divelab/Sys2Bench huggingface dataset:
Question: The cost of an item was reduced from its usual selling price of $23.99 to $15.99. Which of the following is closest to the percent decrease in the price of the item?
Options:
A)17%
B)21%
C)24%
D)25%
E)33%
Rationale: The price decreased by 23.99 - 15.99 = $8.
$8 is a bit more than 33% of original price of $24.
Answer: E.
Answer: E
Question: If x^3 + y^3 = 200, then the greatest possible value of x is between
Options:
A)2 and 3
B)3 and 4
C)4 and 5
D)5 and 6
E)7 and 8
Rationale: for the greatest possible value of x^3, we must minimize the value of y^3 i.e. lets say y^3 = 0
then we need to find a number x such that x^3 < 200. 5^3 = 125 and 6^3 = 216 so we can say that the maximum possible value of x can be a little more than 5 hence answer = between 5 and 6
hence D
Answer: D
Question: Mixture W is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture W, how many kilograms of mixture W must be added to make a 70% material B in the new mixture?
Options:
A)A)6
B)B)7
C)C)8
D)D)9
E)E)10
Rationale: Can be done with weighted avg method.
if 2 kg more of oil is added to 20% oil of 8 kg mix,then a 10kg of mix will have 3.6kg (or 36%) of oil .
W1=20(initial mix.)
Avg. is what we need..ie 70% of material B means 30% of oil
W2=36(36% of 10 kg mix)
w1/w2=(W2-Avg)/(Avg-W1)
(36-30)/(30-20)
6/10
means for every 10 kg of new mix. we need 6 kg of mix W
Ans A
Answer: A
Question: A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 126.Find the number of notes of Rs.50 denomination.
Options:
A)115
B)121
C)117
D)119
E)121
Rationale: Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 126 - X
Now,
50*X + 500 * (126 - X) = 10350
50X + 63000 - 500X = 10350
- 450X = - 52650
X = 117.
No. of 50 rupees note = 117.
Answer: Option C
Answer: C
Question: Eight friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 8-person seating arrangements are possible?
Options:
A)5040
B)15,120
C)30,240
D)35,280
E)40,320
Rationale: The number of ways to arrange 8 people in a row is 8!
From this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 6 other friends is 7! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 8 friends with the 2-person unit together is 7!*2
The total number of permutations where these two friends are not seated next to each other is 8! - 7!*2 = 6*7! = 30,240
The answer is C.
Answer: C
Question: A baseball pitcher won 80% of the games he pitched. If he pitched 35
ballgames, how many games did he win?
Options:
A)21
B)23
C)25
D)28
E)30
Rationale: 80% of 35 is what?
80/100=/35
100)28/2800
28 games
correct answer D
Answer: D
Question: some money is distributed among A,B,C,D in the proportion of 1:3:4:2. If C gets $50 more than D, What is B's share?
Options:
A)50
B)100
C)75
D)27
E)30
Rationale: Let the share of A,B,C,D be 1x, 3x, 4x, 2x
then 4x-2x =50
2x=50
x= 25
B's share = 3*25 = $75
Answer is C
Answer: C
Question: If ghi < 0 and hi > 0, which of the following must be positive?
Options:
A) xy
B) xz
C) (g^2)hi
D) g(h^2)i
E) xy(z^2)
Rationale: Given that hi is positive and ghi is negative, you can say that g MUST be negative. As for h and i either they are both positive or both negative.
Option (C) has g^2 which is positive and hi which is positive. So (C) must be positive.
Answer: C
Question: If x is 20 percent greater than 52, then x =
Options:
A)68
B)62.4
C)86
D)72.8
E)108
Rationale: X is 20% greater than 52 means X is 1.2 times 52 (in other words 52 + 20/100 * 52 = 1.2 * 52)
Therefore, X = 1.2 * 88 = 62.4
ANSWER:B
Answer: B
Question: If a coin is tossed 7 times what is the probability that it will land either heads 7 times or tails 7 times?
Options:
A)1/4
B)1/8
C)1/16
D)1/32
E)1/64
Rationale: The probability of 7 heads is (1/2)^7 = 1/128
The probability of 7 tails is (1/2)^7 = 1/128
The probability of 7 heads or 7 tails is 1/128 + 1/128 = 1/64
The answer is E.
Answer: E
Question: A rectangular courtyard 3.78 meters long 5.25 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?
Options:
A)14 cms
B)21 cms
C)42 cms
D)None of these
E)56 cms
Rationale: Explanation:
3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7
5.25 meters=525 cm = 5 × 5 × 3 × 7
Hence common factors are 3 and 7
Hence LCM = 3 × 7 = 21
Hence largest size of square tiles that can be paved exactly with square tiles is 21 cm. Answer: B
Answer: B
Question: If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?
Options:
A)1200
B)1245
C)1296
D)1340
E)1450
Rationale: Number of rectangles that can be formed by using m horizontal lines and n vertical lines
= mC2 × nC2
Here m = 9, n = 9
Hence, number of rectangles that can be formed
= mC2 × nC2
= 9C2 × 9C2 = (9C2)2
=(9×82×1)2=362=1296=(9×82×1)2=362=1296
ANSWER C 1296
Answer: C
Question: The perimeter of a triangle is 39 cm and the inradius of the triangle is 1.5 cm. What is the area of the triangle?
Options:
A)22
B)35
C)77
D)54
E)29
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 1.5 * 39/2
= 29 cm2
Answer:E
Answer: E
Question: Approximately what percentage of the world’s forested area is represented by Finland given that Finland has 53.42 million hectares of forested land of the world’s 8.076 billion hectares of forested land.
Options:
A)0.0066%
B)0.066%
C)0.66%
D)6.6%
E)66%
Rationale: Since 1 billion is 1000 million
Soc changing all quantities to million
Finland forest area =53.42 million hect.
Worlds's forest area =8.076 billion hect.
% =53.42*100/8.076*1000 =0.66%
Answer C
Answer: C
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 8 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
Options:
A)22 km
B)20 km
C)44 km
D)18 km
E)16 km
Rationale: Distance = Relative Speed * Time
= (8 + 3) * 4 = 44 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: C
Answer: C
Question: 8 men can dig a pit in 20 days.If a men work half as much again as a boy,then 4 men and 9 boys can dig a similar pit.Fint the days for 15 boys can dig?
Options:
A)17
B)10
C)15
D)20
E)16
Rationale: 1 man=3/2 boys
(4 men+9 boys)=15 boys
8 men=[(3/2)+8]=12 boys
now, 12 boys can dig the pit in 20 days.
15 boys can dig=16 days.
Answer is option E
Answer: E
Question: the average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the manager whose salary was Rs. 720, was replaced with a new manager, then the average salary of the team went down to 580. What is the salary of the new manager?
Options:
A)640
B)690
C)420
D)570
E)None
Rationale: Solution:
The total salary amount = 15 � 600 = 9000
The salary of the exiting manager = 720.
Therefore, the salary of 12 workers and the remaining 2 managers,
= 9000−720 = 8280
When a new manager joins, the new average salary drops to Rs.580 for the total team of 15 of them.
The total salary for the 15 people i.e., 12 workers, 2 old managers and 1 new manager =580�15 =8700
Therefore, the salary of the new manager is,
9000 - 8700 = 300 less than that of the old manager who left the company, which is equal to 720 - 300 = 420.
Answer: Option C
Answer: C
Question: A train passes a station platform in 34 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)228
B)240
C)887
D)166
E)210
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/34 = 15 => x = 210 m.
Answer: E
Answer: E
Question: A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2x1/3 hours to fill the tank. The leak can drain all the water of the tank in
Options:
A)5 hrs
B)7 hrs
C)12 hrs
D)14 hrs
E)None
Rationale: Sol.
Work done by the leak in 1 hour = (1/2 - 3/7) = 1/14.
∴ Leak will empty the tank in 14 hrs.
Answer D
Answer: D
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 5kmph and the other is going towards south 5kmph. What time will they take to be 50km apart?
Options:
A)1hr
B)2hrs
C)3hrs
D)5hrs
E)6hrs
Rationale: To be (5+5) km apart, they take 1 hour
To be 50 km apart, they take 1/10 *50 = 5 hrs
Answer is D
Answer: D
Question: Among three numbers, the first is twice the second and thrice the third. If the average of three numbers is 49.50, then what is the difference between the first and the third number?
Options:
A)28
B)54
C)39.5
D)41.5
E)None of these
Rationale: 6x, 3x, 2x.
Now average = 6x+3x+2x/9 = 39.5
On solving we get the difference in between first and the third number = 54.
Answer:B.
Answer: B
Question: In a 2000 m race, A beats B by 150 meters or 50 seconds. Find the speed of B?
Options:
A)10m/s
B)2m/s
C)5m/s
D)7m/s
E)3m/s
Rationale: Since A beats B by 150 m or 50 seconds,
it implies that B covers 150 m in 50 seconds.
Hence speed of B = 150/50 = 3 m/s.
Answer: E
Answer: E
Question: In a village of 2,700 people, 900 people are over 70 years old and 1200 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?
Options:
A)3/5
B)7/10
C)11/15
D)23/30
E)31/45
Rationale: The number of people younger than 70 years old is 2700-900 = 1800
The number of females older than 70 years old is 0.6*1200 = 720
The number of males older than 70 years old is 900-720 = 180
The number of people who are either male or younger than 70 is 1800+180 = 1980.
P(a person is younger than 70 or male) = 1980/2700 = 11/15
The answer is C.
Answer: C
Question: A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. Find out B's contribution in the capital.
Options:
A)5000
B)7000
C)8000
D)9000
E)6000
Rationale: Ratio in which profit is divided =2:3
Assume that B's contribution to the capital =b
3500×12:b×7=2:3
⇒3500×12×3=2×b×7
⇒b=(3500×12×3)/2×7
=500×6×3=9000
Answer is D.
Answer: D
Question: An engine moves at the speed of 90 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 9 coaches are attached speed decreases to 78 kmph.What will be the speed of train when 25 coaches are attached.
Options:
A)90
B)85
C)80
D)60
E)70
Rationale: 1.
No. of coaches =9
sqr root=3
speed decreases by 12
12=k*3
k=4
No. of coaches=25
swr root=5
decrease=5*4=20
New speed=90-20=70
E
Answer: E
Question: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=6?
Options:
A)–108
B)–44
C)10
D)16
E)18.25
Rationale: #p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 6 ---> 8p= 146 ---> p = 18.25, E is the correct answer.
Answer: E
Question: A milk man has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is:
Options:
A)22
B)25
C)27
D)29
E)11
Rationale: Explanation:
when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 20 liters of milk.
Therefore, profit percentage = \inline \frac{5}{20}\times 100=25% % [ profit %= \inline \frac{profit}{cost\: price}\times 100 ]
Answer: B) 25%
Answer: B
Question: If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a four-percent vinegar solution, what was the concentration of the original solution?
Options:
A)19.3%
B)17%
C)20.67%
D)15.5%
E)12.5%
Rationale: Let X be the quantity of non-vinegar in the strong vinegar solution
Thus vinegar quantity will be 12 - X
When 50 ounces of water were added the percentage of vinegar becomes 4%, thus (12 - X)/62 = 4/100
From this equation X = 9.52
Answer (12-9.52)/12 = 20.67%
ANSWER:C
Answer: C
Question: In a group of 80 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
Options:
A)1140
B)1160
C)1180
D)1200
E)1210
Rationale: Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12.
Number of sweets 80 children got = 80 * 12 = 960.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 10 youngsters got = 10 * 20 = 200.
Total number of sweets = 960 + 200 = 1160.
B)
Answer: B
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Options:
A)298 m
B)287 m
C)298 m
D)150 m
E)267 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: D
Answer: D
Question: Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 28% ryegrass, what percent of the weight of the mixture is from mixture X?
Options:
A)10%
B)20%
C)40%
D)50%
E)60%
Rationale: 28% is 3%-points above 25% and 12%-points below 40%.
Thus the ratio of mixture Y to mixture X is 4:1.
The percent of mixture X is 1/5 = 20%.
The answer is B.
Answer: B
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Options:
A)40
B)44
C)48
D)50
E)56
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer:B
Answer: B
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
Options:
A)6 days
B)12 days
C)15 days
D)9 days
E)8 days
Rationale: 3/12 + (3 + x)/16 = 1
x = 9 days
ANSWER:D
Answer: D
Question: In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)10
B)12
C)13
D)15
E)16
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
Answer: B
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 15 m wide at the top and 9 m wide at the bottom and the area of cross-section is 636 sq m, the depth of cannel is?
Options:
A)53
B)28
C)27
D)80
E)25
Rationale: 1/2 * d (15 + 9) = 636
d = 53
Answer: A
Answer: A
Question: Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 65 percent carbonated water, what percent of the volume of the mixture is P?
Options:
A)20%
B)40%
C)50%
D)60%
E)80%
Rationale: 65% is 15%-points below 80% and 10%-points above 55%.
So the ratio of solution P to solution Q is 2:3.
Mixture P is 2/5 = 40% of the volume of mixture PQ.
The answer is B.
Answer: B
Question: In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 48 people were made to stand in a column, how many columns could be formed?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: 16*30 = 48*n
n = 10
The answer is A.
Answer: A
Question: A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were?
Options:
A)22
B)99
C)277
D)08
E)72
Rationale: A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were?
AnswerB
Answer: B
Question: A bag of cat food originally cost $14. After a 20% profit markup by the grocery store, it was then offered on sale for 10% off. What is the current sale price of the cat food?
Options:
A) $14.96
B) $15.00
C) $15.04
D) $15.08
E) $15.12
Rationale: sale price = (original price + 20% increase) - 10% decrease
price = [14 * (120/100)] * (90/100) = 14 * (1.2) * (.90) = 16.8 * .9 = 15.12
The answer is E.
Answer: E
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/4 % his yearly income diminishes by Rs. 61.50, his capital is?
Options:
A)24,607
B)24,609
C)24,600
D)24,602
E)24,604
Rationale: Let the capital be Rs. x. Then,
(x * 8 * 1)/100 - (x * 31/4 * 1/100) = 61.50
32x - 31x = 6150 * 4
x = 24,600.Answer: C
Answer: C
Question: From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?
Options:
A)1/15
B)25/57
C)35/256
D)1/221
E)2/15
Rationale: Let S be the sample space.
Then, n(S) = 52C2 =	(52 x 51)/(2x1)	= 1326.
Let E = event of getting 2 kings out of 4.
n(E) = 4C2 =	(4 x 3)/(2x1)= 6.
P(E) =	n(E)/n(S)	=	6/1326=1/221	.
Option D
Answer: D
Question: Insert the missing number.
8, 7, 11, 12, 14, 17, 17, 22, (....)
Options:
A)27
B)20
C)22
D)24
E)26
Rationale: There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22) increasing by 3 and 5 respectively.
answer : B
Answer: B
Question: The three solutions of the equation f(x) = 0 are - 4, 8, and 11. Therefore, the three solutions of the equation f(2 x) = 0 are
Options:
A)- 2, 4, and 11/2
B)- 8, 16 and 22
C)- 4, 8, and 11
D)2, 19 / 2 and 7 / 2
E)None
Rationale: Solution
If f(x) = 0 at x = - 4, 8 and 11 then f(2x) = 0 for
2x = -4 , 2x = 8 and 2x = 11
Solve the above equations to find
x = -2 , x = 4 and x = 11/2
Answer A
Answer: A
Question: Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $5.43 total. On Tuesday and Wednesday, she spent $3.54 on each day. On Friday, she spent $12.89 on lunch. What was her average daily cost?
Options:
A)a. $3.19
B)b. $3.75
C)c. $3.90
D)d. $5.08
E)e. $4.23
Rationale: On Monday and Thursday, she spent $5.43total.
On Tuesday and Wednesday, she spent $3.54on each day.
On Friday, she spent $12.89 on lunch.
The average = (5.43 + 2*3.54 + 12.89)/5 = 5.08.
Answer: D.
Answer: D
Question: The income tax in country X is 8% of any income up to $5000. For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income?
Options:
A)$10,500
B)$11,000
C)$13,000
D)$13,500
E)$14,000
Rationale: Given : For incomes over $5,000, an 8% tax is imposed on the first $5,000, and a 10% tax is imposed on the portion of the total income in excess of $5000. If Perry paid $950 in income tax last month, then what was Perry's income?
for first 5000 , 8% tax then we get 400$ as tax.
Now Perry paid 950$ tax... we need to check which option is going to yield 550$ on the remaining amount.
A. $10,500 - 5000 = 5500 , then we get 10% tax , we get 550$... ( $10,500 - 5000 - here already for 5000$ we have calculated the tax and we need to tally for the remaining amount)
550+400 = 950$...hence this is the option.
ANSWER :option A.
Answer: A
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
Options:
A)49
B)99
C)24
D)88
E)21
Rationale: B = 1/8 – 1/2 = 1/24 => 24 days Answer:C
Answer: C
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 700 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
Options:
A)2880.
B)4860.
C)5780.
D)5040.
E)6380.
Rationale: Efficiency per machine = 700 watt/hr
Efficiency due to increase in wind speed = 700*120% => 840 watt/hr
Production by each machine in 2 hours is 840*2 => 1680 watt
Production by 3 machines => 1680 watt * 3 = 5040 watt
Answer will be (D)
Answer: D
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Options:
A)898
B)165
C)120
D)168
E)112
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer:C
Answer: C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
Options:
A)23/38
B)23/29
C)23/32
D)23/35
E)23/29
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer: D
Answer: D
Question: If Hema walks at 12 km/hr instead of 8 km/hr, she would have walked 20 km more. The actual distance travelled by Hema is ?
Options:
A)40 kms
B)30 kms
C)46 kms
D)32 kms
E)36 kms
Rationale: Explanation:
Let the actual distance travelled be x km.
Then x/8=(x+20)/12
=> 12x = 8x + 160
=> 4x = 160
=> x = 40 km.
ANSWER IS A
Answer: A
Question: The speed of a car is 95 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
A)76 kmph
B)75 kmph
C)77.5 kmph
D)56 kmph
E)86 kmph
Rationale: S = (95 + 60)/2
= 77.5 kmph
Answer: C
Answer: C
Question: How many times digit 6 is used while writing numbers from 100 to 1400?
Options:
A)648
B)350
C)252
D)225
E)26
Rationale: There are 100 numbers which begin with 600
Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 6 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000
1000 - 100 = 900/10 = 90
Number of 10s interval in this is 90. So 90 '6s'
So far we have calculated 190.
The total now comes to 280. The nearest to which is 350. Hence B.
Answer: B
Question: __2A
x__B
____
CC
In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 6, what is the value of C?
Options:
A)8
B)5
C)4
D)3
E)2
Rationale: If A+B=6
assuming A and B are positive then A*B<10 (they could be either 1,2,3,4,5)
therefore
A*B=C
2*B=C
A+B=6
Three simple equations - divide the 1st/2nd --> A=2 plug it the 3rd --> B=4 --> C=8 (ANSWER A)
Answer: A
Question: If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days?
Options:
A)186
B)188
C)810
D)167
E)861
Rationale: 12 men 120 acres 36 days
54 men ? 54 days
120 * 54/12 * 54/36
10 * 54 * 3/2
54 * 15 = 810
Answer: C
Answer: C