divelab/Sys2Bench huggingface dataset:
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
Options:
A)187 m
B)420 m
C)197 m
D)167 m
E)186 m
Rationale: Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer: B
Answer: B
Question: What is the present worth of Rs. 176 due in 2 years at 5% simple interest per annum
Options:
A)110
B)120
C)150
D)160
E)None of these
Rationale: Explanation:
Let the present worth be Rs.x
Then,S.I.= Rs.(176 - x)
= (x*5*2/100) = 176 - x
= 10x = 17600 - 100x
= 110x = 17600
x= 160
Answer:D
Answer: D
Question: if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Options:
A)11x/y
B)10x/y
C)x/11y
D)11/xy
E)xy/11
Rationale: Answer is B.
The rate of running hards: 10 minutes per y hards.
Thus the time for running x hards = x hards * 10 minutes/y hards = 10x/y
Answer: B
Question: The weight of four dogs is determined to be 25 pounds, 31 pounds, 43 pounds and 41 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?
Options:
A)31
B)33
C)35
D)37
E)39
Rationale: Total weight of the 4 dogs = (25+31+43+41) = 140
Avg = 140/4 = 35
Total weight of 5 dogs = 140+y or 4(35)+y
Average of 5 dogs as per Question = 35
Equation:
4(35) + y = 5 (35), or y = 35.
Choose C
Answer: C
Question: What is the slope of a line on a standard
xy-plane that passes through the point
(1, 3) and (4, –3)?
Options:
A)-1
B)2
C)-2
D)1/2
E)-1/2
Rationale: Plug the values for the coordinates into the formula for the slope of a line:
Slope=y2-y1/x2-x1=-3-3/4-1=-6/3=-2
correct answer C)-2
Answer: C
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
Options:
A)200 m
B)700 m
C)800 m
D)100 metre
E)400 m
Rationale: Explanation:
A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: D
Question: Simplify: (4 – 5) – (13 – 18 + 2).
Options:
A)5
B)4
C)-3
D)2
E)-1
Rationale: (4 – 5) – (13 – 18 + 2).
= -1-(13+2-18).
= -1-(15-18).
= -1-(-3).
= -1+3.
= 2.
correct answer D
Answer: D
Question: I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?
Options:
A)600
B)700
C)800
D)900
E)None
Rationale: Solution:
Let xx be the number I chose, then
x/5−154=6
x/5=160
x=800
Answer C
Answer: C
Question: A rower can row upstream at 7 km/hr and downstream at 13 km/hr. What is the rower's rate in still water?
Options:
A)8 km/hr
B)9 km/hr
C)10 km/hr
D)11 km/hr
E)12 km/hr
Rationale: The rate in still water is 1/2 * (13 + 7) = 10 km/hr
The answer is C.
Answer: C
Question: A work as fast as B. If B can complete a work in 12days independently,the number of days in which A and B can together finish the work in?
Options:
A)2days
B)3days
C)4days
D)5days
E)6days
Rationale: Ratio of rates of working of A and B = 2:1
ratio of times taken = 1:2
A's 1day work = 1/6
B's 1day work = 1/12
A+B 1day work = 1/6 + 1/12 = 3/12 = 1/4
A and B can finish the work in 4days
Answer is C
Answer: C
Question: The equation of line f is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line f?
Options:
A)48
B)50
C)60
D)75
E)100
Rationale: This can be solve in two steps and without any complex calculation.
Given : equation of line f as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).
This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)
So a perpendicular from the (0,0) to hypotenuse will be the answer.
Area of triangle= 0.5*100*75=0.5*125* x
=> x=60;
SO answer is 60=C
Answer: C
Question: seven children, Arya, Betsy, Chen, Daniel, Emily, and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?
Options:
A)240
B)480
C)540
D)720
E)840
Rationale: Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..
total ways = 6!..
ways B and E will be sitting together..
take both B and E as one, then these two together with other 4 can sit in 5! ways ...
Also B and E can sit within themselves in 2! ways..
so the answer required = 6!-2*5!=540..
ans C
Answer: C
Question: There are 1000 doors that are of the open-close type. When a person opens the door he closes it and then opens the other. When the first person goes he opens-closes the doors in the multiples of 1 i.e., he opens and closes all the doors. when the second goes he opens and closes the doors 2, 4 6 8 respectively. Similarly when the third one goes he does this for 3 6 9 12 15th doors respectively. Find number of doors that are open at last.
Options:
A)29
B)31
C)32
D)24
E)21
Rationale: 31. only the perfect squares between 1 to 1k
ANSWER:B
Answer: B
Question: If the simple interest on a sum of money at nineteen percent per annum for two years is Rs.12000, compound interest on the same sum for the same period at the same rate of interest is
Options:
A)13,041.00
B)11,430.00
C)13,410.00
D)11,340.00
E)13,140.00
Rationale: S I for 2 years = 12000 ie for one year =6000
The compound interest for Rs.6000 for the second year = 6000*19/100 = 1140
The CI for two years 12000+1140 = 13,140.00
ANSWER:E
Answer: E
Question: How much time will take for an amount of Rs. 360 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options:
A)8 years
B)4 years
C)3 years
D)9 years
E)5 years
Rationale: Time = (100 * 81) / (360 * 4.5)
= 5 years
Answer: E
Answer: E
Question: Two buses and a van were employed to transport a class of students on a field trip. 2/5 of the class boarded the first bus. 2/3 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
Options:
A)a) 1/2
B)b) 2/3
C)c) 11/15
D)d) 6/10
E)e) 4/5
Rationale: This is a pure ratio question (we aren't given any numbers for anything), so you can just choose any starting number you like, and use it to solve the problem. The best number to pick is almost always the product of all the denominators of your fractions, so here we could start with 30 students. Then we have:
• 2/5 of these, or 12 students, board the first bus
• there are 18 students left. 2/3 of these, or 12 students, board the second bus
• this bus breaks down, and 1/2 of the 12 students, or 6 students, board the first bus
• the first bus now contains 18 out of the original 30 students, so the answer is 18/30 = 6/10
Answer D
Answer: D
Question: Ravi purchased 20 dozens of toys at the rate of Rs. 380 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Options:
A)23%
B)1.2%
C)5.6%
D)4.21%
E)12.2%
Rationale: D
C.P. of 1 toy = 380/12 = Rs. 31.6
S.P of 1 toy = Rs. 33
Profit = 1.33/31.25 * 100 = 4.21%
Answer is D
Answer: D
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
Options:
A)36
B)24
C)12
D)6
E)8
Rationale: x, 2x
(x-2):(2x-2) = 1:3
ANSWER C
Answer: C
Question: If (x-14)(x-3) < 0, which of the following must be true?
Options:
A)x^2 + 5x + 6 < 0
B)14-x > 0
C)5 - x < 0
D)x - 5 < 0
E)11 - x > 0
Rationale: (x-14)(x-3)<0 can be written as (14-x)(x-3)>0
So,to inequality hold true multiple of (14-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<14
Answer Choice E matched which says 14-x>0 or x<14,which must be true (I started to look from E to A for making easy decision first)
Correct Answer B
Answer: B
Question: A firm has 4 senior partners and 5 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
Options:
A)66
B)74
C)82
D)90
E)98
Rationale: The total number of ways to form a group of 3 is 9C3 = 84
The number of groups without a senior partner is 5C3 = 10
The number of groups which include a senior partner is 84-10 = 74
The answer is B.
Answer: B
Question: 3251+587+369-?=3007
Options:
A)1250
B)1300
C)1375
D)1200
E)None of them
Rationale: Let 4207-x=3007
then x=4207-3007
=1200
Answer is D
Answer: D
Question: By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
Options:
A)Rs. 110
B)Rs. 120
C)Rs. 140
D)None of these
E)Not determined
Rationale: Explanation:
Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.
Answer is D
Answer: D
Question: A certain experimental mathematics program was tried out in 2 classes in each of 42 elementary schools and involved 55 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
Options:
A)0 and 13
B)0 and 14
C)1 and 10
D)1 and 9
E)2 and 8
Rationale: One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat.
To find out the greatest value you should count the total classes (42*2=84), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (84-55=29). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is 29/2 = 14.5. So the greatest possible value of the # of teachers who had 3 classes is 14.
Only answer B has this option.
Answer: B
Question: If the number 617*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
Options:
A)3
B)1
C)2
D)4
E)5
Rationale: Sum of digits = (6 + 1 + 7 + x + 3 + 2 + 4) = (23 + x), which must be divisible by 3.
x = 1.
B
Answer: B
Question: The compound interest on Rs.30,000 at 7% per annum is Rs.4347. The period (in years) is
Options:
A)2
B)2½
C)3
D)4
E)5
Rationale: Solution
Amount	=Rs(30000 + 4347)
= Rs.34347.
Let the time be n years.
Then, 30000(1+7/100)^n
= 34347.
=34347/3000
=11449/1000
=(107/100)^n
n= 2years.
Answer A
Answer: A
Question: A certain company had a total annual expenditure of 2.1∗10^7 on employee salaries last year. If the company employed 420 people, what was the average employee salary?
Options:
A)$20,000
B)$25,000
C)$35,000
D)$40,000
E)$50,000
Rationale: Given: Total annual expenditure of 2.1∗10^7 on employee salaries
Total employees = 420
Observe that 420*5 = 2100
Therefore try to bring the numerator in terms of 2100
Average salary = (2100*10^4) /420 = 5*10^4 = 50,000
Option E
Answer: E
Question: Three years ago the average age of a class of six members was 19 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 6 * 22 = 132
7 * 19 = 133
`1
A
Answer: A
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person?
Options:
A)95 kg
B)90 kg
C)85 kg
D)Data inadequate
E)None of these
Rationale: A
95 kg
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (75 + 20) kg = 95 kg.
Answer: A
Question: If y > 0, which of the following could be true?
I. y^3 > y^2
II. y^2 = y
III. y^2 > y^3
Options:
A)I only
B)III
C)IIIII
D)All of the above
E)None of the above
Rationale: 1. y^3 > y^2 Well this is true for all y > +1 (but not for values 0 < y < 1)
2. y^2 = y This is true for only one positive number, 1
3. y^2 > y^3 Again this is true only for values of x such that 0 < y < 1
So the answer is D, since there exists at least one value of y which satisfies the equation/ in equation(s)
Answer: D
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 600 per sq. metre.
Options:
A)Rs. 12375
B)Rs. 15550
C)Rs. 15600
D)Rs. 16500
E)None of these
Rationale: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (600 × 20.625) = 12375. Answer A
Answer: A
Question: Bhajan Singh purchased 120 reams of paper at Rs.80 per ream. He spent Rs.280 on transportation, paid octroi at the rate of 40 paise per ream and paid Rs.72 to the coolie. If he wants to have a gain of 8% , what must be the selling price per ream ?
Options:
A)Rs.86
B)Rs.87.48
C)Rs.89
D)Rs.90
E)None
Rationale: Explanation:
C.P of 120 reams = Rs.(120×80+280+72+120×0.40)= Rs.10000.
C.P. of 1 ream = 10000/120= Rs.250/3
S.P. of 1 ream = Rs.108/100×250/3=Rs.90
Correct Option : D
Answer: D
Question: 2.205 divided by 0.3 gives
Options:
A)7.35
B)6.25
C)8.15
D)6.95
E)None of these
Rationale: Explanation :
2.205/0.3 = 22.05/3 = 7.35. Answer : Option A
Answer: A
Question: The average of 11 results is 52, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
A)A)46
B)B)34
C)C)66
D)D)76
E)E)74
Rationale: 1 to 11 = 11 * 52 = 572
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 572 = 34
Answer:B
Answer: B
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
Options:
A)34500
B)24000
C)24098
D)23007
E)24098
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000)
= Rs. 24000
Answer:B
Answer: B
Question: Of the 5 numbers, whose average is 75, the first is one-fourth of the sum of the last 4. The first number is?
Options:
A)75
B)80
C)78
D)56
E)67
Rationale: Total of 5 numbers = 5 * 75 = 375
Let total of last 4 numbers = x
1st number = x/4
x+ x/4 = 375
5x = 1500 => x =300
1st number = 300/ 4 = 75
Answer :A
Answer: A
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)39%
B)41%
C)60%
D)70%
E)88%
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: Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?
Options:
A)The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 – 2m + 1
B)The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 – 2m + 1.
C)The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1
D)The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1
E)None
Rationale: Explanation :
Given,
=> a + b + c + d = 4m + 1. now squaring this equation:
=> (a+b+c+d)2 = 16m2 + 8m + 1.
=> a2 + b2 + c2 + d2 + 2*( ab + ac + ad + bc + bd + cd ) = 16m2 + 8m + 1.
using the fact that product of two numbers is maximum when they are equal / nearly equal,
expression ab + ac + ad + bc + bd + cd will be maximum when ab , ac , ad, bc , bd , cd will be maximum and this is possible when a, b, c, d are nearly equal to each other. i.e. m , m , m , m+1.
when ab + ac + ad + bc + bd + cd is maximum , obviuosly , a2 + b2 + c2 + d2 will be minimum.
Put values in the above equation we get that the minimum value of a2 + b2 + c2 + d2 comes out to be 4m2 + 2m + 1.
Answer : C
Answer: C
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 1 and 50?
Options:
A)500
B)625
C)750
D)550
E)600
Rationale: numbers are 1,3,5-------,47,49
Average of the set: (largest+smallest)/2=(49+1)/2=25;
# of terms: (largest-smallest)/2+1=(49-1)/2+1=25
The sum = 25*25= 625
Answer: B
Answer: B
Question: Find the area of a cuboid of length 8cm , breadth 6 cm . and height 9cm.
Options:
A)400 cm cube
B)410 cm cube
C)420 cm cube
D)432 cm cube
E)480 cm cube
Rationale: Area of a cuboid = lxbxh =8cm x 6cm x 9cm = 432 cm cube
answer :D
Answer: D
Question: If 10a = 6b = 20, then 120ab =
Options:
A)800
B)1000
C)1200
D)1400
E)1600
Rationale: 10a * 6b = 20 * 20 = 400
60 ab = 400
i.e. 120 ab = 800
Answer: Option A
Answer: A
Question: Positive integer x has n factors; 3x has 3 factors; Which of the following values can n take?
I. 1
II. 2
III. 3
Options:
A)I only
B)II only
C)I or II
D)II or III
E)I or III
Rationale: Squares have odd number of factors.The square which is a multiple of 3 is 9.
3 has factors 1,3 .
Therefore 2 factors
Answer B
Answer: B
Question: In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?
Options:
A)720
B)420
C)320
D)520
E)None of these
Rationale: The word 'LEADING' has 7 letters. It has the vowels 'E','A','I' in it and these 3 vowels should always come together. Hence these 3 vowels can be grouped and considered as a single letter. that is, LDNG(EAI).
Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters
=5!=5×4×3×2×1=120
In the 3 vowels (EAI), all the vowels are different. Number of ways to arrange these vowels among themselves
=3!=3×2×1=6
Hence, required number of ways=120×6=720
Answer : A
Answer: A
Question: If P(A) = 2/15, P(B) = 7/15, and P(A âˆª B) = 16/15 Find P(A|B)
Options:
A)1/2
B)16/7
C)3/2
D)4/5
E)4/7
Rationale: P(A|B) = P(A âˆª B)/P(B)
P(A|B) = (16/15)/(7/15) = 16/7.
B
Answer: B
Question: Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 6 times the amount of the second solution?
Options:
A)62
B)65
C)68
D)70
E)72
Rationale: SOL:
Lets assume that 60L of sol1 was mixed with 10L of sol2.
Alcohol in Sol1: 60*3/4 = 45L
Alcohol in Sol2: 10*2/5 = 4L
Total Alcohol in the mixed solution of 70L = 45 + 4 = 49L
Alcohol concentration in the new sol: (49/70)*100 = 70%
ANSWER:D
Answer: D
Question: A train covers a distance of 12 km in 16 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)80
B)90
C)60
D)75
E)85
Rationale: Speed = (12/16 * 60) km/hr = (45 * 5/18) m/sec = 12.5 m/sec.
Length of the train = 12.5 * 6 = 75 m.Answer:D
Answer: D
Question: A machine puts c caps on bottles in m minutes. How many E hours will it take to put caps on b bottles?
Options:
A)60bm/c
B)E=bm/60c
C)bc/60m
D)60b/cm
E)b/60cm
Rationale: The machine puts c caps in m minutes or c caps in m/60 hours.
Rate = c/m/60 = 60c/m.
To put b caps the machine will take:-
Time = Work/Rate
T = b/60c/m = bm/60c
Answer is B.
Answer: B
Question: What least number should be added to 1056, so that the sum is completely divisible by 23?
A. B. 3
C. 2	D. 1
Options:
A)4
B)3
C)2
D)0
E)5
Rationale: 1056 ÷ 23 = 45 with remainder = 21
21 + 2 = 23.
Hence 2 should be added to 1056 so that the sum will be divisible by 23
Answer: Option C
Answer: C
Question: What is the ratio between the volumes of a cylinder and cone of the same height and of the same diameter
Options:
A)2:1
B)3:1
C)4:1
D)5:1
E)None of these
Rationale: Explanation:
Volume of cylinder/Volume of cone=3/1
Answer: B
Answer: B
Question: What is the probability of getting a King and a Queen in a single draw of two cards from a pack of well-shuffled cards?
Options:
A)1/16
B)(4C1 * 4C1) / 52C2
C)4/52 * 4/51
D)8C2 / 52 C 2
E)(8 * 7) / 52C2
Rationale: there are 4 kings, so we can choose a king in 4C1 way..
there are 4 Queens, so we can choose a Queen in 4C1 way..
total possible way = 4C1∗4C152C24C1∗4C152C2
B
Answer: B
Question: If a boy lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)6
B)8
C)9
D)10
E)12
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
B
Answer: B
Question: On four consecutive flips of a coin, what is the probability that all four produce the same result?
Options:
A)1/16
B)1/8
C)1/4
D)3/8
E)1/2
Rationale: TTTT case --> P = (1/2)^4 = 1/16
HHHH case --> P = (1/2)^4 = 1/16
P(TTTT or HHHH) = 1/16 + 1/16 = 2/16=1/8
Answer: B
Answer: B
Question: What is the greatest positive integer x such that 4^x is a factor of 64^10?
Options:
A)5
B)9
C)10
D)20
E)30
Rationale: 64^10 = (4^3)^10 = 4^30
ANSWER:E
Answer: E
Question: The average of 6 no.'s is 6.40. The average of 2 of them is 6.2, while the average of the other 2 is 6.1. What is the average of the remaining 2 no's?
Options:
A)2.3
B)2.6
C)6.9
D)4.5
E)4.6
Rationale: Sum of the remaining two numbers = (6.4 * 6) - [(6.2 * 2) + (6.1 * 2)]
= 38.40 - (12.4 + 12.2) = 38.40 - 24.6 = 13.80
Required average = (13.8 / 2) = 6.9
Answer : C
Answer: C
Question: 3889 + 12.952 - ? = 3854.002
Options:
A)47.95
B)49.75
C)45.97
D)47.59
E)45.79
Rationale: Let 3889 + 12.952 - x = 3854.002.
Then x = (3889 + 12.952) - 3854.002
= 3901.952 - 3854.002
= 47.95.
Answer is A
Answer: A
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)1:0
C)1:87
D)1:6
E)1:1
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer: A
Answer: A
Question: The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?
Options:
A)2000
B)3000
C)4000
D)5000
E)6200
Rationale: Explanation:
Let monthly income of A = a
monthly income of B = b
monthly income of C = c
a + b = 2 × 5050 .... (Equation 1)
b + c = 2 × 6250 .... (Equation 2)
a + c = 2 × 5200 .... (Equation 3)
(Equation 1) + (Equation 3) - (Equation 2)
=> a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250)
=> 2a = 2(5050 + 5200 - 6250)
=> a = 4000
i.e., Monthly income of A = 4000
ANSWER IS C
Answer: C