divelab/Sys2Bench huggingface dataset:
Question: If one root of the equation 2x^2 + 3x – k = 0 is 7, what is the value of k?
Options:
A)100
B)110
C)119
D)120
E)112
Rationale: We just enter this root into the equation in order to recieve an equation to find the answer!
2*7^2+3*7-k=0
k=98+21=119
The answer is C
Answer: C
Question: Two trains running in opposite directions cross a pole placed on the platform in 47 seconds and 31 seconds respectively. If they cross each other in 33 seconds, what is the ratio of their speeds?
Options:
A)1:7
B)8:7
C)6:7
D)6: 5
E)4:7
Rationale: Explanation:
Let the speed of the trains be x and y respectively
length of train1 = 47x
length of train2 = 31y
Relative speed= x + y
Time taken to cross each other = 33 s
=> = 33
=> (47x + 31 y) = 33(x + y)
=> 14x = 2y
=> x/y = 2/14 = 1/7
= 1:7
Answer: A
Answer: A
Question: If an object travels 400 feet in 4 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
Options:
A)68
B)54
C)87
D)96
E)15
Rationale: 1 mile = 5280 feet
=> 1 feet = 1/5280 miles
If the object travels 400 feet in 4 sec
then it travels 400/4 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)
= 3600 * 100 feet in 1 hour
= 360000 feet in 1 hr
= 360000/5280 miles in 1 hour
= 36000/528 miles/hr ~ 68 miles/hr
Answer - A
Answer: A
Question: How many meters of carpet 50cm, wide will be required to cover the floor of a room 30m * 20m?
Options:
A)3387
B)2888
C)2788
D)1200
E)2881
Rationale: 50/100 * x = 30 * 20 => x
= 1200
Answer: D
Answer: D
Question: In an organisation there are 1000 employees out of which 250 earn below 10k$ and 500 earn between 10k$ and 50k$. What is the total percentage of employees who earn less than 50k$?
Options:
A)66%
B)75%
C)70%
D)50%
E)82%
Rationale: total percentage = (250+500)/1000 = 0.75
B
Answer: B
Question: What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?
Options:
A)9
B)5
C)2
D)7
E)1
Rationale: Explanation:
6)4456(742
42
--------
25
24
-------
16
12
-----
4
------
Required number = (6-4) = 2.
Answer: C) 2
Answer: C
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs.529 is required to paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?
Options:
A)12
B)18
C)20
D)22
E)23
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 529/3 = 176.33 sq m
l b = 176.33 i.e., l * l/3 = 176.33
l^2 = 529 => l =23
E
Answer: E
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 500 m long?
Options:
A)266 Sec
B)170 Sec
C)776 Sec
D)166 Sec
E)997 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1700 m
T = D/S
T = 1700/10
T = 170 Sec
Answer: B
Answer: B
Question: The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits when the jacket is laid on a flat surface. The American size of a suit jacket is P inches, where P is twice the linear distance between the armpits when the jacket is laid on a flat surface. If, for a particular jacket, N = P + 16, which of the following is closest to the value of N? (One inch is approximately 2.54 centimeters.)
Options:
A)36
B)47
C)58
D)65
E)72
Rationale: Since one inch is approximately 2.54 centimeters, then N centimeters is N/2.54 inches.
Next, since the American size (P inches) is twice the Italian size (N/2.54 inches), then P=2*N/2.54.
As given that N = P + 16, then N=2*N/2.54+16 --> N=~72.
Answer: E.
Answer: E
Question: Find the average of first 100 natural numbers?
Options:
A)50.5
B)52
C)60.5
D)75
E)65
Rationale: Sum of first 100 natural numbers = 100*101/2 = 5050
Required average = 5050/100 = 50.5
Answer is A
Answer: A
Question: If r and s are positive integers and r-s=6, which of the following has the greatest value T?
Options:
A)2r
B)2s
C)r +s
D)2r-s
E)2s-r
Rationale: The simplest way to do this is to assume values.
We are told that r and s are positive integers T.
Also, r-s = 6 => r = 6+s
Hence r is 6 more than s.
Let s be 10. Hence r = 16.
Option A: 2r = 2*16 = 32
Option B: 2s = 2 * 10 = 20
Option C: r + s = 16 + 10 = 26
Option D: 2r - s = 2(16) - 10 = 32 - 10 = 22
Option E: 2s - r = 2(10) - 16 = 20 - 16 = 4
Hence option A is the greatest.
Answer: A
Question: Of the 16 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 16 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
Options:
A)22
B)35
C)56
D)110
E)105
Rationale: another approach :
one scenario : [WWWM]
now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.
and 11 ways to select one man
so 5*4*3*11 = 660
now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways
hence 660/3!= 660/6=110
D
Answer: D
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
Options:
A)288
B)277
C)209
D)992
E)612
Rationale: (800*3*3)/100 = 72
920 + 72 = 992
Answer: D
Answer: D
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit C on this shipment?
Options:
A)a) $100
B)b) $115
C)c) $125
D)d) $130
E)e) $135
Rationale: I recommend one should use fractions to solve this one rather than converting it into decimals
Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225
Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600
Profit C= 725-600 = $125
Ans:C
Answer: C
Question: At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Raja,Kamal, Baskar, and Divya get lockers with the numbers 350, 400, 150, and 420, respectively, who is the most popular student?
Options:
A)Divya
B)Kamal
C)Baskar
D)Raja
E)They have equal popularity
Rationale: Distinct prime factors of 350 (Raja) : 2,5,7
Distinct prime factors of 400 (Kamal): 2 and 5.
Distinct prime factors of 150 (Baskar): 2,3, and 5
Distinct prime factors of 420 (Divya): 2,3,5 and 7.
So most popular student - Divya
Answer A
Answer: A
Question: The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell shorof the required amount. What is the amount by which he might have fallen short?
Options:
A)40
B)45
C)54
D)65
E)70
Rationale: Let the price of gift pack be 'aa'
Then number of packs bought =a+1=a+1
Hence total cost is a(a+1)a(a+1)
It is given that 380<a(a+1)380<a(a+1)
If a=19a=19, the total cost =19×20=380=19×20=380
Dexter would not have fallen short, If:
a=20a=20, a(a+1)=420a(a+1)=420
So he would have fallen short by Rs 40.
This is the minimum amount by which he may have fallen short.
A
Answer: A
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)10.60 p.m
B)10.20 p.m
C)10.30 p.m
D)10.10 p.m
E)10.50 p.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: A bus leaves Santa Barbara at 6:00 a.m. traveling east at 50 miles per hour. At 2:00 p.m. a plane leaves Santa Barbara traveling east at 450 miles per hour. At what time will the plane overtake the bus?
Options:
A)2:45 p.m.
B)3:15 p.m.
C)3:30 p.m.
D)3:45 p.m.
E)3:00 p.m.
Rationale: At 2:00pm, the bus is 400 miles ahead of plane
The plane travels at 450 mph, which gains 400 mph on bus
400/400= 1 hour
2:00 + 1:00 = 3:00
The plane will overtake bus at 3:00pm
Answer:E
Answer: E
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit?
Options:
A)3089
B)3098
C)3057
D)3000
E)3012
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
Answer: D
Answer: D
Question: If two numbers are in the ratio 2:3. If 20 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Options:
A)A)10
B)B)20
C)C)25
D)D)30
E)E)40
Rationale: 2:3
2x + 20 : 3x + 20 = 3 : 4
4[2x + 20] = 3[3x + 20]
8x + 80 = 9x + 60
9x - 8x = 80 - 60
x = 20
Then smallest number is = 2
2x = 40
Correct Option E
Answer: E
Question: Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team Q, but each box of Team A’s has 60% fewer booklets than each box of Team Q’s. Which of the following could be the total number of booklets distributed by the two groups?
Options:
A)2,000
B)3,200
C)4,100
D)4,800
E)4,900
Rationale: Let x be the no of booklets in each box that team Q distributes. So, Team A has 60% fewer - 0.4x.
Let y be the no. of boxes distributed by team Q. So, Team A distributes 60% more - 1.6y
Total booklets distributed by team A = xy
Total booklets distributed by team Q=0.64xy
Total booklets distributed = xy+0.64xy=1.64xy
As no. of booklets can only be integer, plugging the answer choice equal to 1.64xy should give an integer.
Choice A - 1.64xy=2000; xy=2000/1.64 = doesn't provide an integer value.
Similarly all answer choices, except choice C, fail to provide an integer value.
Choice C = 4100/1.64= 2500 and is the correct answer.
Answer: C
Question: A is twice as good a work man as B and together they finish the work in 4 days. In how many days A alone can finish the work?
Options:
A)3
B)2
C)7
D)9
E)6
Rationale: WC = 2:1
2x + x = 1/4 => x = 1/12
2x = 1/6
A can do the work in 6 days.
Answer: E
Answer: E
Question: Set A consists of the integers from 1 to 12, inclusive, while set B consists of the integers from 5 to 15, inclusive. How many distinct integers do belong to the both sets at the same time?
Options:
A)8
B)10
C)12
D)15
E)9
Rationale: A = {1,2,3,4, 5,6, 7, 8, 9, 10, 11, 12}
B = {5,6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
Common elements = {5,6, 7, 8, 9, 10, 11, 12} = 8 elements
Answer: Option A.
Answer: A
Question: Kyle is a lumberjack with 12 trees to cut down. How many ways can he cut down one or more of the trees today?
Options:
A)255
B)4095
C)1023
D)8125
E)513
Rationale: Kyle can cut down one or more of 12 trees
=> 2 ^ 12 - 1 = 4095
B
Answer: B
Question: There are 9 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played?
Options:
A)24
B)25
C)28
D)32
E)36
Rationale: 9C2 = 36
The answer is E
Answer: E
Question: The quantity of water needed to reduce 9 ml shaving lotion containing 50% alcohol to a lotion containing 30% alcohol is?
Options:
A)6ml
B)10ml
C)5.5ml
D)8ml
E)9.3ml
Rationale: Quantity of alcohol in 9ml lotion = 50/100 *9 = 4.5ml
Let the water added be x ml
4.5 / 9+x = 30/100
x = 6ml
Answer is A
Answer: A
Question: What was the principal , if at 5% per annum the interest after 10 years amounted to Rs.3100 less than the sum lent?
Options:
A)6200
B)3000
C)3000
D)2000
E)1000
Rationale: P - 2336 = (P*10*5)/100
P = 6200
Answer: A
Answer: A
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1 kmph
B)7 kmph
C)8 kmph
D)9 kmph
E)6 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: A
Question: If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a30 is equal to ?
Options:
A)a. 5*2^99-6
B)b. 5*2^99+6
C)c. 6*2^29 - 5
D)d. 6*2^99-5
E)e. 6*2^99-6
Rationale: Here is my solution:
an+1=2an+5............(1)
lets ADD 5 to both sides....
so (an+1) + 5= 2 (an+5)....................taking 2 as common factor
now a1=1. so for n=1, an+5=6.......
putting n=1. we get both sides as,
a2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)
a2= 2 *6 - 5
a2= 2 * 2 *3 - 5
a2= 2^2 *3 - 5................. so with same progression
a30= 2^30 * 3 - 5
a30=2 * 2^29 * 3 - 5
a30= 6 * 2^29 - 5
C
Answer: C
Question: There are 9 kids and 5 chairs. In how many ways kids can occupy the chairs?
Options:
A)1760
B)1840
C)1560
D)1740
E)15120
Rationale: total kids = 9
total chairs = 5
1st chair can be occupy in 9ways
2nd chair can be occupy in 8ways
3rd chair can be occupy in 7ways
4th chair can be occupy in 6ways
5th chair can be occupy in 5ways
total number of ways =9*8*7*6*5 = 15120 ways
correct option is E
Answer: E
Question: In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ?
Options:
A)12
B)27
C)26
D)11
E)22
Rationale: Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x
= 22 or x
= 11.
Answer: D
Answer: D
Question: The sum of two numbers is 62, and one of them is 12 more than the other. What are the two numbers?
Options:
A)36-48
B)50-34
C)60-24
D)42-42
E)25-37
Rationale: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 62:
word problem = 62
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 62 âˆ’ 12
= 50.
x = 50/2
= 25.
This is the first number. Therefore the other number is
x + 12 = 25 + 12 = 37.
The sum of 25 + 37 is 62.
E
Answer: E
Question: Molly and Max are driving at a rate of 100 kilometers per hour. What is their driving speed in miles per hour? [1km = 0.6 miles]
Options:
A)600
B)60
C)6
D)0.6
E)None of the above
Rationale: To calculate the equivalent of miles in a kilometer
0.6 kilometers= 1 mile
100 kilometers = (0.6)*100 = 60 miles
Speed in kilometers/hour = 60
Correct answer - B
Answer: B
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A
Options:
A)168
B)6289
C)1268
D)1184
E)1232
Rationale: Explanation:
B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 148 = 3k + 148 => 2k = 296 => k = 148
The initial quantity of water in A = 8k = 8 * 148 = 1184 liters.
Answer: Option D
Answer: D
Question: The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was
Options:
A)Rs.12008
B)Rs.12000
C)Rs.12002
D)Rs.1229
E)Rs.12021
Rationale: Explanation:
= Rs.12000
Answer: B
Answer: B
Question: On the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (1, 6) II. (3, 11) III. (5, 4)
Options:
A)I only
B)II only
C)III only
D)I and II
E)I, II, and III
Rationale: Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.
When x = 1, y = 5 lies on the parabola, so (1, 6) will not be enclosed by the parabola and x axis.
When x = 3, y = 9 lies on the parabola, so (3, 11) will not be enclosed by the parabola and x axis.
When x = 5, y = 5 lies on the parabola, so (5, 4) will be enclosed by the parabola and x axis.
The answer is C.
Answer: C
Question: In some quantity of ghee, 50% is pure ghee and 50% is vanaspati. If 20kg of pure ghee is added, then the strength of vanaspati ghee becomes 30%. The original quantity was?
Options:
A)25
B)15
C)30
D)45
E)20
Rationale: Let the original quantity be x
then, vanaspati ghee in xkg = 50x/100 kg= x/2kg
(x/2)/(x+20) = 30/100
x/(2x+40) = 3/10
x = 30
Answer is C
Answer: C
Question: Raj goes to market to buy oranges. If he can bargain and reduce the price per orange by Rs.2, he can buy 30 oranges instead of 20 oranges with the money he has. How much money does he have ?
Options:
A)28
B)2
C)6
D)8
E)1
Rationale: Explanation: Let the money with Raj is M. So M/20−M/30=M/20−M/30=2. Check options. Option D satisfies.
Answer:B
Answer: B
Question: A side of beef lost 25 percent of its weight in processing. If the side of beef weighed 540 pounds after processing, how many pounds did it weigh before processing?
Options:
A)191
B)355
C)720
D)840
E)1,560
Rationale: Let weight of side of beef before processing = x
(75/100)*x = 540
=> x = (540 * 100)/75 = 720
Answer C
Answer: C
Question: A restaurant meal cost $36.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:
Options:
A)$40 and $42
B)$39 and $42
C)$38 and 40
D)$37 and $39
E)$36 and $37
Rationale: let tip=t
meal cost=36.50
range of tip = from 10% of 36.5 to 15% of 36.5 = 3.55 to 5.325
hence range of amount paid= 36.5+T= 40.05 to 41.825
ANSWER:A
Answer: A
Question: There is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 50%
Options:
A)40.8
B)19.75
C)20.75
D)21.75
E)22.75
Rationale: 60*84/100=50.40 lit milk that is 9.60 lit water
let x lit water will be added then
(60+x)*50/100=50.40
so x=40.8
ANSWER:A
Answer: A
Question: On a certain transatlantic crossing, 40 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 50 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Options:
A)40%
B)50%
C)60%
D)80%
E)90%
Rationale: Let T be the total number of passengers.
Let x be the number of people with round trip tickets.
0.4T had round trip tickets and took their cars.
0.5x had round trip tickets and took their cars.
0.5x = 0.4T
x = 0.8T
The answer is D.
Answer: D
Question: 12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work?
Options:
A)2 days
B)7 days
C)8 days
D)9 days
E)45 days
Rationale: 1 man's 1 day work = 1/108
12 men's 6 day's work = 1/9 * 6 = 2/3
Remaining work = 1 - 2/3 = 1/3
18 men's 1 day work = 1/108 * 18 = 1/6
1/6 work is done by them in 1 day.
1/3 work is done by them in 6 * 1/3 = 2 days.
Answer:A
Answer: A
Question: Find the invalid no.from the following series 3, 7, 15, 31 , 63, 127, 257
Options:
A)3
B)7
C)257
D)63
E)31
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 257 is wrong.
C
Answer: C
Question: Find a positive number, which when increased by 8 is equal to 128 times reciprocal of the number.
Options:
A)5
B)6
C)8
D)7
E)9
Rationale: Explanation:
Let the number be x. Then,
x + 8 = 128 x (1/x) => x<sup>2</sup> + 8x - 128 = 0
=> (x + 16)(x - 8) = 0
=> x = 8
Answer: Option C
Answer: C
Question: If x and y are positive integers, then x/y is
Options:
A)Always even
B)Always odd
C)Even whenever x+y is Even
D)Odd whenever x and y is odd
E)It cannot be determined
Rationale: x and y are positive integers, then x/y is
Let's take odd as 25 and odd as 5.
IMO option B is correct answer..
If you consider your fourth scenario, that turns out to be even.
Hence option D should be correct.
Answer: D
Question: 1395 x 1395 = ?
Options:
A)A)1951609
B)B)1946025
C)C)1951602
D)D)1951603
E)E)1951604
Rationale: 1395 x 1395	= (1395)2
= (1400 - 5)2
= (1400)2 + (5)2 - (2 x 1400 x 5)
= 1960000 + 25 - 14000
= 1960025 - 14000
= 1946025.
Answer:B
Answer: B
Question: At Veridux Corporation, there are 210 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 135 male associates, how many female managers are there?
Options:
A)15
B)20
C)25
D)30
E)55
Rationale: Well, first letâ€™s take care of the â€œtotalsâ€. The numbers in the â€œtotalsâ€ row must add up. If 90 are females, the other 210 â€“ 90 = 120 must be males. Similarly, the numbers in the â€œtotalsâ€ column must add up. If 40 are managers, then the other 210 â€“ 40 = 170 must be associates.
Now, in the â€œassociateâ€ row, 135 + E = 170, which means E = 35 â€” the other 35 associates must be female.
Now, to find B, which is what the question is asking, we need only look at the sum in the â€œfemaleâ€ column: B + 35 = 90, which means B = 55. There are fifteen female managers in this company. Thus, the answer = (E).
Answer: E
Question: A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 per cent larger than the original. By what percentage has the area of the logo increased?
Options:
A)50
B)80
C)100
D)125
E)250
Rationale: Let old diameter be 4 , so radius is 2
Old area = 4π
New diameter is 6 , so radius is 3
New area = 9π
Increase in area is 5π
% increase in area = 5/4*100
So, % increase is 125%
Answer will be (D)
Answer: D
Question: A man performs 1/2 of the total journey by rail, 1/3 by bus and the remaining 3km on foot. His total journey is
Options:
A)18km
B)10km
C)12km
D)24km
E)25km
Rationale: Explanation:
Let the journey be x km
Then, 1x/2 + 1x/3 +3 =x
5x +18 =6x
X = 18km
Answer: Option A
Answer: A
Question: The sum of the ages of 5 children born at the intervals of 3 year each is 60 year. what is the age of the youngest child ?
Options:
A)4 year
B)6 year
C)10 year
D)None of these
E)9 year
Rationale: Solution
let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.
then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 60 â‡” 5 x = 30 â‡” x= 6.
âˆ´ Age of the youngest child = x = 6 years. Answer B
Answer: B
Question: Mani paid a sum of money for purchasing 40 pens, which he recovered in full when he sold 25 of them. What was his percentage of profit or loss per pen?
Options:
A)50%
B)60%
C)70%
D)65%
E)55%
Rationale: B
33.33%
If the sum he paid whilst purchasing 40 pens = A,
Then the Cost Price of each pen = A/40.
Since the amount he got whilst selling 25 pens is also = A
Then the Selling Price of each pen = A/25.
Since Selling Price > Cost Price, he made a profit.
Profit per pen = Selling Price - Cost Price = A/25 - A/40 = 3A/200.
Profit percentage per pen = Profit per pen / Cost per pen x 100 = (3A/200) / (A/40) x 100 = 60%. Answer : B
Answer: B
Question: Narasimha, Madhu and pavan started a business by investing Rs.1,20,000, Rs.1,35,000 and Rs 1, 50,000 respectively. Find the share of Pavan, out of an annual profit of Rs.56,700.
Options:
A)21,0009
B)21,008
C)21,000
D)21,002
E)21,0382
Rationale: Explanation:
Ratio of their investments = 120000 : 135000 : 150000 = 8 : 9 : 10
Share of Pavan = 10271027 × 56700 = 21,000
Answer: C
Answer: C