale: Let's start by assigning suitable values to some variables so that we can easily calculate the answer.
$600 simple interest earned in 3 yrs means $200 earned every year. So if dollar amount y = 1000, rate of interest p = 20%
We need $600 in 2 yrs i.e. $300 every year at 20% rate.
300 = 20% of Amount invested
Amount invested = $1500 i.e. (3/2)y
Answer (C)
Answer: C
Question: We run a business that rents out canoes and kayaks. A canoe rental costs $9 per day, and a kayak rental costs $12 dollars per day. One day, our business rents out 4 canoes for every 3 kayaks and receives a total of $432 in revenue. How many more canoes than kayaks were rented out?
Options:
A)10
B)9
C)8
D)7
E)6
Rationale: Let x be the number of canoes.
Then 3x/4 is the number of kayaks.
9x+(3x/4)*12=432
9x+9x=432
18x=432
x=24 (canoes)
3x/4=18 (kayaks)
There were 24-18 = 6 more canoes rented out.
The answer is E.
Answer: E
Question: If x is an integer that has exactly three positive divisors (these include 1 and x), how many positive divisors does x^3 have?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Since factors of '4'are {1,2,4}
4^3=64
Number of factors/divisors of 64= 2^6
We know that when a number is expressed as a product of the prime factors as below:
N = a^x * b^y * c^z
Then no. of divisors = (x+1)*(y+1)*(z+1)
Then here (6+1) = 7
ANSWER:D
Answer: D
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 250 girls, the total number of
students in the college is
Options:
A)420
B)520
C)620
D)650
E)None of these
Rationale: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 250
=> x = 50
Total students = 8x+5x = 13x = 13(50) = 650
Answer: D
Answer: D
Question: 1.45, 2.56, 4.78, 8.11, 12.55, (....)
Options:
A)17.3
B)16.2
C)15.3
D)19.5
E)18.1
Rationale: Explanation:
1.11, 2.22, 3.33, 4.44, 5.55,
Hence 5.55=18.1
Answer: E
Answer: E
Question: If u, v, w, x, y, and z are six different prime numbers, which of the following is the smallest possible value of u + v + w + x + y + z?
Options:
A)35
B)37
C)39
D)41
E)43
Rationale: The sum of the six small smallest primes numbers is 2+3+5+7+11+13=41.
The answer is D.
Answer: D
Question: For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers V are there between #6 +2 and #6 +6 , inclusive?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: None is the answer. A.
Because for every k 6! + k :: k, because 6! :: k, since k is between 2 and 6.A
Answer: A
Question: The cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paisa per meter is Rs. 36. The breadth of the room is ?
Options:
A)6 meters
B)8 meters
C)9 meters
D)10 meters
E)12 meters
Rationale: Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m
Area of carpet = (120 x 75) / 100 m2
= 90 m2
∴ Area of the room = 90 m2
Breadth of the room = Area /Length
= 90 / 15 m
= 6m
ANSWER :A
Answer: A
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 17 more transactions than Cal. How much transactions did Jade handled?
Options:
A)80
B)81
C)82
D)83
E)84
Rationale: Solution:
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 16 more transactions than Cal.
Jade = 66 + 17
= 83
Jade handled = 83 transactions.
Answer: D
Answer: D
Question: A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
Options:
A)9
B)14
C)25
D)30
E)44
Rationale: Since we need to find only an approximate value and the answer choices are quite widespread, then use:
80% instead of 82% (notice that this approximation gives the bigger tank capacity);
140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity);
130 billion gallons instead of 124 billion gallons;.
Notice that the third approximation balances the first two a little bit.
So, we'll have that: capacity∗0.8=140 --> capacity=140/0.8=175
Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately 175−130=45 billion gallons.
Answer: E.
Answer: E
Question: Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 70 km apart both 3 and 6 hours after start, then find the distance between the two stations.
Options:
A)210 km
B)240 km
C)220km
D)180km
E)200km
Rationale: In first 3 hours T1 travels R km and T2 travels S km.
After 6 hours they traveled R+S+70+ 700
2(R+S ) = R+S +140
R+S = 140
Hence distance between XY is R+S+ 70 = 140 +70 =210
Answer : A
Answer: A
Question: A ranch has both horses and ponies. Exactly 3/10 of the ponies have horseshoes, and exactly 5/8 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
Options:
A)130
B)141
C)152
D)163
E)174
Rationale: 3/10*P are ponies with horseshoes, so P is a multiple of 10.
5/8*3/10*P = 3/16*P are Icelandic ponies with horseshoes, so P is a multiple of 16.
The minimum value of P is 80. Then H = P+3 = 83.
The minimum number of horses and ponies is 163.
The answer is D.
Answer: D
Question: The ratio of cats to dogs to birds to fish is 8:9:10:11. There are no other types of animals in the pet store. which of the followingcannotbe the total number of animals in the store?
Options:
A)76
B)114
C)152
D)190
E)345
Rationale: The parts add up to 8 + 9 + 10 + 11 = 38, so we know that any possible number of total answers must be a multiple of 38. All five answer choices are multiples of 38:
(A) 76= 38*2
(B) 114= 38*3
(C) 152= 38*4
(D) 190= 38*5
(E) 345= not a multiple of 38
Answer: E
Question: The value of a stock is Y dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday?
Options:
A)Y.
B)Y/2.
C)2Y/3.
D)Y/3.
E)Y/4.
Rationale: Stock value= Y
AT sunday end= y+.5Y= 1.5 Y
On monday the value drop to 1/3rd of its value on sunday
1.5y/3= .5y= Y/2
B is the answer
Answer: B
Question: Find the missing number of the following series?
16 8 24 12 36 18 54 ? 81
Options:
A)27
B)28
C)29
D)26
E)None
Rationale: Solution:
27
Explanation:
16/2 = 9
8*3 = 24
24/2 = 12
12*3 = 36
36/2 = 18
18*3 = 54
54/2 = 27
27*3 = 81
Answer A
Answer: A
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A)2:5
B)2:9
C)2:2
D)2:2
E)2:8
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer: A
Answer: A
Question: Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 2 dollars .How many apples does she buy to share them equally between her six kids?
Options:
A)8
B)30
C)3
D)7
E)10
Rationale: cost of each apple = 2 dollars
Apples that Benny can buy with the amount she has=360/2 = 180.
Apples that each kid gets evenly = 180/6 =30 Apples.
So the answer is B=30
Answer: B
Question: If the sum and difference of two numbers are 10 and 19 respectively, then the difference of their square is:
Options:
A)12
B)28
C)160
D)180
E)190
Rationale: Let the numbers be x and y.
Then, x + y = 10 and x - y = 19
x2 - y2 = (x + y)(x - y) = 10 * 19 = 190.
ANSWER:E
Answer: E
Question: If 13 = 13w/(1-w) ,then (w)2 =
Options:
A)1/4
B)1/2
C)1
D)2
E)3
Rationale: 13-13w=13w
26w=13
w=1/2
2w*2=1/2*2=1
ANSWER:C
Answer: C
Question: a^(-4x/3) = a^-4
What is the value of x ?
Options:
A)2
B)3
C)-1
D)-4
E)-2/3
Rationale: -4x/3 = -4
-4x = -12; x= 3
Ans: B
Answer: B
Question: From a bunch of seven keys, three particular keys have to be used to open a combination lock, such that the second key can be used only after the first key and the third key can be used only after the second key. What are the chances of opening the lock in a random selection of three keys?
Options:
A)1/20
B)1/70
C)1/140
D)1/210
E)1/350
Rationale: The probability is 1/7*1/6*1/5 = 1/210.
The answer is D.
Answer: D
Question: If A:B = 2:3 and B:C = 4:5 then A:B:C is
Options:
A)2:3:5
B)5:4:6
C)8:12:15
D)6:4:5
E)none
Rationale: Solution:
A/B = 2/3;
B/C = 4/5;
A:B:C = 2*4:3*4:3*5 = 8:12:15.
Answer: Option C
Answer: C
Question: One half of a two digit number exceeds its one fourth by 3. What is the sum of the digits of the number?
Options:
A)3
B)9
C)11
D)12
E)15
Rationale: Explanation:
x/2 – x/4 = 3 => x =12
1 + 2 = 3
A
Answer: A
Question: If a coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land tails up on the first 4 flips and not on the last flip?
Options:
A)1/8
B)1/32
C)1/4
D)1/2
E)1/16
Rationale: (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32 Answer: B
Answer: B
Question: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 0,1,2,3,4 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY4?
Options:
A)1/5
B)5/6
C)2/5
D)7/3
E)2/7
Rationale: If a number is divisible by 4 the last 2 digits of the number has to be divisible by 4.
If the number ends with 10: Number of possibilities = 3 * 2 * 1 = 6
number ends with 20: Possibilities = 3 * 2 * 1 = 6
number ends with 30: Possibilities = 6
number ends with 12: Possibilities = 6
number ends with 14: Possibilities = 6
number ends with 32: Possibilities = 6
number ends with 34: Possibilities = 6
number ends with 24: Possibilities = 6
Total number of possibilities with restriction = 6*8 = 48
Total number of possibilities without restriction = 5! = 120
Probability = 48/120 = 2/5
Answer: C
Answer: C
Question: How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 2?
Options:
A)a. 220
B)b. 249
C)c. 432
D)d. 216
E)e. 288
Rationale: Taking Question with it's same language as given
To make number divisible by 5, the unit digit should be either 0 or 5 only
Case 1: If unit digit is fixed as zero
With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15
With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120
Total Such cases = 120+15 = 135
Case 2: If unit digit is fixed as Five
With two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065]
With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12
With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40
With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60
Total Such cases = 2+12+40+60 = 114
Total numbers = 135+114 = 288
ANSWER OPTION E
Answer: E
Question: Sum of two numbers prime to each other is 15 and their L.C.M. is 56. What are the numbers?
Options:
A)9 and 8
B)5 and 10
C)7 and 9
D)7 and 8
E)10 and 8
Rationale: As two numbers are prime, only options satisfy ie option A and D and C
but option D will make the product of numbers i.e 56
ANSWER:D
Answer: D