divelab/Sys2Bench huggingface dataset:
Question: An staff identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?
Options:
A)211
B)216
C)1075
D)1080
E)2160
Rationale: An staff identification code will be of the type -,-,-,-
first digit can be selected from any of the 5 vowels in 5C1 ways
now for the remaining three digit lets consider the following two cases
case 1: when the number is greater than 200 but less than 300
number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18
now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:
211
233
244
255
266
277
288
299
here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)
thus total possible cases are 18 + 8 =26
case 2: number ranging from 300 to 999
here for first digit we have 7 cases (3,4,5,6,7,8,9)
now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)
if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)
hence total number of ways = 7(18+9) = 189
thus different number of codes = 5(189+26) = 1075
hence C
Answer: C
Question: A thief is spotted by a policeman from a distance of 100metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 15km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?
Options:
A)A)1km
B)B)300m
C)C)650m
D)D)750m
E)E)800m
Rationale: Relative speed of the policeman = 20-15 = 5 km/hr
time taken by policeman to cover 100m = (100/1000)*(1/5) = 1/50 hr
In 1/50 hr the thief covers a distance of 15/50 km = 3/10 km = 300m
Answer is B
Answer: B
Question: The total of the ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Jayant?
Options:
A)24 years
B)32 years
C)34 years
D)38 years
E)None
Rationale: Solution
Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,
(2x + 10)+(3x + 10)+(4x + 10)	= 93.
‹=›9x = 63
x = 7.
∴ Jayant's present age = 2x + 10 = 24 years.
Answer A
Answer: A
Question: Cereal A is 8% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Options:
A) 2:9
B) 2:7
C) 1:2
D) 1:4
E) 1:3
Rationale: (8/100)A+(2/100)B = (4/100)(A+B)
4A =2B
=> A/B = 1/2
Answer is C.
Answer: C
Question: What is the range of all the roots of |x^2 - 3| = x ?
Options:
A)4
B)3
C)2
D)1
E)0
Rationale: we get 2 quadratic equations here ..
1) x^2-x-3=0 ....... roots 2 , -1
2) x^2+x-3=0 ........ roots -2, 1
Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations .
So value of x for given equation .... x=3 or x=1
I guess range is 3-1 =2
C
Answer: C
Question: Will must choose a 3-character computer password, consisting of 3 distinct digits, in any order.From how many different passwords can Will choose?
Options:
A)390
B)2,340
C)4,320
D)7,020
E)14,040
Rationale: 10C1*9C1*8C1 = 720.
=>720 * 3 ! = 4320.
Option E is correct answer...but OA is C.
Answer: C
Question: An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 1 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?
Options:
A)4:5
B)9:10
C)14:15
D)19:20
E)24:25
Rationale: Let the length and width of one carpet be 3x and 2x.
Let the length and width of the other carpet be y and y.
2(3x + 2x) = 2(y + y)
5x = 2y
(5/2) * x = y
The ratio of the areas of the carpet in both cases:
= 3x * 2x : y * y
= 6x^2 : y^2
= 6x^2 : (25/4) * x^2
= 24 : 25
The answer is E.
Answer: E
Question: A train moves past a post and a platform 264 metre long in 8 seconds and 20 seconds respectively. What is the speed of the train?
Options:
A)79.2 km/hr
B)82.4 km/hr
C)69.7 km/hr
D)49.8 km/hr
E)78.9 km/hr
Rationale: The train can cover a distance equal to its length in 8 seconds. Therefore, additional
(20âˆ’8)=12 seconds was taken to cross the platform.
Hence, speed of the train=264/12=22 m/s
=22 Ã— 18/5=79.2 km/hr
ANSWER:A
Answer: A
Question: A person buys 18 local tickets for Rs 110. Each first class ticket costs Rs 10 and each second class ticket costs Rs 3. What will another lot of 18 tickets in which the numbers of first class and second class tickets are interchanged cost?
Options:
A)112
B)118
C)121
D)124
E)None of these
Rationale: Explanation :
Let, there are x first class ticket and (18-x) second class tickets.
Then,
110 = 10x + 3(18−x).
=>110=10x+54−3x.
=>7x=56.
=>x=8.
If the number of the first class and second class tickets are interchanged, then the total cost would be 10×10 + 3 × 8=124.
Answer : D
Answer: D
Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 6 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
Options:
A)30
B)58
C)60
D)90
E)120
Rationale: I believe there is a better way to do it.
Basically one of the options should satisfy the given criteria.
60 did
1/5 *60 =12
2/3*60=40
so total distance
52 + remaining 6 =58
Answer B
Answer: B
Question: A meal cost $ 35.50 adn there was no tax. If the tip was more than 2 pc but less than 12pc of the price, then the total amount paid should be:
Options:
A)40-43
B)39-42
C)39-42
D)38-41
E)36-40
Rationale: 2%(35.5) = 0.71
12%(35.5) = 4.26
total amount could have been 35.5+0.71 and 35.5+4.26
=> could have been between 36.21 and 39.76
=> approximately between 36 and 40
Answer is E.
Answer: E
Question: A monkey ascends a greased pole 26 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options:
A)50th minute
B)41st minute
C)45th minute
D)42nd minute
E)49th minute
Rationale: The money is climbing 1meter in 2min. This pattern will go on till he reaches 24meters. I mean this will continue for first 24*2=48mins. he would have reached 24meters. After that he will climb 2meters and he will reach the pole. So total time taken = 48 + 1 = 49 mins.
So, asnwer will be E
Answer: E
Question: Percentage of profit earned by selling a book for $1680 is equal to the percentage loss incurred by selling the same book for $1120. What price should the book be sold to make 25% profit?
Options:
A)$1250
B)$1050
C)$1550
D)$1750
E)$2050
Rationale: Let C.P. be $ x.
Then, (1680 - x)	x 100 =(x - 1120)x 100
1680 - x = x - 1120
2x = 2800
x = 1400
Required S.P. = 125% of 1400 = 1.25 x 1400 = $1750
Answer : E
Answer: E
Question: The price of a microchip declines by 67 percent every 6 months. At this rate, approximately how many years will it take for the price of an $81 microchip to reach $1?
Options:
A)1.5 years
B)2 years
C)3 years
D)13 years
E)13.5 years
Rationale: I think the fastest way is
81 *(1/3)^n = 1
n =4
So 2 yrs
ANSWER:B
Answer: B
Question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
Options:
A)23
B)26
C)40
D)42
E)49
Rationale: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
C
Answer: C
Question: 20% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
Options:
A)20%
B)30%
C)40%
D)70%
E)90%
Rationale: To maximize the percentage of companies offering both, let's assume that all 20% of companies which offer wireless internet also offer snacks.
The answer is A.
Answer: A
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
Options:
A)5
B)6
C)2
D)3
E)9
Rationale: 40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer: D
Answer: D
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
Options:
A)Rs. 21000
B)Rs. 17500
C)Rs. 19000
D)Rs. 24500
E)None of these
Rationale: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)
x = 28000
35000 - x = 7000
Difference in the cost prices of televisions = Rs. 21000
ANSWER:A
Answer: A
Question: Mother,her daughter and her grand child weighs 140 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?
Options:
A)44
B)47
C)48
D)49
E)50
Rationale: mother + daughter + child = 140kg
daughter + child = 60kg
mother = 140 - 60 = 80kg
child = 1/5th of mother = (1/5)*80 = 16kg
So now daughter = 140 -(mother + child) = 140 - (80+16) = 44kg
ANSWER:A
Answer: A
Question: If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 6 or 7?
Options:
A)5/6
B)7/36
C)5/36
D)11/36
E)12/36
Rationale: The sum of numbers appeared is 6 or 7. Therefore, the required sums are 6 or 7, i.e., the required events are (1,5), (5,1), (2,4), (4,2), (3,3), (1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
i.e., for 6, n(E) = 5 and for 7, n(E) = 6
Therefore, the required probability = n(E)/n(S) = 11/36.
ANSWER:D
Answer: D
Question: The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
Options:
A)66
B)77
C)51
D)98
E)99
Rationale: Explanation:
Age of the teacher = (37 * 15 - 36 * 14) years = 51 years.
Answer: C) 51 years
Answer: C
Question: If a car went the first third of the distance at 80 kmh, the second third at 18 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?
Options:
A)34 kmh
B)40 kmh
C)42 kmh
D)44 kmh
E)50 kmh
Rationale: Assume D/3 = 720 (this number is convenient because it is divisible by 80, 18 and 48)
So:
720 = 80*T1 = 9 hrs
720 = 18*T2 = 40 hrs
720 = 48*T3 = 15 hrs
T = T1 + T2 + T3 = 64 hrs
D = RT
(720*3) = R*64
R = 33.75
ANSWER: A
Answer: A
Question: Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $68 after it went on sale for 15% off, what is the difference between the original price and the final price?
Options:
A)$0.00
B)$1.00
C)$3.40
D)$5.00
E)$6.80
Rationale: 0.85*{Original Price} = $68 --> {Original Price} = $80.
{Final Price} = $68*1.25 = $85.
The difference = $85 - $85 = $5.
Answer: D.
Answer: D
Question: A 6000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?
Options:
A)8
B)12
C)18
D)24
E)36
Rationale: In: we have: 1,000/2min = 500 litres per minute
Out: we have: 1,000/4 + 1,000/6
Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (3,000 by that net inflow to get the minutes) - 36 min. Answer E.
Answer: E
Question: A train 360 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40 sec
B)11 sec
C)88 sec
D)33.33 sec
E)10 sec
Rationale: Speed = 54 * 5/18 = 15 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 1/15 = 33.33 sec
Answer: D
Answer: D
Question: After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 5535. What was the number of original inhabitants?
Options:
A)7900
B)8200
C)8500
D)8800
E)9100
Rationale: Let the total number of original inhabitants be x.
(75/100) * (90/100) * x = 5535
(27/40) * x = 5535
x = 5535 * 40 / 27 = 8200
The answer is B.
Answer: B
Question: A particular parking garage is increasing its rates by 30 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?
Options:
A)12%
B)16%
C)20%
D)23%
E)25%
Rationale: Let x be the original number of days that Bob used the garage.
Let P be the original cost per day.
Let N*x be the new number of days that Bob uses the garage.
N*x*1.3P = x*P
N*x = x/1.3 which is about 0.77x, thus a 23% reduction.
The answer is D.
Answer: D
Question: 20 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
Options:
A)None of these
B)380
C)312
D)324
E)342
Rationale: Explanation :
He can go in any bus out of the 20 buses.
Hence He can go in 20 ways.
Since he can not come back in the same bus that he used for travelling,
He can return in 19 ways.
Total number of ways = 20 x 19 = 380. Answer : Option B
Answer: B
Question: A man sitting in a train which is traveling at 30 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
Options:
A)50 kmph
B)82 kmph
C)62 kmph
D)65 kmph
E)75 kmph
Rationale: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 30) kmph = 82 kmph.
Answer : B.
Answer: B
Question: The average age of 3 boys is 30 years and their ages are in the proportion 1:2:3. The age of the youngest boy is?
Options:
A)15years
B)20years
C)22years
D)25years
E)30years
Rationale: Total age of 3 boys = 30*3 = 90
ratio of their ages = 1:2:3
Age of the youngest = 90*1/6 = 15 years
Answer is A
Answer: A
Question: In the series 0, 3, 8, 15,__ What is the next number?
Options:
A)22
B)23
C)24
D)25
E)26
Rationale: 3-0=3
8-3=5
15-8=7
difference increasing by 2 every time
next difference 9
15+9=24
ANSWER:C
Answer: C
Question: Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 50 units produced by Machine-B 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)a. 0.156
B)b. 0.01506
C)c. 0.0156
D)d. 0.0001566
E)e. 0.00001566
Rationale: Let total Production be 10000 units....
A produces 4000 units and 36 units are defective
B produces 6000 units and 120 units are defective
So, Out of total 10,000 units 156 units are defective...
So the required probability = 156/10000 => 0.0156
Answer will be (C)
Answer: C
Question: In the first hour of a two-hour trip, a car traveled d kilometers, and in the second hour of the trip, the car traveled one that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?
Options:
A) d
B) 1/3*d
C) 1/2*d
D) 3/4*d
E) 3/2*d
Rationale: Solution:
Lets look at the information given in the question...
Total time travelled = 2 hrs
Distance travelled first hour = d
Distance travelled second hour = d
The question is asking for the avg speed at which the car travels for 2 hrs
We know that avg speed = total distance/total time
Lets place the information given in the question to the formula above = (d+d)/2
=d
We find that option A is the answer as it gives the same expression as found in our calculation above. Answer option A.
Answer: A
Question: City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 4:20 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
Options:
A)5:00
B)5:30
C)6:00
D)6:20
E)7:00
Rationale: Train C has traveled 20 mi in the half hour before Train D has started its journey.
140-20=120
40+20 =60 mph
120 mi/ 60 mph = 2 hrs
4:20pm + 2 hrs = 6:20pm
Answer:
D. 6:20
Answer: D
Question: The rate at which a sum becomes four times of itself in 15 years at S.I., will be :
Options:
A)10 %
B)15 %
C)20 %
D)40 %
E)None
Rationale: Sol.
Let sum = x. Then, S.I. = 3x
∴ Rate = [100 * S.I. / P*T] = [100 * 3x / x * 15]% = 20%.
Answer C
Answer: C
Question: Consider a quarter of a circle of radius 25. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
Options:
A)16*(sqr2 -1)
B)8*(sqr3 -1)
C)25*(sqr2 - 1)
D)12* (sqr7 -1)
E)None of these
Rationale: I got 16/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer is C
Answer: C
Question: 78, 64, 48, 30, 10, (...)
Options:
A)-12 number
B)-14
C)2
D)8
E)6
Rationale: Explanation :
78 - 14 = 64
64 - 16 = 48
48 - 18 = 30
30 - 20 = 10
10 - 22 = -12
Answer : Option A
Answer: A
Question: Find large number from below question The difference of two numbers is 1000. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1345
B)1197
C)1540
D)1600
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1000 = 6x + 15
5x = 985
x = 197
Large number = 197 +1365 = 1197
B
Answer: B
Question: From the starting point in a boat race, one competitor started to sail north at a speed of 1.3 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours?
Options:
A)8.8
B)12.
C)12.5.
D)14.
E)15.4.
Rationale: Both competitors are sailing making angle of 90 degrees.
After 5 hrs one competitor will cover a distance of = 1.3 *5= 6.5 KM
And, other competitor will cover a distance of = 1.2*5= 6KM
distance between them after 5 hrs = (6.5^2+ 6^2)^1/2= 8.8KM
A is the answer
Answer: A
Question: What inequality represents the condition 1<x<5?
Options:
A)|x|<3
B)|x+5|<4
C)|x-3|<2
D)|-5+x|<4
E)|3+x|<5
Rationale: 1<x<5 represents segment with
length: 5-1 = 4
center: (5+1)/2 = 3
For any |x-a|<b a is a center and b is a half of length. So, |x-3|<4/2 represents our inequality (answer C)
Answer: C
Question: The ratio of two quantities is 5 to 6. If each of the quantities is increased by 3, what is the ratio of these two new quantities?
Options:
A)2/15
B)7/5
C)9/5
D)It cannot be determined from the information given.
E)12/17
Rationale: let the actual ratio be 5k/6k, increase numerator and denominator by 4=> 5k+3/6k+3
Until the value of k is unknown we can not determine the actual ratio.
OR
let the actual be 3/4. After increasing 3 => 6/7
let the actual be 6/8. After increasing 3 => 9/11
Therefore without actual quantities we cannot determine the actual ratio.
Answer : D
Answer: D
Question: How many different subsets of the set {0, 1, 2, 3, 4, 5,6,7} do not contain 0?
Options:
A)A.16
B)B.72
C)C.93
D)D.32
E)E.64
Rationale: Number of subset
Since we have 7 digits other than 0, we can take any numbers from the set of 7 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.
7c1+7c2+7c3+7c4+7c5+7c6+7c7=92
And one set is the NULL set having no elements in it so
92+1=93.
ANSWER C.
Answer: C
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)4538
B)4529
C)4528
D)4530
E)4598
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5
= Rs. 4530
Answer: D
Answer: D
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
Options:
A)09:20p.m
B)04:40p.m
C)10.30p.m
D)02.32p.m
E)12:23p.m
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer:C
Answer: C
Question: Two positive integers differ by 4, and sum of their reciprocals is 4. Then one of the numbers is
Options:
A)a) 3
B)b) 1
C)2
D)d) 21
E)e) 28
Rationale: Algebraic approach:
Let n be the smaller integer => 1/n + 1/(n+4) = 4
or ((n+4)+n)/n(n+4) =4 or (n^2+4n)*4 =2n+4 or n=2 as n cannot be -negative
Solve for n => n=2. Hence,
C
Answer: C
Question: C and D started a business investing Rs. 49,000 and Rs. 35,000 respectively. In what ratio the profit earned after 4 years be divided between C and D respectively?
Options:
A)7:4
B)7:5
C)6:4
D)5:5
E)None of these
Rationale: C:D= 49000 : 35000 = 7:5.
ANSWER:B
Answer: B
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
Options:
A)18 days
B)20 days
C)24 days
D)30 days
E)34 days
Rationale: Explanation:
2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer: C
Answer: C
Question: Look at this series: 97, 97, 97, 87, 87, 87, 77, 77, 77 ... What number should come next?
Options:
A)66
B)67
C)68
D)69
E)70
Rationale: Explanation:
In this series, each number is repeated, then 10 is subtracted to arrive at the next number.
Answer: Option B
Answer: B
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options:
A)80
B)100
C)25
D)206
E)300
Rationale: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number
of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (24 + 90 + 80 + 15)
= 209.
ANSWER D
Answer: D
Question: The sum of all the integers d such that -26 < d < 24 is
Options:
A)0
B)-2
C)-25
D)-49
E)-51
Rationale: Easy one -
-25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23
Cancel everyhitng and we're left with - -25 and -24 d= -49.
D is the answer.
Answer: D
Question: Of the four numbers, whose average is 80, the first is one-fourth of the sum of the last three. The first number is ?
Options:
A)28
B)64
C)11
D)48
E)10
Rationale: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 80 or x = (80 * 4) / 5 = 64
Answer: B
Answer: B
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)Rs.4532
B)Rs.4526
C)Rs.4598
D)Rs.4530
E)Rs.4528
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5
= Rs.4530
Answer:D
Answer: D
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
Options:
A)700
B)720
C)780
D)800
E)810
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
B
Answer: B