divelab/Sys2Bench huggingface dataset:
Question: In a certain pond, 35 fish were caught, tagged, and returned to the pond. A few days later, 35 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
Options:
A)400
B)625
C)875
D)2500
E)10 000
Rationale: If x is total number of fish in the pond :
4 = 35/x * 100
=> x = 875
So answer is C
Answer: C
Question: What is the value 201st term of a sequence if the first term of the sequence is 2 and each successive term is 3 more the term immediately preceding it?
Options:
A)600
B)602
C)604
D)606
E)608
Rationale: The nth term is 2+3*(n-1).
The 201st term is 2 + 3(200) = 602
The answer is B.
Answer: B
Question: For all integers a and b, a%b = (a + b)(a - b). If 6%x = 11, then which of the following could be a value of x?
Options:
A)-5
B)-3
C)2
D)3
E)6
Rationale: 6%x = (6+x)(6-x)
36-x^2 = 11
x^2 = 25
x=-5,5
Ans: A
Answer: A
Question: If two projectiles are launched at the same moment from 1182 km apart and travel directly towards each other at 460 km per hour and 525 km per hour respectively, how many minutes will it take for them to meet?
Options:
A)68
B)72
C)76
D)80
E)84
Rationale: The projectiles travel a total of 985 km per hour.
The time to meet is 1182/985=1.2 hours = 72 minutes
The answer is B.
Answer: B
Question: In how many different ways can the letters of the word "CLAIM" be rearrangement?
Options:
A)100
B)120
C)140
D)150
E)160
Rationale: The total number of arrangements is
5P5 = 5! = 120
B)
Answer: B
Question: The length of a rectangle is three times of its width. If the length of the diagonal is 8√10 then find the perimeter of the rectangle.
Options:
A)77 cm
B)88 cm
C)64 cm
D)11 cm
E)18 cm
Rationale: Let Breadth = x cm,
then, Length = 3x cm
x2+(3x)2=(810−−√)2=>10x2=640=>x=8
x2+(3x)2=(810)2=>10x2=640=>x=8
So, length = 24 cm and breadth = 8 cm
Perimeter = 2(l+b)
= 2(24+8) = 64 cm
Answer:C
Answer: C
Question: The music class consists of 4 girls and 8 boys. How many ways can a group of 3 be formed if it has to include at least one boy?
Options:
A)155
B)158
C)161
D)165
E)216
Rationale: Reverse combinatorics approach is preferred method on this one
Note that at least 1 boy gives clue to using this method
All combinations - four girls = answer
All combinations is 12C3 = 220
All girls 4C3 = 4
So our answer is 220-4 = 216
Hence, answer is (E)
Answer: E
Question: The average (arithmetic mean) monthly income of four workers is $2,600. After one worker’s income increases by 20 percent the new average income is $2,800. What was the original income of the worker whose monthly income increased?
Options:
A)$4,000
B)$4,500
C)$4,100
D)$4,300
E)$5,000
Rationale: Increase in total income was 200*4=$800, we know that this increase was 20% (1/5th) of the workers original income, thus his/her original income was 800*5=$4,000.
Answer: A
Answer: A
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)11 1/2 min
B)11 1/4 min
C)11 2/4 min
D)11 1/5 min
E)11 7/4 min
Rationale: 3/12 + x/15 = 1
x= 11 1/4
Answer: B
Answer: B
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor.
Options:
A)10
B)12
C)14
D)16
E)17
Rationale: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
B
Answer: B
Question: Which of the following CANNOT be weighed using a balance scale and these unit weights: 2, 4, 7, and 10
Options:
A)16
B)15
C)18
D)19
E)21
Rationale: A. 13 (can be weighed by keeping weights of 10, 2 and 4 )
B. 15 (cannot be weighed)
C. 17 (can be weighed by keeping weights of 10 and 7 kg)
D. 19(can be weighed by keeping weights of 10, 2 and 7 kg)
E. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)
B
Answer: B
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
A)118 km
B)162 km
C)1767 km
D)1887 km
E)177 km
Rationale: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer: B
Answer: B
Question: Bill is golfing with three friends and can either buy generic golf tees that are packaged by the dozen or the higher quality Aero flight tees that come by the pair. What is the minimum number of packages of Aero flight tees Bill must purchase to ensure that he has at least 10 golf tees for each member of his foursome, if he will buy no more than 3 packages of the generic golf tees?
Options:
A)16
B)10
C)8
D)4
E)2
Rationale: At least 10 golf tees for each member of his foursome = total of at least 4*10 = 40 tees.
3 packages of the generic golf tees, that are packaged by the dozen = 3*12 = 36 tees.
So, Bill must by at least 16 Aero tees. They come by the pair, hence he must by at least 4/2 = 2 packages of Aero flight tees.
Answer: E.
Answer: E
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
Options:
A)27
B)76
C)82
D)80
E)23
Rationale: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240
= 80
Answer:D
Answer: D
Question: Jack splits his bucket of apples into 5 groups of equal size, but has 2 left over. The next day, he repeats the process with a bucket that contains exactly 3 times as many apples as the day before. How many does he have left over this time?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Set x = to number of apples in his basket, and y to be the number of apples per group.
x = 5*y +2.
3x = 15*y+6
3x = 3*5*y + 6
3x = 5(3(y+1))+1
Remainder is then 1, so option B.
Answer: B
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 9 m x 6 m x 22.5 cm?
Options:
A)6400
B)6410
C)6440
D)7200
E)6800
Rationale: Number of bricks = Volume of Wall/Volume of Bricks
=900x600x22.5/25x11.25x6= = 7200
answer :D
Answer: D
Question: The price of sugar is increased by 8%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
Options:
A)(800/108) %
B)(107/100) %
C)(100/107)%
D)(7/100)%
E)(100/700)%
Rationale: Old price = $100 (assume);
Old consumption = 1 kg (assume).
New price = $108.
We want the spendings to remain at $100.
(New consumption)*108 = 100 --> (New consumption) = 100/108 kg.
Percent decrease = Change/Original *100 = (1 - 100/108)/1*100 = 800/108%.
Answer: A.
Answer: A
Question: Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 15%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?
Options:
A)$146.6
B)$120
C)$180
D)$220
E)$260
Rationale: Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/12*(A+E) ==> 11A = 13E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 22 + 1.15E ==> 11A =220 +11.5E -------(2)
Substituting (1) in (2):
13E = 220+11.5E ==>1.5E= 220 or E =440/3 =146.6
A
Answer: A
Question: Eleven books consisting of 2 financial management, 4 marketing management and 5 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.
Options:
A)1/1455
B)1/1355
C)1/2255
D)1/1155
E)1/5040
Rationale: Since the denominator will be 11! . And there is no way to divide 11 from numerator and denominator. Use a multiple of 11 in the denominator only answer
D
Answer: D
Question: P and Q invested in a business. The profit earned was divided in the ratio 3 : 5. If P invested Rs 12000, the amount invested by Q is
Options:
A)30000
B)50000
C)40000
D)20000
E)60000
Rationale: Let the amount invested by Q = q
12000:q=3:5
⇒12000×5=3q
⇒q=(12000×5)/3=30000
Answer is A
Answer: A
Question: A single discount equivalent to the discount series of 20%, 10% and 8% is?
Options:
A)31.6
B)31.0
C)31.6
D)31.1
E)33.76
Rationale: 100*(80/100)*(90/100)*(92/100)
= 68.4
100 - 66.24 = 33.76
Answer: E
Answer: E
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
Options:
A)1 hour
B)2 hour
C)3 hour
D)4 hour
E)5 hour
Rationale: Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/3
3 --------- ? è 1 hour
Option A
Answer: A
Question: What is the value of (P + Q)/(P - Q) if P/Q is 6?
Options:
A)4/3
B)2/3
C)2/6
D)7/5
E)8/7
Rationale: (P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]
= (6 + 1)/(6 - 1)
= 7/5
ANSWER:D
Answer: D
Question: Two brothers took the GMAT exam, the higher score is R and the lower one is S. If the difference between the two scores is equal to their average, what is the value of S/R ?
Options:
A)3
B)2
C)1/2
D)1/3
E)There isn't enough data to answer the question.
Rationale: Answer is D : 1/3
R - S = (R + S)/2
Solving for S/R = 1/3
D
Answer: D
Question: If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3?
I. 1
II. -1
III. 2
Options:
A)II only
B)III only
C)I and II only
D)II and III only
E)I and III only
Rationale: Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.
n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.
It can be 1 for n=2 and 2 for n=5.
Answer: E.
Answer: E
Question: If x and y are integers and x + y = 8, which of the following must be true?
Options:
A)x and y are consecutive integers.
B)Both x and y are even.
C)If x > 0, then y < 0.
D)If x < 0, then y > 0.
E)Both x and y are less than 5.
Rationale: In option C if x > 0,then y<0 means x is +ve and y is -ve
In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.
How option D is right could you explain
Answer: D
Question: The probability is 0.6 that an “unfair” coin will turn up tails on any given toss. If the coin is tossed 3 times, what is the probability that at least o ne of the tosses will turn up tails?
Options:
A)0.064
B)0.36
C)0.64
D)0.784
E)0.936
Rationale: probability that at least one of the tosses will turn up tails = 1 - probability that all will be heads
= 1 - (0.4*0.4*0.4)
= 1 - 0.064
= 0.936 E
Answer: E
Question: if 4y = 12x + 20,4x + 2y = 20 ,what is the value of y?
Options:
A)8.5
B)6
C)7
D)8
E)9
Rationale: solution:
I---> y = 3x + 5
sub in II
4x + 2(3x + 5) = 20
10x = 10
x = 1
sub x=1 in other equation
4y = 12(1) + 20
y = 8
answer is D
Answer: D
Question: The radius of a wheel is 20 cm. What is the distance covered by the wheel in making 500 resolutions?
Options:
A)708 m
B)704 m
C)314.3 m
D)714 m
E)744 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 20 = 31428.5 cm
= 314.3 m
Answer:C
Answer: C
Question: Half of 4 percent written as decimal is
Options:
A)0.02
B)0.5
C)0.05
D)0.005
E)None of these
Rationale: Explanation:
It will be 1/2(4%) = 1/2(4/100) = 4/200 = 0.02
Answer: Option A
Answer: A
Question: The pages of a report are numbered consecutively from 1 to 6. If the sum of the page numbers up to and including page number x of the report is equal to one less than the sum of the page numbers following page number x, then x =
Options:
A)4
B)5
C)6
D)3
E)2
Rationale: sum of the first few numbers =1+2+3+4 =10
sum of the last few = 5 +6 =11 page no.4 answer .A
Answer: A
Question: Kelvin earns $60 a week from his job. His income increased and now makes $70 a week. What is the percent increase?
Options:
A)16.66%
B)20%
C)22.5%
D)23%
E)24.5%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
A
Answer: A
Question: Suraj has a certain average of runs for 16 innings. In the 17th innings he scores 112 runs thereby increasing his average by 6 runs. What is his average after the 17th innings?
Options:
A)18
B)25
C)16
D)72
E)27
Rationale: To improve his average by 6 runs per innings he has to contribute 16 x 6 = 96 runs for the previous 16 innings.
Thus, the average after the 17th innings
= 112 - 96 = 16.
ANSWER:C
Answer: C
Question: In a group of ducks and cows, the total number of legs are 8 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)5
B)4
C)6
D)3
E)2
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 8
=> 2x = 8 => x = 4
B
Answer: B
Question: Agnes has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?
Options:
A) 32
B) 30
C) 29
D) 28
E) 27
Rationale: 5v + 10y = 460
v > y
Pick an easy number to work with.
suppose v=30.
Then you have 150.
You need another 310 and that means you need y=31 which is greater than v.
Therefore, v > 30.
The only answer choice where v > 30 is if v = 32.
A is the answer.
Answer: A
Question: If a positive integer n is divisible by both 3 and 5, then n must also be divisible by which of the following?
I. 15
II. 8
III. 45
Options:
A)None
B)I only
C)II only
D)I and II
E)II and III
Rationale: A multiple of 3 and 5 is also a multiple of 15, but not necessarily a multiple of 8 or 45.
The answer is B.
Answer: B
Question: If a supermarket shows $49 of sales for apples, and on that same day there are sales of $64 in oranges. What is the ratio of sales for apples to oranges?
Options:
A)1 : 2
B)2 : 3
C)4 : 7
D)1 : 5
E)None
Rationale: Solution
Let us name the apples
as A and the oranges as B.	= (A'S sales) : (B's sales)
=âˆšb : âˆša
= âˆš49 : âˆš64
= 7 : 8
Answer E
Answer: E
Question: 6 highschool boys gather at the gym for a game of mini-volleyball. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?
Options:
A)27
B)51
C)90
D)45
E)450
Rationale: Arrange the 6 boys in a straight line in 6! ways.
The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)
Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.
You get 6!/(2! * 2! * 2!) * 2! = 45
Answer (D)
You get 6!/(2! * 2! * 2!) * 2!
Answer : D
Answer: D
Question: A corporation paid $9 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?
Options:
A) 6%
B) 14%
C) 20%
D) 23%
E) 14%
Rationale: Difference in Ratios = (30/150) - (9/50) = (1/50)
% Change = (Change (1/50) / Original ratio (7/50)) *100 = 14%
Answer - E
Answer: E
Question: Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Options:
A)1000
B)1055
C)1065
D)1075
E)1080
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055.
B)
Answer: B
Question: Find the total number of prime factors in the expression (4)11 x (7)5 x (11)2.
Options:
A)22
B)29
C)19
D)5
E)2
Rationale: (4)11x (7)5 x (11)2 = (2 x 2)11 x (7)5 x (11)2 = 211 x 211 x75x 112
= 222 x 75 x112
Total number of prime factors = (22 + 5 + 2)
= 29.
ANSWER B 29
Answer: B
Question: Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $109300, how many months will it take Joan to pay back her mortgage?
Options:
A)7
B)8
C)10
D)11
E)13
Rationale: Joan starts off with 100 $ .. which is to be tripled every month
Her monthly payments look like this :
100 , 300 , 900 , 2700 ......... Upto 109300
This can be re written as :
100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 1093
So we have 1 , 3 , 9 , 27 ..... 109300 in GP
We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)
Therefore to find the Sum of n terms of a GP we use this formula :
Sn = a (1-r^n) / 1 -r
Using this and plugging in the information we get ...
1093 = 1 - 3^n / 1-3 ; 1-3^n / -2
Cross multiplying we get
1093 x -2 = 1- 3^n
- 2186 = 1 - 3^n
- 2187 = - 3 ^n
2187 = 3 ^n (negatives cancel out)
2187 can also be re written as 3 ^ 7
Therefore ; 3 ^7 = 3 ^n
Thus n = 7 (A)
Answer: A
Question: Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8210/-. Find out the amount that he borrowed.
Options:
A)s. 5331
B)s. 5269
C)s. 5228
D)s. 5218
E)s. 52192
Rationale: Explanation:
Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)
By formula of simple interest, S.I. = PRT / 100
Where P = The principal, R = Rate of interest as a %, T = Time in years
S.I. = (P * 6 * 9)/100 = 54 P/100
Amount = Principal + S.I.
8210 = P + (54P/100)
8210 = (100P + 54P)/100
8210 = 154P/100
P = (8210 * 100)/154 = Rs. 5331.169
ANSWER: A
Answer: A
Question: If G is a negative integer, which of the following must be a negative integer?
Options:
A)G + 1
B)G/2+3
C)G^4
D)G – y
E)G^11
Rationale: We need to check each option here:
A. G + 1
This will depend on the value of G. Nothing can be said
B. G/2+3
This will depend on the value of G. Nothing can be said
C. G^4
This will always be positive. Even powers of negative numbers are positive and odd powers are negative
D. G – y
This will depend on the value of G. Nothing can be said
E. G^11
This will always be negative. Even powers of negative numbers are positive and odd powers are negative
Correct Option: E
Answer: E
Question: Mary has 1803 dollars with her. What is the amount that she should keep with her inorder to distribute the same among nine kids equally?
Options:
A)3
B)0
C)10
D)2
E)6
Rationale: The answer is 3. (1803-3=1800). 1800 is divisible by nine which gives an answer of 20.So,she will be distributing 20 each for the nine kids and the remaining 3 will be left with her. So the answer is A=3
Answer: A
Question: Circles X and Y are concentric. If the radius of circle X is two times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?
Options:
A)13
B)Pi/3
C)Pi/2
D)5/6
E)3/4
Rationale: Small circle radius = a, so area = PI a ^ 2
Large circle radius = 2a, so area =4. PI a ^ 2
Area of shaded region = 4PI a^2 - PI a^2 = 3 PI a^2
So, probability = ( 3 PI a^2 ) / (4 PI a^2 )
= 3/4 = Answer = E
Answer: E
Question: The average age of three boys is 15 years. If their ages are in ratio 3:5:7, the age of the youngest boy is
Options:
A)21 years
B)18 years
C)15 years
D)9 years
E)None
Rationale: Solution: Sum of ages of three boys = 45 years
Now, (3x+5x+7x) = 45
Or, 15x = 45
Or, x = 3
So, age of youngest boy = 3x = 3*3 = 9 years.
Answer: Option D
Answer: D
Question: A snail, climbing a 66 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?
Options:
A)42
B)63
C)77
D)80
E)91
Rationale: total transaction in two days = 4-2 = 2 feet
in 62 days it will climb 62 feet
on the 63rd day , the snail will climb 4 feet , thus reaching the top
therefore , total no of days required =63
B
Answer: B
Question: A jar of 364 marbles is divided equally among a group of marble-players today. If 2 people joined the group in the future, each person would receive 1 marble less. How many people are there in the group today?
Options:
A)20
B)22
C)24
D)26
E)28
Rationale: 364 = 26*14 = 28*13
There are 26 people in the group today.
The answer is D.
Answer: D
Question: Mary replaced 20% of an 60% juice concentrate with water. Upon finding the resultant juice too sweet, she further replaced 30% of this solution with water, then fine tuned it by replacing 10% of that solution with water.
What is the final juice concentration Mary liked best?
Options:
A)25.5%
B)41.68%
C)30.24%
D)21%
E)39.54%
Rationale: The answer can be quickly calculated as: (60)(0.8)(0.7)(0.9)
How it works: By calculating how much juice is removed from an assumed 100 ml mixture, we can find out the final percentage.
In step 1, 20% of a 60% juice concentrate is replaced with water. With 100 ml of juice concentrate, this translates to removing 20% of juice, or rather keeping 80% of it. Hence, we multiply 60x0.8 = 48 ml.
In step 2, 30% of the solution is mixed with water. This translates to keeping 70% of the concentrate. Hence, 48x0.7 = 33.6 ml.
Finally in step 3, 10% of the solution is replaced with water. This means 90% of the concentrate remains. So, final amount of concentrate = 33.6x0.9 = 30.24 ml.
30.24 ml of concentrate in a 100 ml solution makes 30.24%
Answer: C
Answer: C
Question: A can contains a mixture of liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter M of liquid A was contained by the can initially?
Options:
A)10
B)20
C)21
D)25
E)27
Rationale: As A:B::7:5 ---> only option C is a multiple of 7 and hence it is a good place to start. Also A:B::7:5 means that , A = (712)*Total and B = (5/12)*Total
If A = 21 , B = 15 ---> remove 9 litres ---> you remove (7/12)*9 of A ---> A remaining = 21-(7/12)*9 = 63/4
Similarly, for B, you remove (5/12)*9 ---> B remaining = 15 - (5/12)*9 = 45/4 and then add 9 more litres of B ---> 9+45/4 = 81/4
Thus A/B (final ratio) = (45/4)/(81/4) = 7:9 , the same as the final ratio mentioned in the question.
Hence C is the correct answer.
A/B = 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9), where 7x and 5x are initial quantities of A and B respectively.
Thus, 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9) ---> giving you x=3. Thus A (original) M= 7*3 = 21.C
Answer: C
Question: A person want to give his money of $1000 to his 4 children A,B,C,D in the ratio 2:4:3:1. What is the A+D share?
Options:
A)$100
B)$200
C)$300
D)$500
E)$600
Rationale: A's share = 1000*2/10 = $200
D's share = 1000*1/10 = $100
A+D = $300
Answer is C
Answer: C
Question: [(13/2 ÷ 1/2 × 13/2)]/[(13/2 × 1/2 ÷ 13/2)] = ?
Options:
A)159
B)149
C)169
D)179
E)189
Rationale: Explanation:
[(13/2 ÷ 1/2 × 13/2)]/[(13/2 × 1/2 ÷ 13/2)]
= [13/2 × 2/1 × 13/2]/[13/2 × 1/2 × 2/13]
= 169/2 / 1/2 = 169/2 x 2/1 = 169
Answer: Option C
Answer: C
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o'clock noon?
Options:
A)180°
B)120°
C)160°
D)170°
E)150°
Rationale: The angle traced by the hour hand in 12 hours is 360°, which is 30° per hour.
In 4 hours, the angle traced by the hour hand is 4×30° = 120°
The answer is B.
Answer: B
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Options:
A)20/9
B)40/9
C)50/9
D)60/9
E)80/9
Rationale: one day work of A = 1/8
one day work of B = 1/10
so one day work of A and B together = 1/8 + 1/10 = 9/40
so total days required = 40/9
ANSWER:B
Answer: B