divelab/Sys2Bench huggingface dataset:
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
Options:
A)2.07%
B)2.71%
C)2.41%
D)2.01%
E)2.31%
Rationale: Explanation:
r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
Answer: D
Answer: D
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Options:
A)12
B)26
C)16
D)97
E)12
Rationale: 10 * 15 + 36 – 26
= 160/10
= 16
Answer: C
Answer: C
Question: David covered a distance of 50 miles on his first trip. On a later trip he traveled 450 miles while going three times as fast. His new time compared with the old time was:
Options:
A)twice as much
B)three times as much
C)the same
D)half as much
E)a third as much
Rationale: Let t be the time of the first trip.
On the later trip, David can travel 150 miles in time t.
The trip of 450 miles takes 3t.
The answer is B.
Answer: B
Question: An amount of Rs.1000 is divided between 5 persons. Each man gets Rs.250 while each woman gets Rs.125. Find the number of men and women.
Options:
A)2 men, 3 women
B)4 men, 1 woman
C)1 man, 4 women
D)3 men, 2 women
E)None of the above
Rationale: Let x be men, y be women
x+y=5.............eq(1)
250x+125y=1000..........eq(2)
solve eq 1 and 2
we get
x=3,y=2
ANSWER:D
Answer: D
Question: An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
Options:
A)18
B)30
C)60
D)120
E)216
Rationale: Arrangment means permutations questions..
5P3 = 5!/3! = 60.
IMO option C is correct answer..
Answer: C
Question: How many no.'s with 3 different digits, 2, 3, 5, 6, 7 and 9, which are divisible by 5?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20
B
Answer: B
Question: Company X provides bottled water to its employees in 5 liter bottles, $3 each. At least how many 5L bottles must Company X buy monthly, so that new contract with $50 fixed monthly rate and $1 for 20L bottle each paid off? (Assume that no other costs apply)
Options:
A) 15
B) 17
C) 19
D) 20
E) 21
Rationale: let the no. of 5 liter bottles be x, so the no. of 20l bottles will be x/4 (to equate the vol.) since the total cost will be equal , 3x= 50+x/4 so x= 18.18 or 19. Answer is (C).
Answer: C
Question: sunil start from home at 4 pm and reaches school everyday at 5pm to pick up his children.on saturday the school got over ai 4 pm and children started walking towards home.sunil met them on the way and returned home 15min early.if speed of sunil is 35km/hr then for how many min did children walk? what is speed of children???
Options:
A)4 km/hr.
B)5 km/hr.
C)6 km/hr.
D)7 km/hr.
E)8 km/hr.
Rationale: sunil reach 15 min early. it is time save at both for going to school and coming to home.
so, sunil meet children befor 15/2= 7.5 min.
speed of sunil is 35km/hr i.e. 583.33 m/min.
remaining distance to cover by sunil or else we can say total distance cover by children is 7.5*583.33=4375 m
Sunil meet children after 52.5 min i.e. (1hr-7.5min).
so 4375 is distance cover by children in 52.5min.
so, speed of children is 4375/52.5=83.33m/min=5 km/hr.
ANSWER:B
Answer: B
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Options:
A)833 1/7 grams
B)833 1/3 grams
C)833 8/3 grams
D)883 1/3 grams
E)832 1/3 grams
Rationale: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer:B
Answer: B
Question: What number should replace the question mark in this series?
13 44 88 176 847 ?
Options:
A)1495
B)1595
C)1695
D)1458
E)1795
Rationale: First number is 13. Second number is 13+31 = 44. Third number is 44+44=88. Fourth number is 88+88 = 176. Fifth number is 176+671=847. So, next number is 847+748 = 1595
ANSWER:B
Answer: B
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)70 m
B)60 m
C)80 m
D)90 m
E)100 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: B
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 21 years(the child was born during the interval). What is the present age of the child?
Options:
A)7 years
B)9 years
C)6 years
D)4 years
E)5 years
Rationale: 28 * 2 = 56
21 * 3 = 63
-----------
7 years
Answer: A
Answer: A
Question: If w,x,y,z are consecutive positive integers ; then which of the following is always odd?
[1] w*x+(y+2)^2*z
[2] w^x + z^y
[3] 6z^2
Options:
A)1
B)2
C)3
D)2
E)1 and 3
Rationale: Plug in some numbers
w = 1
x = 2
y = 3
z = 4
Check the options -
[1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4 = 102{ Not an odd Number }
[2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number }
[3] 6z^2 = 6* 4^2 even
[2]
D
Answer: D
Question: 2.2 cubic dm of lead is to be drawn into a cylindrical wire 0.50 cm diameter. Find the length of the wire in meters.
Options:
A)110
B)111
C)113
D)112
E)None of them
Rationale: Let the length of the wire be h meters. Then,
∏ (0.50/(2 x 100))^2 x h = 2.2/1000
=h = ( (2.2/1000) x (100 x 100)/(0.25 x 0.25) x (7/22) ) = 112 m.
Answer is D.
Answer: D
Question: A and B start a business jointly. A invests Rs.18000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
Options:
A)A)Rs.12829
B)B)Rs.14400
C)C)Rs.12293
D)D)Rs.12804
E)E)Rs.12830
Rationale: 18*8: x*4 = 5:2
x = 14.4 =>
Rs.14400
Answer: B
Answer: B
Question: Rajat, Vikas and Abhishek are submitting questions in the ratio 7:3:2. If total number of questions submitted by them is 24. Find the number of questions submitted by Vikas.
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Explanation :
Number of questions submitted by Vikas
= (24 * 3)/(7+3+2) = 6
Answer : D
Answer: D
Question: From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 6 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 3 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The distance traveled by Ferry P is 18 km.
Then the distance traveled by Ferry Q is 54 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 54/9 = 6 hours, which is 3 hours more than Ferry P. The answer is C.
Answer: C
Question: In a class, candies were distributed among the children. Each child got candies equal to one-eighth of the total number of children in the class. If the number of children were half of the present number of children, then each child would have received 16 candies in total. Find the total number of candies distributed.
Options:
A)450
B)598
C)512
D)658
E)544
Rationale: Suppose the total number of children in the class be X. Then,
(X)*(1/8*X)=(X/2)*16
=> X=64
=>Total number of candies = (1/8)*X*X =(1/8)*64*64=512
Option C
Answer: C
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Options:
A)187 sq.cm
B)877 sq.cm
C)279 sq.cm
D)279 sq.cm
E)600 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE
= √(625 - 225) = √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30
=600 sq.cm.
Answer: E
Answer: E
Question: In what ratio must tea at Rs.62 per kg be mixed with tea at Rs. 72 per kg so that the mixture must be worth Rs. 64.50 per kg?
Options:
A)3:1
B)2:1
C)5:2
D)3:2
E)3:4
Rationale: Mean price = (72-64.5 = 7.5) (64.5-62=2.5)
req ratio = 7.5:2.5 = 3:1
ANSWER A
Answer: A
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 180 inclusive?
Options:
A)90
B)95
C)100
D)105
E)110
Rationale: 10 and 190 inclusive would mean there are 19 terms.
No need to add up all the terms and further divide by 19 since the terms are evenly spaced in ascending order from 10, 20, 30........180
The middle term is the average which is the tenth term = 90
A is the answer.
Answer: A
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 300 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Options:
A)219
B)246
C)252
D)262
E)270
Rationale: Number of newborns that can die in first month = 1/10 * 300 = 30
Survived = 270
Number of newborns that can die in second month = 1/10 * 270 = 27
Survived = 243
Number of newborns that can die in third month = 1/10 * 243 = 24
Survived = 219
Answer:A
Answer: A
Question: The average of 10 numbers was calculated as 16. It is discovered later on that while calculating the average, one number, namely 46, was incorrectly read as 26. What is the correct average?
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: 10*16 - 26 + 46 = 180
180 / 10 = 18
The answer is A.
Answer: A
Question: If 75 percent of a class answered the first question on a certain test correctly, 65 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
Options:
A) 10%
B)(8) 20%
C) 30%
D) 50%
E) 60%
Rationale: {Total} = {First} + {Second} - {Both} + {Neither}
100% = 75% + 65% - {Both} + 20% --> {Both} = 60%.
Answer: E.
Answer: E
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
Options:
A)3 1/5 Km
B)2 1/5 Km
C)4 Km
D)4 1/5 Km
E)3 3/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
A
Answer: A
Question: What amount does an investor receive if the investor invests $6000 at 10% p.a. compound interest for two years, compounding done annually?
Options:
A)$6980
B)$7070
C)$7120
D)$7260
E)$7340
Rationale: A = (1 + R/100)^n * P
(1.1)^2 * 6000 = 1.21 * 6000 = 7260
The answer is D.
Answer: D
Question: A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?
Options:
A)2
B)4
C)8
D)6
E)5
Rationale: Quantity of milk in the mixture = 90/100 (70) = 63 litres.
After adding water, milk would form 87 1/2% of the mixture.
Hence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72
Hence 72 - 70 = 2 litres of water must be added.
ANSWER A
Answer: A
Question: The smallest number which when diminished by 9, is divisible 13, 26, 39, 52 and 65 is:
Options:
A)789
B)769
C)790
D)787
E)788
Rationale: Required number = (L.C.M. of 13, 26, 39, 52,65) + 9
= 780 + 7
= 789
Answer: Option A
Answer: A
Question: Set A is {1, 3, 5, 7, 9}
Set B is {8, 10, 12, 14, 16}
For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.
Options:
A)I only
B)I and II only
C)I and III only
D)II and III only
E)I, II, and III
Rationale: The mean and median of Set A is 5.
The mean and median of Set B is 12.
Thus statements I and II are both true.
The standard deviation is related to the distance from the mean.
Since the elements of both sets are spaced identically around the mean (+/- 2, +/- 4), the standard deviations of both sets are equal.
The answer is B.
Answer: B
Question: A company seeks to hire a sales manager, a shipping clerk, and a receptionist. The company has narrowed its candidate search and plans to interview all remaining candidates including 8 persons for the position of sales manager, 4 persons for the position of shipping clerk, and 10 persons for the position of receptionist. How many different hirings of these three people are possible?
Options:
A)8 + 4 + 10
B)8 × 4 × 10
C)21 × 20 × 19
D)8! + 4! + 10!
E)8! × 4! × 10!
Rationale: 1 sales manager can be selected out of 8 in 8 ways
1 clerk can be selected out of 4 in 4 ways
1 receptionist can be selected out of 10 in 10 ways
total no. of ways these 3 can be selected = 8 *4 * 10
Ans. B)8 × 4 × 10
Answer: B
Question: If you wish to live to be 100 years old (hypothetically), you must consume 500 calories less than your Average Daily Allowance for your age. If you are in your 60's, and your Average Daily allowance is 2000 calories per day, how many calories are you allowed in a week?
Options:
A)7000
B)10500
C)14000
D)12000
E)3500
Rationale: To determine the amount of calories allowed per day, you need to subtract 500 from 2000, for a total of 1500
To determine the amount of calories allowed per week, you need to multiply the daily amount allowed (1500) by the number of days in a week (7) for a total of 10500
The correct answer is B
Answer: B
Question: How many pieces can a square pizza be cut into by making 5 linear cuts?
Options:
A)16
B)17
C)13
D)14
E)15
Rationale: 1 cut can make 2 pieces
a second cut can make 4 pieces by cutting through 2 pieces
a third cut can make 7 pieces by cutting through 3 of the pieces
a fourth cut can make 11 pieces by cutting through 4 of the pieces
a fifth cut can make 16 pieces by cutting through 5 of the pieces
A
Answer: A
Question: A and B can do a piece of work in 48 days, A and C can do it in 60 days, b and c can do it 72 days. In what time can c alone do it?
Options:
A)84 days
B)84 ½ days
C)85 days
D)87 days
E)89 days
Rationale: Explanation:
(A+B) 1 day work = 1/48
(B+C) 1 day work = 1/72
(A+C) 1 day work = 1/60
By adding 2(A+B+C) = 1/48 +1/72+1/60 = 37/720
(A+B+C) 1 day work = 37/1440
A 1 day work = 37/1440 – 1/72 = 17/1440 = 85 days (approximately)
Answer: Option C
Answer: C
Question: A cement mixture is composed of 3 elements. By weight, 1/5 of the mixture is sand, 3/4 of the mixture is water, and the remaining 6 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?
Options:
A)100
B)120
C)130
D)140
E)150
Rationale: Let the total weight be x.
Sand content= (1/5)x
Water content= (3/4)x
Gravel=x-(1/5)x-(3/4)x=(1/20)x=6
x=120
Then answer will be B=120
Answer: B
Question: Mary deposits a certain sum of money in a bank at 16% p.a. simple interest. After how many years will she receive double her amount?
Options:
A)10 years 2 months
B)12 years 6 months
C)9 years
D)8 years
E)14 years
Rationale: Solution: simple interest question
B=A[1+ (tr/100)]; where A is principal amount, B final amount, t time in years and r interest rate
after putting the values 16
3= [1+(16t/100)]
t= 25/2 which is 12 years 6 months
Answer is B
Answer: B
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)Rs. 2000
B)Rs. 2200
C)Rs. 2400
D)Data inadequate
E)Cannot be determined
Rationale: Explanation :
Let the C.P. of the article be Rs. x
Given that % profit earned by selling article at Rs. 1920 = % loss incurred by selling article at Rs. 1280
(1920−x/x)∗100 = (x−1280/x)∗100
=> 1920 - x = x - 1280
=> 2x = 3200
=> x = 1600
S.P. for 25% profit = Rs. 1600 + 25% of Rs. 1600 = Rs. 1600*(125/100) = Rs. 2000
Answer : A
Answer: A
Question: Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
Options:
A)8 hrs 18 min
B)8 hrs 85 min
C)8 hrs 15 min
D)7 hrs 15 min
E)8 hrs 25 min
Rationale: Number of pages typed by Ronald in 1 hour = 32/6 = 16/3
Number of pages typed by Elan in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3
Time taken by both to type 110 pages = (110 * 3/40) = 8 1/4 = 8 hrs 15 min
Answer: C
Answer: C
Question: Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 480 pounds of the seed mixture?
Options:
A)6
B)12
C)20
D)24
E)120
Rationale: If the mixture contains 2 pounds of timothy, the mixture must be 40 pounds.
Thus we need 40 pounds of mixture per acre.
480 / 40 = 12 acres
The answer is B.
Answer: B
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. What is the ratio of their present ages?
Options:
A)7:3
B)3:7
C)4:8
D)8:4
E)2:3
Rationale: Let age of the son before 10 years =x and
age of the father before 10 years =3x
(3x+20)=2(x+20)⇒x=20
Age of the son at present =x+10=20+10=30
Age of the father at present =3x+10=3×20+10=70
Required ratio =70:30=7:3
Answer is A.
Answer: A
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
Options:
A)1/3
B)2/5
C)2/7
D)3/5
E)4/7
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A
Answer: A
Question: A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5.5 hours, then the distance covered at 40 kmph is
Options:
A)130 km
B)160km
C)100km
D)140km
E)none of these
Rationale: Let the partial distance covered at 40 kmph be X
Let the another partial distance covered at 60 kmph be (250 - x)
Thus, x/40 - (250 - x)/60 = 5.5
or, x/40 + (250 - x)/60 = 5.5
or, (3x + 500 - 2x)//120 = 5.5
or 500 + x = 660
x=160
ANSWER:B
Answer: B
Question: 23 × 19 × ? ÷ 19 ÷ 17 = 115
Options:
A)65
B)75
C)85
D)95
E)45
Rationale: Explanation:
23 × 19 × ? ÷ 19 ÷ 17 = 115
=> (23 × 19 × ?)/(19 × 17) = 115
=> ? = (115 × 19 × 17)/(23 × 19) = 85
Answer: Option C
Answer: C
Question: How many bricks each measuring 20cm x 13.25cm x 8cm, will be needed to build a wall 7m x 8m x 15.5m
Options:
A)5600
B)4600
C)4094
D)7200
E)None of these
Rationale: Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (700 x 800 x 15.5) / (20 x 13.25 x 8) = 4094
Answer: C
Answer: C
Question: A train 360 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 120 meters long is?
Options:
A)29
B)18
C)48
D)99
E)32
Rationale: D = 360 + 120 = 480
S = 54 * 5/18 = 15 mps
T = 480/15 = 32 sec
Answer: E
Answer: E
Question: How many numbers between 200 and 400 begin or end with 3?
Options:
A)20
B)60
C)100
D)110
E)120
Rationale: There will be 10 numbers from 200 to 299 that will end with 3 ( 203, 213, 223........ 293 ).
There will be 100 numbers from 300 to 400 that will begin with 3, we will not count the numbers that will end with because they will be repeated.
Total numbers = 10 + 100 = 110
Answer is D.
Answer: D
Question: What is the area of a square field whose diagonal of length 16 m?
Options:
A)128
B)289
C)200
D)112
E)178
Rationale: d2/2 = (16 * 16)/2
= 128
Answer: A
Answer: A
Question: A clock strikes 4 taking 9 seconds. In order to strike 12 at the same rate, the time taken is
Options:
A)33 seconds
B)30 seconds
C)32 seconds
D)31 seconds
E)34 seconds
Rationale: There are 3 intervals when the clock strikes 4
Time taken for 3 intervals = 9 seconds
Time taken for 1 interval =9/3=3 seconds
In order to strike 12, there are 11 intervals.
Hence time needed =3Ã—11=33 seconds
Answer: A
Answer: A
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)2
B)4
C)6
D)5
E)1
Rationale: Explanation:
65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: B
Answer: B
Question: Ajay pays Rs 6.4 per litre of spirit, He adds water and sells the mixture at Rs 8 per Iitre, thereby making 37.5% profit. Find the proportion of the water to that of the spirit received by the customers.
Options:
A)1:15
B)1:10
C)1:20
D)1:12
E)1:13
Rationale: Suppose the quantity of spirit purchased= X litres
Suppose quantity of water mixed = Y litres
Required ratio of the water and the spirit in the mixture = Y : X
C.P of X lts of spirit = Rs 6.4X
S.P of X lts of milk = Rs 8(X + Y)
profit % = 37.5
Thus, C.P = S.P x 100/(100 + gain% )
=> 64 =( 8X + 8Y)/(100 + 37.5) x 100
880 X= 800X +800Y
=> 80X = 800Y => X = 10Y
=> X/10 = Y/1
Required ratio = 1:10
ANSWER:B
Answer: B
Question: What percent of a day is four hours?
Options:
A)16.67%
B)16x1/2%
C)18x2/3%
D)22x1/2%
E)None of these
Rationale: Explanation :
Required percentage = (4/24100)%.
= 16.67%.
Answer : A
Answer: A
Question: In measuring the sides of a rectangle, one side is taken 8% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.
Options:
A)3.5%
B)2.4%
C)3%
D)5%
E)2.6%
Rationale: Let the sides of the rectangle be a and b.
actual area of the rectangle without error = ab
New side a ( 8% in excess) = a+0.08a = 1.08a
New side b ( 5% in deficit) = b-0.05b = 0.95b
Area of the new rectangle = (1.08a)(0.95b)= (1.0260)ab
say a=1 and b=1
area of the original rectangle = 1
area of the new rectangle = 1.026
change in the area calculation = .026
error percentage in the area calculated = 2.6%
ANSWER:E
Answer: E
Question: How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
Options:
A)20
B)30
C)83
D)82
E)50
Rationale: The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = ⁵P₃ = 60.
Answer:E
Answer: E
Question: Robin's average (arithmetic mean) test score on 9 tests is 82. What must be Robin's score on a 10th test for his average score on the 10 tests to be 83?
Options:
A)92
B)82
C)72
D)62
E)52
Rationale: (9*82+x)/10=83
x=(10*83)-(9*82)
x= 830 - 738
total score required 830 - 738=92
Correct answer is A
Answer: A
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Options:
A)Rs. 450
B)Rs. 600
C)Rs. 800
D)Rs. 375
E)Rs. 400
Rationale: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/24.
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4 : 3 : 1.
C's share (for 3 days) = Rs. ( 3 x 1/24 x 3200) = Rs. 400.
CORRECT OPTION "E".
Answer: E
Question: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years replaced by a new boy. The age of the new boy is?
Options:
A)14 years 8 months
B)15 years
C)16 years 4 months
D)17 years 10 months
E)17 years
Rationale: Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 18 years - 3 years 4 months.
= 14 years 8 months.
ANSWER:A
Answer: A