divelab/Sys2Bench huggingface dataset:
Question: If the number 42573 * is exactly divisible by 72, then the minimum value of * is:
Options:
A)4
B)5
C)2
D)6
E)1
Rationale: .
If the number 42573 * is exactly divisible by 72, then the minimum value of * is:
A.	4
B.	5
C.	6
D.	7
E.	8
Answer: Option C
Explanation:
72 = 9 x8, where 9 and 8 are co-prime.
The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.
Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.
Required value of * is 6.
ANSWER D
Answer: D
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)266
B)288
C)245
D)776
E)232
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: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
Options:
A)28%
B)25%
C)95%
D)05%
E)22%
Rationale: 800 --- 200
100 --- ? => 25%
Answer:B
Answer: B
Question: How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 6 cannot appear more than once in the number.
Options:
A)2300
B)2385
C)2380
D)2375
E)2390
Rationale: N=(4*5-1)*5*5*5=2375
where
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
1 case of 66 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
5 cases of fourth digit {1,3,5,7,9}
5 cases of fifth digit {1,3,5,7,9}
D
Answer: D
Question: Fresh grapes contain 75% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 25 kgs of raisins?
Options:
A)75 kgs
B)64kgs
C)72 kgs
D)65 kgs
E)70 kgs
Rationale: The weight of non-water in 20 kg of dried grapes (which is 100-25=75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-75=25% of whole weight),
so 25*0.75 = x*0.25
--> x = 75.
Answer: A.
Answer: A
Question: The average salary of all the employees in a small company is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of employees in the company is:
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: Explanation :
Let the total number of employees be x. then,
8000x = (12000 x 7) + 6000 (x 7)
2000x = 42000
x = 21.
Answer : B
Answer: B
Question: Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (2)?
Options:
A)5
B)11
C)12
D)25
E)55
Rationale: (21)(3^7) is divisible by 3 but 2 is not divisible by 3.
Therefore (21)(3^7) - 2 is not divisible by 3 and thus not divisible by 12.
The answer is C.
Answer: C
Question: If Jake loses 8 pounds, he will weigh half as much as his sister. Together they now weigh 278 pounds. What is Jake's present weight, in pounds?
Options:
A) 131
B) 135
C) 188
D) 147
E) 188
Rationale: J = Jake’s current weight, in pounds
S = Sister’s current weight, in pounds
We are told that “If Jake loses 8 pounds, he will weigh twice as much as his sister.We put this into an equation:
J – 8 = S/2
J = S/ + 8 (Equation 1)
Next, we are told that “Together they now weigh 278 pounds.” We can also put this into an equation.
J + S = 278 (Equation 2)
To solve this equation, we can substitute 2S + 8 from Equation 1 for the variable J in Equation 2:
S/2 + 8 = 278-S
3S = 540
S = 90
J + 90 = 278
J = 188
Answer: C
Answer: C
Question: Club X has more than 70 but fewer than 100 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
Options:
A)1.
B)2.
C)3.
D)4.
E)5.
Rationale: The number of members is 4j+3 = 5k+3.
Let's start at 4(17)+3 = 71 and keep adding 4 until we find a number in the form 5k+3.
71, 75, 79, 83 = 5(16) + 3
The club has 83 members.
83/6 = 6(13) + 5
The answer is E.
Answer: E
Question: If f(x) = 2x^2 + y, and f(2) = 60, what is the value of f(5)?
Options:
A)104
B)60
C)52
D)50
E)102
Rationale: f(x) = 2x^2 + y
f(2) = 60
=> 2*(2)^2 + y = 60
=> 8 + y = 60
=> y = 52
f(5)= 2*(5)^2 + 52
= 102
Answer E
Answer: E
Question: If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x?
Options:
A)10,573
B)11,908
C)12,322
D)13,924
E)14,537
Rationale: The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.
The answer is D.
Answer: D
Question: A man purchased a grinder for Rs. 660 and sold it at a profit of 10%. The selling price is:
Options:
A)Rs. 736
B)Rs. 812
C)Rs. 660
D)None of these
E)Cannot be determined
Rationale: s.p.=110/100 × 600 = 660
Answer: C
Answer: C
Question: Of the 5 distinguishable wires that lead into an apartment, 3 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Given:
Total number of wires = 5
Number of cable wires = 2
Number of telephone wires = 3
To find:
Number of combination which has at least one cable wires
Solution:
No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2
Since it is a combination of wires, the arrangement is not important
Approach 1:
Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire)
Selection 1
Number of ways of selecting one cable wire = 2C1 = 2
Number of ways of selecting 2 telephone wires = 3C2 = 3
Total = 2C1 * 3C2 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 2
Number of ways of selecting one cable wire = 2C2 = 1
Number of ways of selecting 2 telephone wires = 3C1 = 3
Total = 2C2 * 3C1 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire
Approach 2
Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires)
Total number of ways of selecting 3 wires out of 5 = 5C2 = 10
Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 3C3 ( 3 telephone wires and we are selecting all the three at once) = 1
Selection X - Selection Y = 7
Answer is Option B
Answer: B
Question: If a fair 6-sided die is rolled three times, what is the probability that exactly one 1 is rolled?
Options:
A)25/216
B)50/216
C)25/72
D)25/36
E)5/6
Rationale: Total ways in which a 6-sided die can be rolled three times = 6*6*6 = 216
To get exactly one 1, there are three ways:
A 1 on the first roll and non 1 on other two rolls. This can be done in 1*5*5 = 25 ways.
The 1 could be on the second or third roll too. So total favorable cases = 25*3 = 75
Required Probability = 75/216 = 25/72
Answer (C)
Answer: C
Question: Jane spent $42 for shoes. This was $14 less than twice what she spent for a blouse. How much was the blouse?
Options:
A)10
B)25
C)14
D)16
E)28
Rationale: Every word problem has an unknown number. In this problem, it is the price of the blouse. Always let x represent the unknown number. That is, let x answer the question.
Let x, then, be how much she spent for the blouse. The problem states that "This" -- that is, $42 -- was $14 less than two times x.
Here is the equation:
2x − 14= 42.
2x= 42 + 14
= 56
x= 56/2
=28.
Ans is E
Answer: E
Question: Molly can do a task in 18 days while Sandy can do the task in 12 days. How many days will it take to complete the task if both work together?
Options:
A)6.2
B)6.6
C)7.2
D)7.8
E)8.4
Rationale: Each day, Molly can do 1/18 of the task.
Each day, Sandy can do 1/12 of the task.
Each day, they can do 1/18 + 1/12 = 5/36 of the task.
The task will be completed in 36/5 = 7.2 days.
The answer is D.
Answer: D
Question: There are 9 people and 9 chairs. In how many different ways people can occupy the chairs?
Options:
A)362880
B)340009
C)250909
D)345008
E)1000
Rationale: number of ways =9! = 362880
Answer is A
Answer: A
Question: Two pipes A and B can fill a cistern in 10 and 15 minutes respectively. Both fill pipes are opened together,but at the end of 3 minutes, ‘B’ is turned off. How much time will the cistern take to fill ?
Options:
A)6 min
B)8 min
C)10 min
D)12 min
E)None of these
Rationale: In one min, (A + B) fill the cistern = 1⁄10 + 1⁄15 = 1⁄6th
In 3 min, (A + B) fill the cistern = 3⁄6 = 1⁄2th
Remaining part = 1 - 1⁄2 = 1⁄2
∵ 1⁄10th part filled by A in one min.
∴ 1⁄2nd part filled by A in 10 × 1⁄2 = 5 min.
∴ Total time = 3 + 5 = 8 min.
Answer B
Answer: B
Question: The average of 26,29,n,35 and 43 lies between 25 and 35. If n is always an integer and greater than the average of the given integers then the value of n is :
Options:
A)36
B)29
C)33
D)28
E)21
Rationale: Explanation:
Average of 26,29,35 and 43 is 33.25 . Also the average of 26 , 29, n, 35 and 43 lies between 25 and 35 i.e,
Rightarrow 125 < 26+29+n+35+43 < 175
Rightarrow 125 < 133 + n < 175
Rightarrow n < 42
Since the value of n is an integer and greater than 33.25 then 33 < n < 42 for every integer n.
Answer: C
Answer: C
Question: For every $20 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $6 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
Options:
A)1 : 4 : 400
B)1 : 4 : 100
C)20 : 4 : 1
D)100 : 4 : 1
E)400 : 4 : 1
Rationale: millionaire 20 cents = 1/5 dollar ..therefore 1 dollar M = 100 dollar of B
therefore 6 dollar M = 600 dollar of B also 1 dollar Y
Y:M:B = 1:6:600
= 1:6:600
B
Answer: B
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
Options:
A)Rs.6152
B)Rs.6159
C)Rs.6156
D)Rs.6150
E)Rs.6196
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs.6150.
Answer: D
Answer: D
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1: 96
B)1: 97
C)1: 98
D)1: 99
E)1: 92
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer: Option A
Answer: A
Question: Given that 268x74= 19732, find the value of 2.68x.74.
Options:
A)1.9732
B)1.0025
C)1.5693
D)1.0266
E)None
Rationale: Solution
Sum of decimals places	=(2+2)
= 4.
Therefore,	= 2.68×.74
= 1.9732
Answer A
Answer: A
Question: A man can row his boat with the stream at 12 km/h and against the stream in 8 km/h. The man's rate is?
Options:
A)2 kmph
B)6 kmph
C)7 kmph
D)4 kmph
E)9 kmph
Rationale: Explanation:
DS = 12
US = 8
S = ?
S = (12- 8)/2 =2 kmph
Answer: A
Answer: A
Question: A and B enter into a partnership. A contributed Rs.5000 for 8 months and B Rs.6000 for 5 months. Find A's share in a total profit of rs.8400.
Options:
A)Rs. 4800
B)Rs. 2400
C)Rs. 3600
D)Rs. 5600
E)None of these
Rationale: Explanation:
Ratio of capitals of A and B
= Ratio of their investments
= 5000 × 8 : 6000 × 5
= 40000 : 30000 = 4 : 3
.: A's share = Rs. [(4/7) × 8400] = Rs. 4800
Answer: Option A
Answer: A
Question: On a ferry, there are 22 cars and 10 trucks. The cars have an average mass of 1200 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 32 vehicles on the ferry?
Options:
A)1686.5
B)1762.5
C)1824.5
D)1878.5
E)1906.5
Rationale: The total mass of the vehicles is 22*1200+10*3000=56400
The average mass is 56400/32=1762.5
The answer is B.
Answer: B
Question: factor: 3y (x-3)-2(x-3)
Options:
A)(x-3)-2(x-3)
B)(x-3)power2
C)(x-3)(3y-2)
D)3y(x-3)
E)x-3
Rationale: 3y(x-3)-2(x-3), = (x-3)(3y-2). Answer: (C)
Answer: C
Question: fill in the blank space.
1, 9, 25, 49, 81, ?
Options:
A)100
B)121
C)144
D)169
E)172
Rationale: The series consists of squares of consecutive prime numbers.
Answer : B.
Answer: B
Question: The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 3, what is the value of H?
Options:
A)2
B)3
C)5
D)4
E)9
Rationale: Integer is divisible by 3 - Sum of digits is divisible by 3
Answer: D
Answer: D
Question: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and if the repetition is allowed?
Options:
A)20
B)5
C)10
D)36
E)25
Rationale: Since, each desired number is divisible by 5, so we must have 5 at the unit place.
So , the tens place can now be filled by any of the remaining 6 digits (2, 3, 6, 7, 9, 5)
therefore the 3-digit no can be formed by (6 * 6 * 1) = 36 ways ------(since repetition is allowed)
Ans- D
Answer: D
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options:
A)70 min
B)16 min
C)20 min
D)10 min
E)40 min
Rationale: D
10 min
Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9/54 x 60) min = 10 min
Answer: D
Question: If ‘POOJA’ is coded as ‘SRRMD’, then ‘PRIYA’ is coded as
Options:
A)THGFE
B)GVFED
C)FREDCV
D)SULBD
E)SUUNF
Rationale: P= 16 = 16+3 = 19 = S
O = 15 =15+3 =18 = R
SIMILARLY,
P = 16 = 16+3 = 19 = S
R = 18 = 18+3 = 21 = U
I = 9 = 9+3 = 12 = L
Y = 25 = 25 +3 = 28 = B
A = 1 = 1+3 = 4 = D
SO ANS IS
SULBD
Answer: D
Question: In the sea there are 3 fishers in a boat and they take 4 hours to complete one third of a fish container. They went to rest and were supplanted by 8 fishers. If they continue to fish at the same rate, how many hours will take to all of the fishers complete all the container?
Options:
A) 16 hours
B) 12 hours
C) 8 hours
D) 7 hours
E) 5 hours
Rationale: We have that: 3 fishers ----- 4 hours, 8F ----- xhr, that is: (Xhr/ 3F) = (4hr/8F), then: Xhr = (4hr/8F)3F = (3/2)hr. Is to say, they did the same work in 3/2 hours; it is only one third of the container. Then, all the container is: C = C1 + C2 + C3 = 4 hr + (3/2) hr + (3/2) hr = (4 + 3) hr = 7 hr. Answer D.
Answer: D
Question: By using the numbers 0, 1, 3, 5 and 6 only once, how many five digit numbers can be made that are divisible by 15?
Options:
A)12
B)18
C)24
D)36
E)42
Rationale: A number to be divisible by 15 must end with 15, 30, 45,60,75 or 70.
So, there are the following cases possible:
035-15 --> the first three digits can be arranged in 3=6 ways.
156-30 --> the first three digits can be arranged in 3=6 ways.
135-60 --> the first three digits can be arranged in 3=6 ways.
Total = 6+6+6= 18.
Answer:B.
Answer: B
Question: How many three digit numbers E are divisible by 78 or 91?
Options:
A)17
B)19
C)20
D)21
E)22
Rationale: The answer will be 19.
Explanation:
78= 2*3*13 now multiples of 78, 156 ....780, now 1000-780 = 220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are 9+2=11
91= 13*7--Total number of three digit multiples --9
No remember we have a common multiples as well-- 13*7*6=91*6=546
So total number of multiples E--11+9 -1 =19.
Hence Answer is 19.B
Answer: B
Question: Nine people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?
Options:
A)1 / 9
B)1 / 8
C)1 / 7
D)7 / 8
E)8 / 7
Rationale: Let P = total cost of the rental van.
The original share per person is P/9.
The new share per person is P/8.
P/8 = P/9 * 9/8 = (1 + 1/8)*original share
The answer is B.
Answer: B
Question: The G.C.D of 1.08, 0.36 and 0.9 is
Options:
A)0.03
B)0.9
C)0.18
D)0.108
E)None
Rationale: Solution
Given numbers are 1.08 , 0.36 and 0.90.
H.C.F of 108 ,36 and 90 is 18.
‹=› H.C.F of given numbers = 0.18.
Answer C
Answer: C
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)65
B)86
C)30
D)78
E)38
Rationale: US = 25
DS = 35
M = (35 + 25)/2
= 30
Answer: C
Answer: C
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 25%?
Options:
A)600
B)887
C)625
D)654
E)712
Rationale: Cost price = Rs.500
profit = 25% of 500 = Rs.125
Selling price = Cost price + Profit
= 500 + 125 = 625
Answer: C
Answer: C
Question: Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.
Options:
A)Rs 400
B)Rs 300
C)Rs 3109
D)Rs 250
E)Rs 400
Rationale: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+¬(15/100))2 X (1+((1/3)*15)/100)]
=Rs. [8000 * (23/20) * (23/20) * (21/20)]
= Rs. 11109.	.
:. C.I. = Rs. (11109 - 8000) = Rs. 3109.
ANSWER C Rs 3109
Answer: C
Question: How many ways could two people sit at a table with four seats in which two of the four seats will remain empty?
Options:
A)60
B)12
C)112
D)118
E)120
Rationale: ways in which 2 seats out 4 can be selected = 4C2
ways in which 2 people can be arranged in 2 seats = 2!
Total ways of arrangement = 4C2*2!
=4*3
=12
Ans = B
Answer: B
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Options:
A)21 (1/9)
B)21 (1/3)
C)21 (1/2)
D)21 (5/3)
E)21 (1/6)
Rationale: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph.'
Answer: B
Answer: B
Question: A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price
Options:
A)Rs.500/-
B)Rs.510/-
C)Rs.515/-
D)Rs.530/-
E)Rs.540/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
90 % ------> 540 (90 * 6 = 540)
Selling price = Rs.540/-
E
Answer: E
Question: Real-estate salesman Z is selling a house at a 25 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 5 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 30 percent discount. Salesman Y's final price is what fraction of salesman X's final price?
Options:
A)21/34
B)55/71
C)25/34
D)26/34
E)27/34
Rationale: Let the retail price be = x
Selling price of Z = 0.75x
Selling price of X = 0.95*0.75x = 0.71x
Selling price of Y = ((0.75x + 0.71x)/2)*0.70 = 0.73x * 0.75 = 0.55x
0.55x = k * 0.71x
k = 0.55/0.71 = 55/71
Answer: B
Answer: B
Question: Combine terms: 12a + 26b -4b – 16a.
Options:
A)4a + 22b
B)-28a + 30b
C)-4a + 22b
D)28a + 30b
E)5a + 30b
Rationale: Solution:
12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22b.
Answer: (C)
Answer: C
Question: An eccentric casino owner decides that his casino should only use chips in $5 and $8 denominations. Which of the following amount cannot be paid out using these chips?
Options:
A)$34
B)$27
C)$31
D)$29
E)$24
Rationale: Yes, the number of 5 or/and 8 dollar chips can be zero, however both being zero mean that the casino is paying out $0, which is not realistic.
Each option but B can be represented as the sum of a multiple of 5 and a multiple of 8:
A. $34 = 8*3 + 5*2
B. $31 = 8*2 + 5*3
C. $29 = 8*3 + 5*1
E. $24 = 8*3
Answer: B.
Answer: B
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)6
B)5
C)4
D)3
E)2
Rationale: 40*(40/100)
= 16 --- 64
? --- 12
=> Rs.3
Answer: D
Answer: D
Question: Mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 80 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 2 hours, how long after he passed the gas station did Paul catch up with Mary?
Options:
A)35
B)15
C)20
D)25
E)30
Rationale: d = rt
M: r = 50mph, t = t + 1/4hr
d = 50 (t + 1/4)
P: r = 80, t = t
d = 80t
since they went the same distance:
50t + 50/4 = 80t
30t = 50/4 = 50/120 *60 =25 min
t = 25 min
D
Answer: D
Question: The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 900. What is the banker's discount?
Options:
A)1240
B)1120
C)1190
D)2150
E)None of these
Rationale: Explanation :
TD = (BG ×100)/TR = (900×100)/(6×12) = Rs. 1250
BG = BD – TD
=> 900 = BD - 1250
=> BD = 2150 Answer : Option D
Answer: D
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $40,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
Options:
A)$14,000
B)$11,200
C)$12,000
D)$12,800
E)$13,200
Rationale: 1 machine of type B will cost: 20% down payment of 40,000 = 8,000plusremaining sum (50,000-8,000=42,000) with 40% of finance charges 42,000*1.4=58,800 --> 8,000+58,800=66,800;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 66,800 - 52,800 = 14,000.
Answer: A.
Answer: A
Question: Running 3/4th of his usual rate, a man is 9min late. Find his usual time in hours ?
Options:
A)6/4 hrs
B)3/4 hrs
C)9/20 hrs
D)3/4 hrs
E)1/4 hrs
Rationale: Explanation:
Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time
so 1/3rd of the usual time = 9min
or usual time = 3 x 9 = 27min = 27/60 hrs = 9/20 hrs.
Answer: C
Answer: C
Question: A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 90 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
Options:
A)160
B)240
C)360
D)495
E)560
Rationale: The number of jumbo tiles = x.
The number of regular tiles = 2x.
Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.
The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.
The area of regular tiles = 2x*a^2 = 90.
The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*90 =405.
Total area = 90 + 405 = 495
Answer: D.
Answer: D
Question: A man bought some mangoes at Rs12 per dozen and bought the same number of at Rs 10 per kg. He sold these mangoes at Rs 13 per dozen and gained Rs 160.The total number of mangos bought by him are
Options:
A)40dozens
B)60dozens
C)70dozens
D)80dozens
E)90dozens
Rationale: let total no of mangoes is 2x..
then we profit=sp-cp
160=13*2x-(12x+10x)
160=4x
x=40
hence 2x=80
so total no are 80dozens
ANSWER:D
Answer: D