MU-NLPC/Calc-aqua_rat huggingface dataset:
Three seventh of a number is 12 more than 40% of that number. What will be the 90% of that number? Answers.
A) A)148
B) B)210
C) C)189
D) D)248
E) E)258

Solution: 3/7 x – 40/100 x = 12   x = 35 * 12   35 * 12 * 90/100= 
35 * 12 * 90/100 = 378
378/2= 
378/2 = 189
189   ANSWER:189
Answer: C
Bob finishes the first half of an exam in one-fifth the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam? Choices:
A) 20
B) 24
C) 27
D) 36
E) 40

Solution: Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/5's the time of the second half (6/6's), we can see that the hour the entire exam took to finish can be broken down into sixth's. (Another way to look at this problem is via ratio's - first half is 1:6 and the second half is 5:6). With each sixth of an hour being 10 minutes (60/6), the first half of the exam would have taken 20 minutes. Correct answer is 20.
Answer: A
Josh and Dan have a 12 apples each. Together they flip a coin 6 times. For every heads, Josh receives an apple from Dan, and for every tails Dan receives an apple from Josh. After the coin has been flipped 6 times, what is the probability that Josh has more than 12 apples but fewer than 18? Select the correct option:  A) 1/64  B) 15/64  C) 21/64  D) 21/32  E) 5/6

Solution: minimum number of times to win is 4 to have more than 12 apples .   coz: if he wins 3 times => he gets 3 apples and give 3 apples ; no change   so he needs to win 4 times OR 5 times   Not 6 times because ,   if he wins 6 times => he gets 6 apples and he will have 18 apples   Now number of ways to win 4 times out of 6 times 621/644   Now number of ways to win 5 times out of 6 times 621/645   Total number of ways 2626 ways   Probability =(621/644) + (621/645)/2^6   =21/64   Answer :21/64
Answer: C
If 4x+y+z=800, 2x-y-z=40,3x+y-z = 12 for integers of x,y and z, find z =?
Choices:
A) 250 B) 464 C) 525 D) 256 E) 324

Solution: 4x+y+z = 800----------1)   2x-y-z = 40-------------2)   3x+y-z = 12 ------------3)   from 1) and 2)   6x = 840   x = 140 substitute in 1) and 3)   560+y+z = 800   y+z = 240-------4)   420+y-z = 12   y-z = -408-------5)   from 4) and 5)   2z = 648   z = 324   Answer is 324
Answer: E
Bruce and Bhishma are running on a circular track of length 600m. Speed of Bruce is 30 m/s and that of Bhishma is 20 m/s .They start fro the same point at the same time in the same direction. When will they meet again for the first time?	Choose the correct option
A) 30
B) 40
C) 50
D) 60
E) 80

Solution: Actually Arjun has to make a lead of 600 m, because when Arjun will be 600m ahead of Bhishma, they will be together again as a person when completes the total length it starts retracing he same path and thus Arjun and Bhishma can be together again.   Since , they make a difference of 10 m in 1 second. so, he will create 600m difference in 60 second.   60
Answer: D
In an engineering class that contained 100 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?	Choose the correct choice from the following choices:
A) 4 B) 6 C) 8 D) 12 E) 24

Solution: 1st Question : Three fifths of the students answered the first question correctly - so 3/5âˆ—100=60   2nd Question : four fifths of the remainder answered the second question correctly so 4/5âˆ—(100âˆ’60)=4/5âˆ—40=32   total students who answered at least one Q correct =60+32= 
60+32 = 92
92   so students who answered BOTH incorrectly= 100âˆ’92=8   ANSWER:8
Answer: C
How many multiples of 5 are there between 0 and 358? Options
A) 54
B) 75
C) 76
D) 71
E) 58

Solution: 5 * 1= 
5 * 1 = 5
5   5 * 71= 
5 * 71 = 355
355   Total number of multiples= (71 + 1)= 
(71 + 1) = 72
72   Answer 71
Answer: D
Sachin is older than Rahul by 7 years. If the ratio of their ages is 11:9, find the age of Sachin Choose the most appropriate option:
A) 24.5  B) 24.8  C) 38.5  D) 24.88  E) 24.19

Solution: Explanation:   If Rahul age is x, then Sachin age is x + 7,   so,   9x + 63 = 11x   2x = 63   x = 31.5   So Sachin age is   31.5 + 7= 
  31.5 + 7 = 38.5
38.5   Answer: 38.5) 38.5
Answer: C
A certain company has budgeted $1320 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $300, how much was the company under budget or over budget?
Pick:
A) $60 under budget
B) $30 under budget
C) $30 over budget
D) $60 over budget
E) $180 over budget

Solution: The budget for 3 months is (3/12)*$1320 = $330   The company is $30 under budget.   The answer is $30 under budget.  (3/12)* 1320= 
  (3/12)* 1320 = 330
$330   The company is $30 under budget.   The answer is $30 under budget.
Answer: B
If Rs.460 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?	Answers: A) Rs.575 B) Rs.595 C) Rs.590 D) Rs.580 E) Rs.585

Solution: 80 = (460*4*R)/100   R = 4.34%   I = (460*6*4.34)/100 = 120   460 + 120= 
460 + 120 = 580
580   ANSWER:Rs.580
Answer: D
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12200 after a year?	Choose the correct choice:
A) 3660
B) 2881
C) 2887
D) 9977
E) 2212

Solution: 6300:4200:10500   3:2:5   3/10 * 12200 = 3660.3660nswer: 3660
Answer: A
When N is divided by T, the quotient is S and the remainder is Q. Which of the following expressions is equal to N? Answers.
A) ST  B) S + V  C) ST + Q  D) T(S+V)  E) T(S – V)

Solution: Using the rule dividend = Quotient * divisor + remainder =>ST + Q ST + Q is correct
Answer: C
In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
Choose the correct choice from the following choices.
A) 235	B) 256	C) 260	D) 350	E) 480

Solution: Total ways of arranging 7 person in a circle = 6! = 720 ways   If we consider two women as one, then we have   5+1= 
  5+1 = 6
6 persons. Arranging these six persons in circle will take= 5! = 120 ways   And two women can arrange themselves in 2! ways   Total ways in which two women sit together in circle = 5!*2! = 240 ways   Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240= 
720 - 240 = 480
480 ways   480
Answer: E
If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3?
Choose the correct choice from the following answers.
A) 1	B) 2	C) 3	D) 5	E) 0

Solution: 1s per question => N=3P+2 for some integer p   hence 2N => 6Q + 4 => remainder => 1 for some integer Q   hence 1
Answer: A
Population of a city in 2004 was 1000000. If in 2005 there is an increment of 25% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007  Choose the correct choice from the following:
A) 967532  B) 977522  C) 984424  D) 997454  E) 1178125

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 25/100)(1 - 35/100)(1 + 45/100)   = 1178125   1178125
Answer: E
If among 5 children there are 2 siblings, in how many ways can the children be seated in a row so that the siblings do not sit together?
A. 38
B. 46
C. 72
D. 86
E. 102  Choose the correct choice:
A) 38 B) 46 C) 72 D) 86 E) 102

Solution: Without limitations, 5 children can be seated in 5!=120 ways. Find the number of ways to seat the 5 children so that the siblings DO sit together. The siblings can be regarded as one unit so there are 4! combinations. But within this unit the siblings can sit in two different ways. So the number of ways to seat the 5 children so that the siblings DO sit together is 4!∗2=48. Thus, the number of combinations in which the siblings DO NOT sit together is  120 - 48= 
 120 - 48 = 72
72.   Answer: 72
Answer: C
In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent S of his family’s total income? Pick: A) 15% B) 17% C) 24% D) 30% E) 33%

Solution: Lets suppose the Total Family income in Feb = 100x   Wilson's earning in Feb = 40% of 100x = 40x   33%arnings of remaining family in Feb = 100x - 40x = 60x   Wilson's earning in March 100  - 40= 
100  - 40 = 60
60x   Wilson's earning in March= 75% of Wilson's Feb earnings = 75% of 40x = 30x   33%arnings of remaining family in March = 33%arnings of remaining family in Feb = 60x   Thus Wilson's earning as % of Total family income in March S= 30x/ (30+60)x = 30x/90x = 33.33%   Thus Answer is 33%
Answer: E
If the seller selling his goods with the profit of 200 and profit percentage of the good is 50%, then what is the Cost price of that goods. Pick one:
A) 200	B) 300	C) 400	D) 500	E) 600

Solution: Explanation:   Profit = 200   Profit% = 50% = (Profit/C.P)*100   C.P = (200*100) / 50= 
(200*100) / 50 = 400
400. Answer: 400
Answer: C
A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?	Choose the correct option.
A) 59
B) 33
C) 52
D) 68
E) 80

Solution: A   59   The first 56 balls could be of all colours except red. This would leave 8 balls, all of which are red. so any three chosen would be red.
Answer: A
In a school of 300 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? Pick one:
A) 54
B) 63
C) 70
D) 42
E) 31

Solution: 44 + 28 + 10= 
44 + 28 + 10 = 82
82%   100 – 82= 18%    300 * 18/100= 
 300 * 18/100 = 54
54   54NSWER:54
Answer: A
What percent of 50 is 80? Select the correct option:
A) 133 1⁄3 B) 75 C) 160 D) 33 1⁄3 E) 25

Solution: To find out the % of 80 in 50   Do 80/50 = 160%   Answer 160)
Answer: C
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Select.
A) 1/455
B) 1/459
C) 1/458
D) 1/451
E) 1/451

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that all the three marbles picked at random are blue = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455   1/455nswer:1/455
Answer: A
A, B, C hired a car for Rs. 520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B were?	Choose the correct choice from the following.
A) 127
B) 160
C) 287
D) 237
E) 111

Solution: A : B : C = 7 : 8 : 11.   Hire charges paid by B = Rs. (520 * 8/26) = Rs. 160.   Answer: 160
Answer: B
A train running at certain speed crosses a stationary engine in 20 seconds. To find out the speed of the train, which of the following information is necessary:	Choose the correct choice.
A) Only the length of the train	B) Only the length of the engine	C) Either the length of the train or the length of the engine.	D) Both the length of the train and the length of the engine.	E) none of these

Solution: Explanation:   Since the sum of the length of the train and the length of the engine is needed, so both the lengths must be known.   Correct Option : Both the length of the train and the length of the engine.
Answer: D
what is the compound interest on rs:50,000 for 4 months at the rate of 5% per annum	Choose the correct answer.
A) 1058.24 B) 2006.24 C) 838.55 D) 848.55 E) 858.55

Solution: it is monthly compound   rate=5/12% per month   50000*(1+5/1200)^4-50000=838.55   ANSWER:838.55
Answer: C
Diana picked a number of pears, each of which she sold, canned, or poached. If she canned 60 percent more than she poached, and she poached 50 percent less than she sold. If there were a total of 115 pears, then how many pears did she sell?	Choose the correct answer.
A) 41
B) 44
C) 47
D) 50
E) 53

Solution: Let x be the amount of pears that she sold.   Then she poached 0.5x.   Then she canned  1.6*0.5= 
 1.6*0.5 = 0.8
0.8x.   The total amount of pears is x+0.5x+0.8x=2.3x   The fraction of pears that she sold is 1/2.3=10/23.   The number of pears she sold is   (10/23)*115= 
  (10/23)*115 = 50
50.   The answer is 50.
Answer: D
Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.
Choose the correct choice from the following choices: A) 1 B) 3 C) 5 D) 7 E) 9

Solution: 7x-15=10+2x   7x-2x=25   x=5   ANSWER:5
Answer: C
A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
Select:
A) 10  B) 99  C) 77  D) 55  E) 21

Solution: 1/6 – 1/15 = 1/10   => 10   10nswer: 10
Answer: A
x =3 4 5
y= 27 36 9 then what is the relation between x and y  Select:
A) 1*X)^2	B) 1*X)^3	C) 1*X)^4	D) 1*X)^5	E) 1*X)^6

Solution: Y=(1*X)^2   9=(1*3)^2   9=9   1*X)^2NSWER:1*X)^2
Answer: A
Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?  Select:
A) 8789
B) 7500
C) 8392
D) 8390
E) 2804

Solution: Let Mohan's salary be Rs.100.   When increased by 20%, Mohan's salary = Rs.120   Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.   But present salary is Rs. 7200   for, 96 ---> 100 ; 7200 ---> ?   Required salary is 7200/96 * 100 = Rs. 7500   Answer:7500
Answer: B
50% of the apartments in a certain building have windows and hardwood floors. 25% of the apartments without windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what D percent of the apartments with windows have hardwood floors?	Choose the correct answer.
A) 10 B) 16 2/3 C) 40 D) 50 E) 83 1/3

Solution: yup you need to construct a matrix   X********| Windows'|No Windows'''| total   hardFl****'|50*****''|10*********'|60   Not hardFl*|10******|30*********'|40   Total*****|60******'|40*********'|100   so D percent of the apartments with windows have hardwood floors = 50/60 *100   = 83 1/3   so 83 1/3 is the answer.[/u]
Answer: E
John's lottery get prize on any given day is 1/2. What is the probability that it get prize on 4 out of 7 consecutive days?  Choose the correct choice from the following options:
A) 4/7	B) 3/7	C) 31/128	D) 4/28	E) 35/128

Solution: using Binomial. theorem   nCr (p)^r (q)^n-r   7C4 (1/2)^4 (1/2)^r   which is 35/128   Answer is 35/128
Answer: E
How many prime numbers between 100 to 150? Choose the correct choice from the following options:  A) 10  B) 11  C) 15  D) 14  E) 13

Solution: primes are of the form 6n+1 or 6n-1   Put n=25 ==> 151   for n=26 ==> 157   for n=27 , ==>163   for n=28 , ==> 167   for n =29 ==> 173   for n =30 ==> 179 and 181   for n =31 ==> no prime no.   for n= 32 ==> 191   for n =33 ==> 199   therefore total number of prime numbers = 11   Ans - 11
Answer: B
The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 25 percent of a, and m equals b decreased by 20 percent of b, what is the value of m/x?
Choose the most appropriate option.
A) 2/5
B) 3/4
C) 4/5
D) 5/4
E) 3/2

Solution: x equals a increased by 25 percent of a => x = a + 25%a = 1.25a   m equals b decreased by 20 percent of b => m = b - 20%b = 0.8b   m/x = 0.8b/1.25a   Putting the value of b/a = 5/4 we get m/x = 4/5   ANSWER:4/5
Answer: C
2 is what percent of 50	Answers:
A) 2%  B) 4%  C) 6%  D) 8%  E) None of these

Solution: Explanation:   2/50 * 100 = 1/25 * 100= 
1/25 * 100 = 4
4 %   Option 4%
Answer: B
If Y = 2Z+1 where Y is an Integer then which of the following is true? Choose the correct choice from the following choices.
A) Y is always Odd B) Y is always Even C) Y is even if Z is a non integer and a multiple of 0.5 D) Y= 1 E) Y is a non multiple of 2

Solution: Y is even if Z is a non integer and a multiple of 0.5
Answer: C
The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?  Answers:
A) 640  B) 500  C) 3000  D) 1000  E) 2000

Solution: (P*5*15)/100 - (P*3.5*15)/100 = 144   75P/100 â€“ 52.5P/100 = 144   22.5P = 144 * 100   => P = Rs.640   640NSWER 640
Answer: A
A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 200km less in time. Find his speed?  Choose the correct choice from the following answers
A) 20km/hr	B) 30km/hr	C) 40km/hr	D) 50km/hr	E) 60km/hr

Solution: Let the speed be x km/hr   50x-50* 9/10 *x = 200   50x - 45x = 200   5x = 200   x = 40km/hr   Answer is 40km/hr
Answer: C
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?  Select the correct option:  A) 153  B) 150  C) 143  D) 141  E) 89

Solution: Let x be the original 2-digit number.   If each digit is halved, then the sum of G and H is 3x/2.   Note the sum must be a multiple of 3 and less than 150.   Of these five choices, only 141 satisfies these two conditions.   The answer is 141.
Answer: D
In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?	Answers: A) 30,000 B) 35,000 C) 37,000 D) None of these E) Cannot be determined

Solution: Solution   Let the number of applicants be x.Number of eligible candidates	= 95% of x.   Eligible candidates of each other categories	= 15% of (95% of x).   =(15/100×95/100×x)   = 57/400×x.   Therefore, 57/400×x	= 4275   ‹=› x =(4275×400 / 57)   ‹=› 30000   30,000nswer 30,000
Answer: A
The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum	Choices.
A) Rs.17037 B) Rs.17000 C) Rs.17276 D) Rs.170287 E) Rs.171881

Solution: Explanation:   The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year   So rate of the interest = (100 * 1530)/ (5100 * 1)= 
(100 * 1530)/ (5100 * 1) = 30
30% p.a.   So P= (100 * 10200)/ (30 * 2) = Rs.17000   Answer:Rs.17000
Answer: B
A sum of money at simple interest amounts to Rs. 820 in 3 years and to Rs. 854 in 4 years. The sum is:
Choose the most appropriate option.
A) 647  B) 718  C) 654  D) 847  E) 976

Solution: S.I. for 1 year = Rs. (854 - 820) = Rs. 34.   S.I. for 3 years = Rs.(34 x 3) = Rs. 102.   Principal = Rs. (820 - 102) = Rs. 718.   Answer:718
Answer: B
If the sum of two positive integers is 26 and the difference of their squares is 52, what is the product of the two integers? Choose the correct option: A) 108 B) 119 C) 128 D) 135 E) 168

Solution: Let the 2 positive numbers x and y   x+ y = 26 -- 1   x^2 - y^2 = 52   => (x+y)(x-y)=52 -- 2   Using equation 1 in 2 , we get   => x-y = 2 -- 3   Solving equation 1 and 3 , we get   x= 14   y= 12   Product = 14*12= 
14*12 = 168
168   Answer 168
Answer: E
On day one, a store sold 86 cups. On each of the next d days, the company sold 50 cups. If the average daily sales of cups over this time period (including day one) is 53 cups, what is the value of d?	Pick one:
A) 9
B) 10
C) 11
D) 12
E) 13

Solution: 86 + 50d = 53(d+1).   3d = 33.   d = 11.   The answer is 11.
Answer: C
Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
16 minutes more to walk to work than to ride his bicycle, then x equals Choose the correct answer:
A) 4	B) 7	C) 10	D) 15	E) 24

Solution: The best way would be...   Per km, he takes 40 secs extra if he walks   So he will take 16 mins or 16*60 secs in 16*60/40= 
16*60/40 = 24
24 km   ANSW24R:24
Answer: E
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is  Choose the correct choice from the following options:  A) 12  B) 13  C) 15  D) 17  E) 18

Solution: Explanation:   Let the three integers be x, x+2 and x+4.   Then, 3x = 2(x+4)+3,   x= 11   Therefore, third integer x+4 = 15   Answer: Option 15
Answer: C
A bag contains 23 purple jellybeans, 12 green jellybeans, and 15 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be purple?
Choose the most appropriate option: A) 15% B) 20% C) 25% D) 30% E) 46%

Solution: p = 23 , g=12 , y=15   total = 50   p(purple)=(23/50)*100= 
(23/50)*100 = 46
46% . Ans= 46%
Answer: E
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs? Pick one
A) 6.25	B) 7.25	C) 7.75	D) 7.35	E) 8.25

Solution: Runs scored in the first 10 overs = 10 × 3.2 = 32   Total runs = 282   Remaining runs to be scored = 282 - 32= 
282 - 32 = 250
250   Remaining overs= 40   Run rate needed = 25040=6.25   6.25NSWER:6.25
Answer: A
85 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?	Answers
A) 80 litres  B) 90 litres  C) 120 litres  D) 170 litres  E) None of these

Solution: Explanatory Answer   To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*85= 113.33 litres.   However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.   i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.   Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*113.33 = 170 litres.   Answer 170 litres
Answer: D
How many ways can 5 friends be arranged around a circular dinner table? Choose the correct choice.
A) A)24
B) B)48
C) C)96
D) D)120
E) E)720

Solution: The number of arrangements of n distinct objects in a row is given by n!n!.   The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.   The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:   n!n=(n−1)!n!n=(n−1)!.   So, the answer is (5 - 1)= 
(5 - 1) = 4
4!= 24.   24nswer: 24.
Answer: A
(A% of 3B + B% of A) is equal to ?
Choose the correct choice from the following options
A) A% of B B) B% of A C) 4% of AB D) AB% of 3 E) None

Solution: Answer   A% of 3B + B% of A =3AB/100 + AB/100   = 4AB/100 = 4% of AB   4% of ABorrect Option: 4% of AB
Answer: C
A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?  Choose the correct choice from the following:  A) 20 years  B) 28 years  C) 24 years  D) 27 years  E) 57 years

Solution: 100 ---- 100 --- 10   100 --- 10   --------------------   300 ---- 20 years   20 yearsnswer:20 years
Answer: A
In a group of cows and chickens, the number of legs was 12 more than twice the number of heads. The number of cows was:
Choose the correct option:
A) 6 B) 7 C) 10 D) 12 E) 14

Solution: Let the number of cows be x and their legs be 4x.   Let the number of chicken be y and their legs be 2x.   Total number of legs = 4x + 2y.   Total number of heads = x + y.   The number of legs was 12 more than twice the number of heads.   Therefore, 2 × (x + y) + 14 = 4x + 2y.   or, 2x + 2y + 12 = 4x + 2y.   or, 2x + 12 = 4x [subtracting 2y from both sides].   or, 12 = 4x – 2x [subtracting 2x from both sides].   or, 12 = 2x.   or, x = 6 [dividing by 2 on both sides].   Therefore, the number of cows = 6.   Correct 6nswer:6)6
Answer: A