divelab/Sys2Bench huggingface dataset:
Question: Bert left the house with N dollars. He spent 1/4 of this at the hardware store, then $9 at the dry cleaners, and then half of what was left at the grocery store. When he got home, he had $15 left in his pocket. What was the value of N?
Options:
A)$36
B)$44
C)$52
D)$60
E)$68
Rationale: started to test answer C
if he had 52, then he spent 13 at hardware store
now he was left with 39$
he spent 9 dollars on cleaning, thus he remained with 30$
he then spent 1/2 of 30, or 15, and was left with 15.
hence, the only option that can be right is C.
Answer: C
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 136, then the number of hens will be:
Options:
A)22
B)23
C)24
D)26
E)28
Rationale: let hens be x and cows be y
now,
feet: x*2+y*4=136
heads: x*1+y*1=48
implies, 2x+4y=136 and x+y=48
solving these two equations, we get x=28 and y=20
Therefore, hens are 28.
ANSWER:E
Answer: E
Question: 6+2=42
4+9=48
8+2=72
3+7=27
1+4=??
Solve it?
Options:
A)9
B)3
C)42
D)4
E)16
Rationale: x+y=x[y+(x-1)]=x^2+xy-x
6+2=6[2+(6-1)]=36+12-6=42
4+9=4[9+(4-1)]=16+36-4=48
8+2=8[2+(8-1)]=64+16-8=72
3+7=3[7+(3-1)]=9+21-3=27
1+4=1[4+(4-1)]=1+4-1=4
Answer :D
Answer: D
Question: 4/6 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is
Options:
A)28%
B)41%
C)45%
D)64%
E)78%
Rationale: Total population = 60 (assume).
4/6*60=40 people from Montague.
2/6*60=20 people from Capulet.
0.2*40=8 people from Montague support Juliet.
0.7*20=14 people from Capulet support Juliet.
The probability that a Juliet supporter chosen at random resides in Capulet is 14/(8+14)=~64.
Answer: D
Answer: D
Question: find value for x from below equation? x + 1 = 2
Options:
A)-5
B)1
C)4
D)3
E)2
Rationale: 1. Subtract 1 from both sides:
x + 1 - 1 = 2 - 1
2. Simplify both sides:
x = 1
B
Answer: B
Question: What is the tens digit of 36^12?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: 36^10 = 6^24
(6^2)=6*6 = 36
(6^3)= 36*6 = .16
(6^4)= .16*6 = ..96
(6^5) = ..96*6 = ..76
(6^6) = ..76*6 = ...56
(6^7) = ....56*6 = ....36
If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on...
Continue the pattern up to 6^24 ( dont actually calculate full values) and answer is E: 9
Answer: E
Question: Among 400 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?
Options:
A)20
B)60
C)80
D)86
E)120
Rationale: 56%+44%-30%=70% who like either Strawberry, Apple, or both.
That means 100%-70% = 30% do not like either Apple of Strawberry jam.
30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)
E
Answer: E
Question: Randy can rebuild an automobile engine in b hours. Alvin can rebuild the same engine in a hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Alvin will have to complete?
Options:
A)ab/(a+b)
B)(b)/(a+b)
C)b/(b-a)
D)a/(a+b)
E)b/(a-b)
Rationale: Randy can do the job in a hrs, Alvin can do the job in b hrs.
When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin.
Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b)
So Alvin does b/(a+b) of the work
Answer (B).
Answer: B
Question: If x is an integer and 2.134 × 10^x is less than 21,000, what is the greatest possible value for x?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: x is an integer and 2.134 × 10x is less than 21,000, what is the greatest possible value for x?
for 2.134 × 10x is less than 21,000 to remain true, the greatest number is 2,134, which makes x=3
E. 3
Answer: E
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
Options:
A)20/68
B)20/63
C)20/29
D)20/20
E)20/69
Rationale: Required probability
= (⁵C₃ . ⁴C₁)/⁹C₄
= (10 * 4)/126 = 20/63
Answer:B
Answer: B
Question: 8900 ÷ 6 ÷ 4 = ?
Options:
A)349
B)541.75
C)224.37
D)370.833
E)None of these
Rationale: Explanation:
Given Exp. 8900 * 1/6 * 1/4
= 370.833
ANSWER: D
Answer: D
Question: On retirement, a person gets 1.53 lakhs of his provident fund which he invests in a scheme at 20% p.a. His monthly income from this scheme will be
Options:
A)2,450
B)2,500
C)2,550
D)2,600
E)None of these
Rationale: Let S.I. = x
= 1.53×10(5)×20/100
= 2,500
Answer B
Answer: B
Question: Three runners Q, B and C run a race, with runner A finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?
Options:
A)36m
B)48m
C)60m
D)72m
E)84m
Rationale: Let distance of race be x mtrs. Then when Q finishes x m , B has run (x- 12)mtrs and C has run x-18 mtrs. so at this point B is 6 m ahead of C. Now to finish race b needs to run another 12 m, so he runs another 12 m. when B finishes race he is 8 m ahead of C. so last 12 m B has run, C has run 10 m.
as speeds are constant, we have equation,
x-12/ x-18 = 12/10 > x = 48.
Answer B
Answer: B
Question: In racing over a given distance d at uniform speed, A can beat B by 10 meters, B can beat C by 4 meters, and A can beat C by 12 meters. What is the distance d in meters?
Options:
A)16
B)20
C)30
D)40
E)50
Rationale: When A is at the finish line, B is 10 meters back, and C is 12 meters back.
When B runs another 10 meters to the finish line, C is 4 meters back.
So B gains 2 meters every 10 meters covered.
To gain a final difference of 4 meters, B runs a total of 20 meters.
The answer is B.
Answer: B
Question: A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.200 more. What was the Sum?
Options:
A)s.550
B)s.1000
C)s.600
D)s.200
E)s.400
Rationale: At 5% more rate, the increase in S.I for 10 years = Rs.200 (given)
So, at 5% more rate, the increase in SI for 1 year = 200/10 = Rs.20/-
i.e. Rs.20 is 5% of the invested sum
So, 1% of the invested sum = 20/5
Therefore, the invested sum = 20 × 100/5 = Rs.400 Answer: E
Answer: E
Question: If a=2/3b , b=2/3c, and c=2/3d what part of d is b/
Options:
A)8/27
B)4/9
C)2/3
D)7/8
E)4/3
Rationale: now put c=2/3d in b=2/3c
so b=2/3*2/3d
b=4/9d
ANSWER:B
Answer: B
Question: I. j; k; m; n; p
II. j - 10; m; m; m; p + 15
III. j + 2; k + 1; m; n - 1; p - 2
If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation D to least standard deviation in which of the following?
Options:
A) I, III, II
B) II, I, III
C) II, III, I
D) III, I, II
E) III, II, I
Rationale: Range of 1st Set = (p-j)
Range of 2nd Set = P+15 - j +10 = (p-j) +25
Range of 3rd Set = P -2 - j - 2 = (p-j) - 4
R2 > R1 > R3 ==> SD2 > SD1 > SD3
Since,D= Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B
Answer: B
Question: The ages of 2 persons differ by 32 years. If 9 years ago the elder one be 5 times as old as the younger one, find the present age of elder person.
Options:
A)30
B)42.5
C)45
D)49
E)47.9
Rationale: age of the younger person = x
age of the elder person = x+32
5(x-9) = x+32-9
x= 17
age of elder person =17+32=49
Answer is D
Answer: D
Question: Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/7 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?
Options:
A)7
B)21
C)11
D)D.13
E)15
Rationale: rate of bob to paint n rooms is n/T(bob)
rate of Albert to paint n rooms is n/T(albert).
albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1
Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time
Therefore
n/x + n/x-1 = (3n/5)/(4/3) =
n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic
4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.
7*3 = 3n
21 = 3n.
Answer is B
Answer: B
Question: We had $840 left after spending 30% of the money that we took for shopping. How much money did we start with?
Options:
A)$1000
B)$1050
C)$1100
D)$1150
E)$1200
Rationale: Let x be the amount of money we started with.
0.7x = 840
x = 1200
The answer is E.
Answer: E
Question: In a certain supermarket, a triangular display of cans is arranged in 10 rows, numbered 1 through 10 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 150 cans in the entire display, how many cans are in the seventh row?
Options:
A)13
B)15
C)17
D)19
E)21
Rationale: Let x be the number of cans in row 1.
The total number of cans is x + (x+3) + ... + (x+27) =
10x + 3(1+2+...+9) =
10x + 3(9)(10)/2 =
10x + 135
Since the total is less than 150, x must equal 1.
The number of cans in the 7th row is 1 + 3(6) = 19
The answer is D.
Answer: D
Question: Average of 13 results is 65. If the average of first six results is 61 and average of last six results is 59 Then find the seventh result?
Options:
A)118
B)120
C)125
D)130
E)134
Rationale: 125
Option 'C'
Answer: C
Question: Four bells ring at an interval of 4, 8, 6, 10 minutes. If they toll together at 2:00 A.M, when will they toll together again?
Options:
A)4 am
B)5 am
C)6 am
D)7 am
E)8 am
Rationale: l.c.m of 4,8,6,10 is 120 min i.e 2 hours
so ans is 2 am + 2=4 am
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 short of the required amount. What is theamount by which he might have fallen short.
Options:
A)38
B)40
C)45
D)48
E)49
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.
B)
Answer: B
Question: A reduction of 20% in the price of salt enables a lady to obtain 4 kgs more for Rs.100, find the original price per kg?
Options:
A)6.16
B)6.21
C)6.25
D)2.4
E)2.7
Rationale: 100*(20/100) = 20 --- 4
? --- 1 => Rs.5
100 --- 80
? --- 5 => Rs.6.25
Answer: C
Answer: C
Question: A rectangular window is twice as long as it is wide. If its perimeter is 12 feet, then what are its dimensions in feet?
Options:
A)2 by 4
B)5/3 by 10/3
C)2.5 by 5
D)3 by 6
E)10/3 by 20/3
Rationale: Let x be the width of the window. Then the length is 2x.
x+2x+x+2x = 12
6x = 12
x = 2
The width is 2 and the length is 4.
The answer is A.
Answer: A
Question: 99^n is such a number begin with 8, least value of n?
Options:
A)11
B)10
C)9
D)8
E)n does not exist
Rationale: 99^1=9801
99^2=971299
99^3=96157601
like this......
take only first two digit for n=1 99
n=2 98
n=3 97
n=4 96
......................................................
n=10 90
n=11 89
so for n=11 number start with 8
ANSWER:A
Answer: A
Question: If u clothes can be purchased for v dollars, how many clothes can be purchased for z dollars?
Options:
A)u/z
B)z/uv
C)uv/z
D)uz/v
E)u/vz
Rationale: Ans = D
Answer: D
Question: The area of a triangle is with base 4m and height 5m?
Options:
A)65 m2
B)10 m2
C)70 m2
D)90 m2
E)12 m2
Rationale: 1/2 * 4 * 5
= 10 m2
Answer:B
Answer: B
Question: The sale price shirts listed for Rs.400 after successive discount is 10% and 5% is?
Options:
A)280
B)290
C)342
D)250
E)253
Rationale: 400*(90/100)*(95/100) = 342
C
Answer: C
Question: Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it ?
Options:
A)110 hours
B)112 hours
C)115 hours
D)100 hours
E)None of these
Rationale: Cistern filled by both pipes in one hour
= 1⁄14 + 1⁄16 = 15⁄112th
∴ Both pipes filled the cistern in 112⁄15 hrs.
Now, due to leakage both pipes filled the cistern in
112⁄15 + 32⁄60 = 8 hrs.
∴ due to leakage, filled part in one hour 1⁄8
∴ part of cistern emptied, due to leakage in one hour
= 15⁄112 - 1⁄8 = 1⁄112th
∴ in 112 hr, the leakage would empty the cistern.
Answer B
Answer: B
Question: In how many ways can Ram choose a vowel and a constant from the letters of the word ALLAHABAD?
Options:
A)4
B)6
C)9
D)5
E)3
Rationale: Solution
In the letters of the word ALLAHABAD there is only 1 vowel available for selection (A). Note that the fact that A is available 4 times has no impact on this fact.
Also, there are 4 consonants available – viz. L, H, Band D. Thus, the number of ways of selecting a vowel and a consonant would be 1 × 4C1 = 4.
Answer A
Answer: A
Question: The ratio of the areas of a square and rhombus whose base is same is:
Options:
A)1:2
B)2:1
C)1:1
D)3:1
E)2:3
Rationale: SOLUTION :
The square and the rhombus are equal in area if they have a common base.
ANSWER IS C
Answer: C
Question: A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $200. The cost for 1 bat and 6 balls is $220, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $210 for the purchase?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: IMO it should be C that is 3
reason:
formed an equation... bat = b ball = c
2b+4c=200
1b+6c=220
solving both we get b that is bat = 40 and c that is ball = 30
new equation 210 to be divided in equal
3b+3c=210
3*40 + 3*30 = 210
120 + 90 = 210
Answer: C
Question: If the perimeter of square region W and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of W
Options:
A)25:16
B)24:25
C)5:6
D)4:5
E)4:9
Rationale: We know Perimeter of a square (Pw) = 4*side
Perimeter of a rectangle (Pr) = 2(length+breath)
Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)
Therefore,
Pw = Pr = 40
Area of the square = 100 sq. units
We know 2(length+breadth) = 40
i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)
Therefore length = 8, breath = 12
Area of the rectangle = 8*12 = 96 sq. units
Question asked = Area of the rectangle : Area of the square = 96:100 ==> 24:25=B
Answer: B
Question: If x and y are numbers such that (x+4)(y-4)=0, what is the smallest possible value of x^2 + y^2
Options:
A)0
B)9
C)12
D)16
E)18
Rationale: From (x+4)(y-4)=0 it follows that either x=-4 or y=4. Thus either x^2=16 or y^2=16.
Now, if x^2=16, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 16 + 0 = 16.
Similarly if y^2=16, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 16 = 16.
Answer: D.
Answer: D
Question: 24 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
Options:
A)24
B)23
C)44
D)45
E)46
Rationale: n for cyclic hand shake and n-1 for linear handshake.
so here no of hand shake is 24.
ANSWER:A
Answer: A
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
Options:
A)30
B)20
C)40
D)57
E)63
Rationale: A
30
There is a meal for 200 children.
150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children 120 men.
50 children = (120/200)x 50 = 30 men.
Answer: A
Question: In a 6 digit ID number, what is the probability of exactly four digits are the digit 0?
Options:
A)9/2000
B)81/20000
C)12/36001
D)81/16000
E)84/3600
Rationale: Total number of 6 digit numbers = 9*10*10*10*10*10 = 9,00,000
No. of ways of arranging 4 digits as 0 = 5C4=5.
Arrangements are as follows. Here X can be any digit other than 0
1) XX000X ==> no. of ways - 729
2) XXX000 ==> no. of ways - 729
3) X0XX00 ==> no. of ways - 729
4) XX00X0 ==> no. of ways - 729
5) X00XX0 ==> no. of ways - 729
Probability = (729*5)/90000
=81/20000
Ans - B
Answer: B
Question: On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him?
Options:
A)1/4
B)4/5
C)1/5
D)1/6
E)1/7
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: E
Answer: E
Question: A, B, C, D, E, F are the only six families in Indira Nagar. A, B, C, D, E and F has 7, 8, 10, 13, 6, and 10 member in their families respectively. If 1 member from all the six families left their respective families to accommodate themselves in the hostel of IIM Lucknow, then the average number of member now in each family of Indira nagar is
Options:
A)8
B)9
C)10
D)13
E)15
Rationale: Answer
Required average
= (( 7 - 1 ) + ( 8 - 1 ) + ( 10 - 1 ) + ( 13 - 1 ) + (6 - 1) +( 10 - 1 ) )/ 6
= ( 7 + 8 +10 + 13 + 6 + 10 ) / 6 - ( 6 x 1 ) / 6
=9 - 1 = 8
Correct Option: A
Answer: A
Question: Two taps can fill a tank in 12 and 18 minutes respectively. Both are kept open for 2 minutes and the first is turned off. In how many minutes more will the tank be filled ?
Options:
A)15 min.
B)20 min.
C)11 min.
D)13 min.
E)None of these
Rationale: Part filled by first tap in one min = 1⁄12th
Part filled by second tap in one min = 1⁄18th
Now, 2[1⁄12 + 1⁄18] + unfilled part = 1
⇒ unfilled part = 13⁄18th
∵ 1⁄18th part of tank is filled by second tap in 1 min.
∴ 13⁄18th part of tank is filled by second tap in 1 min.
= 18 × 13⁄18 min = 13 min.
Answer D
Answer: D
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h = 9 cm
Answer: Option E
Answer: E
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Options:
A)176 m
B)198 m
C)197 m
D)150 m
E)168 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15
=> y = x/15
x + 100 / 25
= x / 15
x = 150 m.
Answer:D
Answer: D
Question: The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 40 percent, then the value of T decreases by what percent?
Options:
A)25%
B)33 ¹/₃%
C)50%
D)66 ²/₃%
E)75%
Rationale: We can assign numbers:
lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T)
Now increasing S by 40% gives S=3, K remains constant, so T = 2 (6/2=3)
decrease in T= 1, percent decrease in T = (1/3)*100 = 33.33%
Answer B
Answer: B
Question: If 10 litres of an oil of Rs.55 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre?
Options:
A)Rs.49.17
B)Rs.51.03
C)Rs.58.66
D)Rs.55.33
E)None of the above
Rationale: 55*10 = 550
66*5 = 330
880/15 = 58.66
ANSWER:C
Answer: C
Question: What should be added to 4872 so that it may become a perfect square?
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: 70x70=4900
4900-4872 = 28
If added to 28 get perfect square
answer =E
Answer: E
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1234
B)1345
C)1564
D)1670
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: E
Question: There is a sequence An for a positive integer n such that when An-2 is divided by An-1 the remainder is An. If A3=6, A4=0, which of the following can be the value of A1?
Options:
A)48
B)50
C)52
D)56
E)58
Rationale: When A1/A2, Remainder = A3 = 6 --> A1 = xA2 + 6
When A2/A3, Remainder = A4 = 0 --> A2 = yA3
A1 = xyA3 + 6 = kA3 + 6 = 6(k + 1) --> A1 must be a multiple of 6
Only option A is a multiple of 6
Answer: A
Answer: A
Question: In a colony of 70 residents, the ratio of the number of men and women is 5: 2. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
Options:
A)A)1:5
B)B)1:1
C)C)1:8
D)D)1:9
E)E)1:3
Rationale: Number of men in the colony = 5/7 * 70 = 50.
Number of women in the colony = 2/7 * 70 = 20.
Number educated women in the colony = 1/5 * 30 = 6.
Number of uneducated women in the colony = 4/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 50 - 10 = 40.
Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4.
Answer:A
Answer: A
Question: Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 32% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?
Options:
A)60%
B)72%
C)88%
D)95%
E)110%
Rationale: Let x be the number of new biographies added to the library.
Let b be the original number of biographies, so the original number of books was 5b.
0.32(5b+x) = b+x
0.6b = 0.68x
x = 0.88b
The answer is C.
Answer: C
Question: Which of the following is the best approximation for y?
1/2−1/3+1/6−1/10+1/12−1/14+1/16
Options:
A)0.1
B)0.31
C)0.35
D)0.4
E)0.6
Rationale: 1/2 - 1/3 +1/6-1/10+1/12-1/14+1/16
=> 1/2 [1+1/3-1/5+1/6-1/7+1/8] - 1/3
=> 0.5 [ 1+0.33-0.2+0.167-0.142+0.125] - 0.33
=> 0.31
Option B
Answer: B
Question: The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test.
You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it?
Options:
A)48%
B)55%
C)60%
D)71%
E)80%
Rationale: C
60%
In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability.
In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already.
Therefore, P(Second/First) = P (First and Second)/ P (First)
= 0.25/0.42
=0.60
=60 %
Answer: C
Question: How many different possible arrangements can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?
Options:
A)360
B)720
C)900
D)1800
E)5040
Rationale: A= all possible permutations = 7!/2!2!
B= permutations with II together = 6!/2!
A-B = 900
ANSWER:C
Answer: C