divelab/Sys2Bench huggingface dataset:
Question: An article was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was Rs. 6 less than the discount offered on it, find its selling price?
Options:
A)Rs. 72
B)Rs. 90
C)Rs. 66
D)Rs. 96
E)None of these
Rationale: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
ANSWER:A
Answer: A
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)170
B)180
C)190
D)120
E)130
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: Option B
Answer: B
Question: The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 12 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
Options:
A)$223
B)$225
C)$224
D)$213
E)$215
Rationale: Final price = (1+12/100) * Original Price
= 1.12 * Original Price
From options given only 224 is divisible by 1.12 as it is stated OP is whole dollar amount.
Hence C
Answer: C
Question: If the sides of a square are multiplied by 10, the area of the original square is how many times as large as the area of the resultant square?
Options:
A)1%
B)10%
C)100%
D)500%
E)1000%
Rationale: Let x be the original length of one side.
Then the original area is x^2.
The new square has sides of length 10x, so the area is 100x^2.
The area of the original square is 1/100 = 1% times the area of the new square.
The answer is A.
Answer: A
Question: Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 9/49, what is the probability that the next one she draws will be pink?
Options:
A)1/49
B)4/7
C)3/7
D)16/49
E)40/49
Rationale: The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 9/49 = (3/7) * (3/7)
Therefore probability that the next one she draws is pink = 4/7
Option (B)
Answer: B
Question: In a race, the odds in favour of cars P, Q, R, S are 1 : 3, 1 : 4, 1 : 5 and 1 : 6 respectively. Find the probability that one of them wins the race.
Options:
A)9/17
B)114/121
C)319/420
D)27/111
E)37/111
Rationale: P(P) = 1/4, P(Q) = 1/5, P(R) = 1/6 and P(S) = 1/7.
All the events are mutually exclusive and hence,
the required probability:
= P(P) + P(Q) + P(R) + P(S)
= 1/4 + 1/5 + 1/6 + 1/7
= 319/420
ANSWER:C
Answer: C
Question: At a game of billiards, A can give B 15 points in 60 & A can give C 20 points in 60. How many points can B give C in a game of 90?
Options:
A)30 points
B)20 points
C)10 points
D)5 points
E)0 points
Rationale: 10 points
ANSWER:C
Answer: C
Question: A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 20 km, if the person completes half of the distance by walking and the other half by running?
Options:
A)2.75
B)3.25
C)3.75
D)4.25
E)4.75
Rationale: time = 10/4 + 10/8 = 30/8 = 3.75 hours
The answer is C.
Answer: C
Question: If a man's rate with the current is 15 km/hr and the rate of the current is 11⁄2 km/hr, then his rate against the current is
Options:
A)12 km/hr
B)22 km/hr
C)23 km/hr
D)28 km/hr
E)13 km/hr
Rationale: Speed downstream = 15 km/hr
Rate of the current= 11⁄2 km/hr
Speed in still water = 15 - 11⁄2 = 131⁄2 km/hr
Rate against the current = 131⁄2 km/hr - 11⁄2 = 12 km/hr
Answer is A
Answer: A
Question: What approximate value should come in place of the question mark (?) in the following equation?47.05 Ã— 8.65 â€“ 25.22 Ã— 6.4 = (28 + ?) Ã— 5
Options:
A)28.1149
B)24.1149
C)21.1149
D)22.1149
E)31.1149
Rationale: Solve using approximation
Answer C
Answer: C
Question: A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
Options:
A)10,700
B)10,800
C)10,900
D)11,000
E)11,100
Rationale: population that is 10% greater than the population of any other district..
11000.. 10% of 11000 = 1100.. so the next population will be 12100..
10*12,100 + 11000 = 132000. D
Answer: D
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.162. Find the unknown rate of two blankets?
Options:
A)420
B)550
C)490
D)570
E)457
Rationale: 10 * 162 = 1620
3 * 100 + 5 * 150 = 1050
1620 – 1050 = 570
Answer:D
Answer: D
Question: If the set S is composed of the following numbers {99, 100, 100, 105, 106, 116, 123}, which of the following is largest?
Options:
A)The average (arithmetic mean) of set S
B)The median of set S
C)The mode of set S
D)The range of set S
E)The standard deviation of set S
Rationale: Time consuming question...
A) 99, 100, 100, 105, 106, 116, 123 = 749 and its mean is 749/7 = 107.
B) The list is of 7 numbers and median is 105.
C) Mode is number of repetition of a number in the list , here it is 100.
D) Range = Max value - min value = 123 -99 = 24.
E) SD = square root of (sum of ( mean of series - number)^2 ) / n
=> sq root (64+49+49+4+1+676)/7
= sq rt ( 893/7)
= sq rt ( 127) < 100
Answer: option A is correct answer..
Answer: A
Question: On thrusday mabel handled 90 transactions. anthony handled 10 % more transaction than mabel, cal handled 2/3rds of the transactions that anthony handled and jade handled 16 more transaction than cal. how much transaction did jade handled?
Options:
A)92
B)80
C)72
D)82
E)28
Rationale: Mabel handled 90 transaction, anthony 10 % more transaction the mabel. anthony = 90+90 * 10%, = 90 + 90 * 0.10 , = 90 + 9, =99, cal handled 2/3rds than anthony handled, cal = 2/3 * 99=66, jade handled 16 more than cal. jade = 66 + 16= 82, jade handled = 82 tranasactions.
correct answer: (D)
Answer: D
Question: Which of the following statements is equivalent to 8+2X<18−6X<23+2X8+2X<18−6X<23+2X?
Options:
A)4/5 < X < 2.5.
B)4/5 < X < 8/5.
C)-5/8 < X < 5/4.
D)2.5 < X < 3.5.
E)5 < 8X < 12.
Rationale: 8+2X<18−6X<23+2X
8<18-8x<23 (add -2x on all sides)
-10<-8x<5
10>8x>-5 (multiply by -1 on all sides)
5/4>x>-5/8
C is the answer
Answer: C
Question: Two numbers are in ratio 4:5 and their LCM is 180. The smaller number is
Options:
A)9
B)15
C)36
D)45
E)None
Rationale: Solution: Let two numbers be 4x and 5x;
their LCM = 180 and HCF = x; Now,
1st number * 2nd number = LCM*HCF
Or, 4x*5x = 180*x;
Or, 20x = 180;
Or, x = 9;
then, the smaller number = 4*9 = 36.
Answer: Option C
Answer: C
Question: A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges he had originally?
Options:
A)700
B)300
C)200
D)500
E)250
Rationale: sell 40% oranges and 420 oranges remaining
=>60% of oranges = 420
total oranges * 60/100 = 420
total oranges = 420*100/60 = 700
ANSWER A
Answer: A
Question: A can do a piece of work in 4 hours. B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
Options:
A)10 hr
B)12 hr
C)15 hr
D)13 hr
E)9 hr
Rationale: A's 1 hour work = 1/4
B+C 1 hour work = 1/3
A+C 1 hour work = 1/2
A+B+C 1 hour work = 1/4 + 1/3 = 7/12
B's 1 hour work = 7/12 - 1/2 = 1/12
B alone will take 12 hours to do the work
Answer is B
Answer: B
Question: x+(1/x) = 2 find x^2 + (1/x^2)
Options:
A)2
B)3.25
C)4.25
D)5.25
E)6.25
Rationale: squaring on both sides (x+1/x)^2=2^2
x^2+1/X^2=4-2
x^2+1/X^2=2
ANSWER:A
Answer: A
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 70/kg. how much did a kg of coffee cost in june ?
Options:
A)70
B)60
C)80
D)100
E)120
Rationale: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (700gm) of tea and 1/2 kg (700gm) of coffee (equal quantities) = 70
1.2x(1/2) + 0.8x(1/2) = 70
=> x =70
Thus proved...option A.
Answer: A
Question: A man's age is 125% of what it was 10 years ago, but 83 1/3%
of what it will be after 10 years. What is his present age?
Options:
A)50
B)70
C)80
D)55
E)40
Rationale: 125x/100 = x + 10
x = 40
present age = x + 10 =40+10 = 50
ANSWER A
Answer: A
Question: A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 80 inches. Find b.
Options:
A)8
B)16
C)24
D)32
E)48
Rationale: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.
From the second premise, we know that the LCM of 12 (2^2*3) andbis 80 (2^4*5), sob=2^4 or 2^4*5 (16 or 80).
Combining 2 premises shows the answer is B(16).
Answer: B
Question: For an upcoming charity event, a male vocalist has agreed to sing 3 out of 8 “old songs” and 4 out of 7 “new songs.” How many ways can the singer make his selection?
Options:
A)25
B)50
C)150
D)147
E)600
Rationale: =8C6*7C4
=8*7/4*7*6/4
=7*7*3
=147
Ans = D
Answer: D
Question: Kim bought a total of $4.65 worth of postage stamps in four denominations. If she bought an equal number of 10-cent and 25-cent stamps and twice as many 20-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought?
Options:
A)5
B)10
C)75
D)90
E)95
Rationale: Let:
# of 10 and 25 cents stamps = n
# of 20 cent stamps = 2n
# of 1 cent stamps = m
Therefore:
10n + 25n + 20(2n) + m = 465 cents
75n + m = 465
Forleastnumber of 1 cents stamps, maximize 50n. Hence,
75*5 + m = 465
m = 90 i.e. 90 stamps 1 cents each
Answer: D
Answer: D
Question: The average earning of a person for the first four days of a week is Rs 18 and for the last four days is Rs 22. If he earns Rs 20 on the fourth day, his average earning for the whole week is?
Options:
A)Rs 18.95
B)Rs 16
C)Rs 20
D)Rs 25.71
E)None of these
Rationale: Total earning for the week
= Rs (4 × 18 + 4 × 22 - 20) = Rs 140
Average earning = Rs 140/7 = Rs 20.
ANSWER:C
Answer: C
Question: For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.25 – 6.25*?
Options:
A)1.5
B)0.5
C)6.25
D)0.25
E)6.0
Rationale: Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.25* =6 (the greatest positive even integer less than or equal to 6.25 is 6).
Hence, 6.25 – 6.25* = 6.25 - 6 = 0.25
Answer: D.
Answer: D
Question: How many consonants are present between the first and fourth vowel in the sequence of English alphabet ?
Options:
A)12
B)13
C)11
D)10
E)None of these
Rationale: Explanation:
Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The first and fourth vowels are A and O respectively. There are 13 letters between A and O; out of which 'E' and 'I' are vowels. Thus, there are 11 consonants between A and O.
ANSWER C
Answer: C
Question: How many 9's are there between 1 and 100?
Options:
A)10
B)20
C)22
D)18
E)27
Rationale: B
20
Answer: B
Question: A, B and C started a partnership business by investing Rs.8000, Rs.4000, Rs.2000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?
Options:
A)70000
B)60000
C)80000
D)90000
E)252000
Rationale: A:B:C =8000:4000:2000
=4:2:1
Let total profit =p
Then pÃ—1/7=36000
p=(36000Ã—7)/1=252000
Answer is E.
Answer: E
Question: P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 336 is divided among them . What is Q's share?
Options:
A)114
B)128
C)134
D)144
E)None of these
Rationale: Explanation :
The ratio of their initial investment = 1/2 : 1/3 : 1/4
= 6 : 4: 3
Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively
A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12
= (12+30) : 4*12 : 3*12
=(4+10) : 4*4 : 12
= 14 : 16 : 12
= 7 : 8 : 6
Q's share = 336 * (8/21) = 128. Answer : Option B
Answer: B
Question: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $57000 and Ingrid makes $72000, what is their combined tax rate?
Options:
A)32%
B)34.4%
C)35%
D)35.6%
E)36.4%
Rationale: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.
(2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.
(3) Get 72000/129000 = 24/43. 24/43 is a little above 24/48 = 1/2. Thus, our answer is just a little above 35.
Answer: D
Answer: D
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
Options:
A)12 hours
B)24 hours
C)36 hours
D)48 hours
E)None
Rationale: Sol.
Speed upstream = 7.5 kmph; Speed downstream = 10.5 kmph.
∴ total time taken = [105/7.5 + 105/10.5] hours = 24 hours.
Answer B
Answer: B
Question: The parameter of a square is equal to the perimeter of a rectangle of length 14 cm and breadth 10 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
Options:
A)23.56
B)23.59
C)23.55
D)18.86
E)23.57
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(14 + 10) = 48 cm Parameter of the square = 48 cm
i.e. 4a = 48
A = 12
Diameter of the semicircle = 12cm
Circimference of the semicircle
= 1/2(âˆ)(12)
= 1/2(22/7)(12) = 264/14 = 18.86 cm to two decimal places
Answer: D
Answer: D
Question: In a lottery, there are 10 prizes and 25 blanks . A lottery is drawn at random .What is the probability of getting a prize?
Options:
A)1/10
B)2/5
C)2/7
D)5/7
E)10/7
Rationale: Total number of prizes and blanks= 10+25= 35
no.of prize in a lottery= 10
probability of one lottery is drawn = 10/35= 2/7
Answer is C
Answer: C
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
Options:
A)90
B)99
C)77
D)66
E)221
Rationale: 200*2 = 400
580
-----
180
1----2
?----180 = 90
Answer:C
Answer: C
Question: Find the average of all the numbers between 6 and 34 which are divisible by 5?
Options:
A)10
B)20
C)25
D)30
E)15
Rationale: Average = (10+15+20+25+30) 5 = 100/5 = 20
Answer is B
Answer: B
Question: Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction K of the work will be done by Adam?
Options:
A) 1/4
B) 12/47
C) 1/3
D) 5/12
E) 20/47
Rationale: Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.
adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work
K>( 60/47 *12)/60 =12/47
Answer B
Answer: B
Question: A, B and C can independently complete a piece of work in 8,12 and 6 days respectively. A and B work together for 4 days and leave. How long will C take to finish the remaining work?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: A and B work together for 4 days and completed 4*(1/8 +1/12) =5/6 work.
Balance 1/6 work will be completed by C in one day.
ANSWER:A
Answer: A
Question: z is a positive integer and multiple of 2; w = 4^z, what is the remainder when w is divided by 10?
Options:
A)10
B)6
C)4
D)0
E)It Cannot Be Determined
Rationale: It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:
4/10 is 0 with a remainder of 4
14/10 is 1 with a remainder of 4
5/10 is 0 with a remainder of 5
105/10 is 10 with a remainder of 5
It is also essential to remember that the z is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, z must be a positive even integer.
With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?
The units digit of 4 raised to an integer follows a specific repeating pattern:
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^(odd number) --> units digit of 4
4^(even number) --> units digit of 6
There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.
Since z must be an even integer, the units digit of w=4^z will always be 6. Consequently, the remainder when w=4^z is divided by 10 will always be 6.
In case this is too theoretical, consider the following examples:
z=2 --> w=4^z=16 --> w/10 = 1 with a remainder of 6
z=4 --> w=4^z=256 -->w/10 = 25 with a remainder of 6
z=6 --> w=4^z=4096 --> w/10 = 409 with a remainder of 6
z=8 --> w=4^z=65536 --> w/10 = 6553 with a remainder of 6
Answer: B.
Answer: B
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 370 m long platform?
Options:
A)37 min
B)55 min
C)47 min
D)67 min
E)49 min
Rationale: E
49 min
Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +370)/ 36 * 5/18 = 49 min.
Answer: E
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 12 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
Options:
A)96%
B)105%
C)120%
D)124.2%
E)138%
Rationale: x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,12 = 12/100
x= 80*12/100
x= 9.6
9.6/10 = 0.96 = 96%, Answer A
Answer: A
Question: Which of the following fractions is the largest?
Options:
A)7/8
B)7/7
C)7/2
D)7/5
E)7/6
Rationale: L.C.M of 8, 16, 40 and 80 = 80.
7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80
Since, 70/80 > 63/80 > 65/80 > 62/80,
So, 7/8 > 63/80 > 13/16 > 31/40
So, 7/8 is the largest.
Answer: A
Answer: A
Question: The value of ((x – y)³ + (y - z)³ + (z – x)³)/(15 (x – y) (y – z) (z – x))
is equal to :
Options:
A)0
B)1/12
C)1
D)1/5
E)1/3
Rationale: Since (x – y) + (y – z) + (z – x) = 0,
so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).
(3 (x – y) (y – z) (z – x))/(15(x – y) (y – z) (z – x)) = 1/5.
ANSWER:D
Answer: D
Question: A crate of apples contains 1 bruised apple for every 20 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
Options:
A)270
B)360
C)480
D)600
E)320
Rationale: as given 3 out of every 4 bruised apple is not fit to sell
or, 75% of the bruised apples are not fit to sell.
as per the question 12 are not fit to sell
or,
0.75x=12
x=1200/75=16
thus total number of bruised apples =16
total number of apples =20*16=320
Answer: E
Answer: E
Question: If x = y+3+4.5x and y = x+33, what is the value of x/y ?
Options:
A)-6/5.
B)-8/25
C)1/4.
D)5/6.
E)1.5.
Rationale: (1) x = y + 3 + 4.5x
Substitute y for y = x + 33 (Eq. we are given)
x = x + 33 + 3 + 4.5x
Combine like terms
x = 5.5x +36 --> -4.5x = 36 --> x = -8
(2) y = x + 18
Substitute x for x = -8
y = (-8) + 33 = 25
(3) x/y = ?
Substitute x and y we found above
x/y = (-8) / (25) =-8/25
My answer: B
Answer: B
Question: Working alone at its constant rate, machine K took 3 hours to produce 1/6 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
Options:
A)8
B)12
C)16
D)24
E)30
Rationale: Machine K works at a rate of 1/18 of the units per hour.
The rate of K + M together is 5/6 * 1/6 = 5/36 of the units per hour.
The rate of machine M is 5/36 - 1/18 = 1/12.
It would have taken machine M a total time of 12 hours.
The answer is B.
Answer: B
Question: If y ≠ 3 and 2b/y is a prime integer greater than 2, which of the following must be true?
I. b = y
II. y = 1
III. b and y are prime integers.
Options:
A) None
B) I only
C) II only
D) III only
E) I and II
Rationale: Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So we should try to make the listed statements not true for some b and y (which satisfy y≠3 and 2b/y=prime>2).
I. b = y --> not necessarily true: b=3 and y=2 (2b/y=3=prime>2);
II. y=1 --> not necessarily true: b=3 and y=2 (2b/y=3=prime>2);
III. b and y are prime integers --> not necessarily true: b=10 and y=4 (2b/y=5=prime>2).
Answer: A.
Answer: A
Question: Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 72th number in this set?
Options:
A) 573
B) 608
C) 613
D) 616
E) 621
Rationale: The set S = {5, 13, 21, 29, ..................... }
1st Number = 8 * 0 + 5 = 5
2nd Number = 8 * 1 + 5 = 13
3rd Number = 8 * 2 + 5 = 21
72th Number = 8 * (72-1) + 5 = 573
Answer = A
Answer: A
Question: what is the compound interest on rs:80,000 for 4 months at the rate of 5% per annum
Options:
A)1341.69
B)1342.69
C)1343.69
D)1344.69
E)1345.69
Rationale: it is monthly compound
rate=5/12% per month
80000*(1+5/1200)^4-80000=1341.69
ANSWER:A
Answer: A
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)m
B)m
C)m
D)m
E)m
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X
= 245 m.
Answer:C
Answer: C
Question: What is the least number that should be added to 1077, so the sum of the number is divisible by 23?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: (1077 / 23) gives a remainder 19 so we need to add 4.
The answer is D.
Answer: D
Question: Tough and Tricky questions: Number Properties.
What is the smallest positive integer x such that 500x is the cube of a positive integer?
Options:
A)2
B)3
C)5
D)10
E)15
Rationale: We want to know the smallest x that will make 500x a CUBE of some number. Let's call that number y.
Let's first figure out what we're working with. The prime factorization of 500 can be visualized:
...........500
......../.......\
......50.......10
...../..\....../...\
...25...2...2.....5
.../..\
..5....5
So, we have 5 * 5 * 5 * 2 * 2 that can be multiplied together to get 500. Now we need to figure out what we need to make 450 * x into a cube of y (y^3=500*x).
We have two 5s, two 3s, and one 2. To arrange these numbers in identical sets (2,5), we need at least one more 2. Each of these numbers will give us the value of y (2*5=10), which, multiplied by itself three times, gives us 500 * x.
Looking at the factors we need to complete the sets, we get x= 2. We know this is the smallest number possible because prime factors by definition cannot be broken down any further.
Therefore, we can go with answer choice A.
If time permits, we can do a sanity check. We calculated that y should be 2 * 5, or 10. 10 * 10 * 10 = 1000. Also, 500 * 2 = 1000.
Answer: A