MU-NLPC/Calc-aqua_rat huggingface dataset:
How many keystrokes are needed to type numbers from 1 to 100? Choose the correct answer: A) 192 B) 100 C) 90 D) 110 E) None of these

Solution: Explanatory Answer   While typing numbers from 1 to 100, there are 9 single digit numbers: from 1 to 9.   Each of these numbers requires one keystroke.   That is 9 key strokes.   There are 90 two-digit numbers: from 10 to 99.   Each of these numbers requires 2 keystrokes.   Therefore, 180 keystrokes to type the 2-digit numbers.   100 is a three-digit number which requires 3 keystrokes.   Totally, therefore, one requires   9 + 180 + 3= 
  9 + 180 + 3 = 192
192 keystrokes.   Choice 192 is the correct answer.
Answer: A
The average waight of A,B,C is 45 Kg. The avg wgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.	Choose the correct choice from the following answers.
A) 34Kg	B) 40Kg	C) 42Kg	D) 41Kg	E) 31Kg

Solution: Let A,B,c represent their individual wgts.   Then,   A+B+C=(45*3)= 
(45*3) = 135
135Kg   A+B=(40*2)= 
(40*2) = 80
80Kg & B+C=(43*2)= 
(43*2) = 86
86Kg   B=(A+B)+(B+C)-(A+B+C)   =(80+86-135)= 
(80+86-135) = 31
31Kg.   Answer is 31Kg.
Answer: E
2400÷20÷10=?
Answers:
A) 43
B) 12
C) 15
D) 20
E) 24

Solution: 2400 ÷ 20 = 120   120 ÷ 10 = 12   Answer is 12
Answer: B
If a positive odd integer N has p positive factors, how many positive factors will 6N have ?
Choose the correct choice from the following:  A) p  B) 2p  C) P+1  D) 2p+1  E) Cannot be determined

Solution: I have added some extra text to make this question more GMAT-like:   Let's TEST some values of N   Try N = 3   The factors of 3 are {1, 3}. Here, p =2   So, 2N = (2)(3) = 6   The factors of 6 are {1, 2, 3, 6}. So, we have a total of4   Now check the answer choices:   A) p =2No good. We want an output of4. ELIMINATE   B) 2p = (2)(2) = 4. PERFECT! KEEP B   C) P+1 =2+ 1= 
2+ 1 = 3
3 No good. We want an output of4. ELIMINATE   D) 2p+1= (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE   E) Cannot be determined. POSSIBLE. KEEP E   Let's TEST another value of N   Try N = 7   The factors of 7 are {1, 7}. Here, p =2   So, 2N = (2)(7) = 14   The factors of 14 are {1, 2, 7, 14}. So, we have a total of4   Now check the REMAINING answer choices:   B) 2p = (2)(2) =4. PERFECT! KEEP B   E) Cannot be determined. POSSIBLE. KEEP E   Let's TEST one more (non-prime) value of N   Try N = 9   The factors of 9 are {1, 3, 9}. Here, p =3   So, 2N = (2)(9) = 18   The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6   Now check the REMAINING answer choices:   B) 2p = (2)(3) =6. PERFECT! KEEP B   E) Cannot be determined. POSSIBLE. KEEP E   pt this point, it SEEMS LIKELY that the correct answer is p
Answer: A
If x and y and z are two-digit integers such that x > 40, y<70, and z is > 80 and < 90, which of the following is closest to the maximum possible value of xyz ?	Pick
A) 700
B) 607,959
C) 4,000
D) 7,000
E) 28,000

Solution: To get the maximum possible value of xyz, we need maximize the value of x,y, and z.   max x can be = 99 (given x is a two-digit integer > 40)   max y can be = 69 (given y is a two-digit integer < 70)   max z can be = 89 (given z is a two-digit integer > 80 and < 90)   xy = 99*69*89 = 607,959   Answer (607,959)
Answer: B
A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 12 brown mice in the experiment, how many mice in total are in the experiment?  Select:
A) 39	B) 33	C) 26	D) 21	E) 36

Solution: Let total number of mice = M   Number of white mice = 2/3 M   Number of brown mice = 1/3 M = 12   => M = 36   Answer 36
Answer: E
The total of company C's assets in 1994 was 150% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:	Choose the correct choice
A) 7N
B) 8N
C) 9N
D) 12.5
E) 20

Solution: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.   In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:   $100 + 4x$100 = $100 + $400 =$500   In 1994, the total assets were 150% GREATER than they were in 1993, which means 1993 PLUS 150% of 1993:   $500 + 1.5x$500 100 +  400= 
100 +  400 = 500
$500   In 1994, the total assets were 150% GREATER than they were in 1993, which means 1993 PLUS 150% of 1993:   $500 + 1.5x$500= $1250   This is 12.5 times the 1992 number, so the correct answer is 12.5N.   12.5
Answer: D
A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/4 % his yearly income diminishes by Rs. 61.50, his capital is?	Choices:
A) 24,609
B) 24,607
C) 24,600
D) 24,638
E) 24,602

Solution: Let the capital be Rs. x. Then,   (x * 8 * 1)/100 - (x * 31/4 * 1/100) = 61.50   32x - 31x = 6150 * 4   x = 24,600.   Answer:24,600
Answer: C
Using all the letters of the word "THURSDAY", how many different words can be formed?	Choices: A) 8 B) 8! C) 7! D) 6 E) 2

Solution: Total number of letters = 8   Using these letters the number of 8 letters words formed is   ⁸P₈ = 8!.   Answer:8!
Answer: B
There are 15 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station? Choose the correct choice from the following answers:
A) 272  B) 167  C) 157  D) 352  E) 380

Solution: The total number of stations = 17   From 17 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 17P₂ ways.   17P₂ = 17 * 16= 
17 * 16 = 272
272.   272nswer: 272
Answer: A
What is the perimeter of a triangle with sides 7 and 3 that has the maximum possible area?	Choose the correct option
A) 10 + 3√7	B) 10 + 3√3	C) 10 + √58	D) 10 + √71	E) 10 + √83

Solution: We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+9)= 
(49+9) = 58
√58   The perimeter is 10 + √58   The answer is 10 + √58.
Answer: C
Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph,
he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1
P.M.?  Choose the correct answer:	A) 9 km/hour	B) 10 km/hour	C) 11 km/hour	D) 12 km/hour	E) None of these

Solution: Explanation:   We need to calculate the distance, then we can calculate the Ɵme and finally our answer.   Lets solve this,   Let the distance travelled by x km   Time = Distance/Speed   x10−x15=2[because, 2 pm - 12 noon = 2   hours]3x−2x=60x=60.Time=DistanceSpeedTime@10km/hr=6010=6hours   So 2 P.M. - 6 = 8 A.M   Robert starts at 8 A.M.   He have to reach at 1 P.M. i.e, in 5 hours   So, Speed = 60/5= 
60/5 = 12
12 km/hr   Answer: 12 km/hour
Answer: D
If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers?
I. x
II. x + y
III. y/x
Select.
A) I only B) II only C) III only D) I and II E) I, II and III

Solution: x - y is an even integer: Therefore, for the equation to hold true, both x and y have to be even.   x/y is an even integer: Therefore, this implies that x has to be greater than y.   We can eliminate option III as y/x will never be an integer (Since x>y)   Statement I, x: x>y, hence x has to greater than 2 and even, therefore divisible by 2 and non-prime.   Statement II, x+y: x+y will be divisible by at least 2 since both x and y are even, hence the sum is non prime.   Thus, option I and II is the correct answer
Answer: D
If x is an integer, which of the following is a possible value of Q=(x^2 +2x – 7)/9?	Select the correct option:
A) -2.4
B) 0.268
C) 1.166 repeating
D) 4.555 repeating
E) 8.125

Solution: x is an integer, which of the following is a possible value of Q=(x^2 +2x – 7)/9?   Used process of elimination   A. -2.4   when this is multiplied by 9, x is not an integer   B. 0.268   when this is multiplied by 9, x is not an integer   C. 1.166 repeating   when this is multiplied by 9, x is not an integer   D. 4.555 repeating   E. 8.125   when this is multiplied by 9, x is not an integer   Answer choice 4.555 repeating seems to fit.4.555 repeating
Answer: D
In a partnership between A, B and C. A's capital is Rs.4000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Choose the correct choice from the following answers:
A) 9400
B) 12798
C) 26908
D) 11750
E) 22073

Solution: 200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 4000   470 ---- ?=> 9400   9400nswer: 9400
Answer: A
How many odd, positive divisors does 500 have?  Select the correct option.
A) 6	B) 5	C) 12	D) 15	E) 24

Solution: Make a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=5 factors.   Another example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.   Answer: 5.
Answer: B
A vessel of capacity 3 litre has 25% of alcohol and another vessel of capacity 5 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?	Choose the correct choice from the following:
A) 31%.
B) 71%.
C) 27.5%.
D) 29%.
E) 51%.

Solution: 25% of 3 litres = 0.75 litres   40% of 5 litres = 2 litres   Therefore, total quantity of alcohol is 2.75 litres.   This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 27.5%   27.5%.
Answer: C
A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, one boggies were detached. The train now crosses a telegraph post in Choices.
A) 16.5 sec  B) 12 sec  C) 15 sec  D) 20 sec  E) None of these

Solution: Length of train = 12 Ã— 15 = 180 m.   Then, speed of train = 180â„18 = 10 m/s   Now, length of train = 11 Ã— 15 = 165m   âˆ´ Required time = 165â„10 = 16.5 sec.   16.5 secnswer 16.5 sec
Answer: A
The ratio of the ages of three people is 4:6:7. Eight years ago, the sum of their ages was 44. Find their present ages. Pick one
A) 28,42,49  B) 24,36,42  C) 20, 30,35  D) 16,24,28  E) 12,18,21

Solution: Let the present ages be 4x, 6x, 7x.   (4x-8) + (6x-8) + (7x-8) = 44   17x = 68   x = 4   Their present ages are 16, 24, and 28.   The answer is 16,24,28.
Answer: D
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 W of the total distance did he cover while the sun was shining on him?  Pick.
A) 1/4
B) 4/5
C) 1/5
D) 1/6
E) 1/7

Solution: 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 W=2/14 = 1/7. Answer: 1/7
Answer: E
ACME’s manufacturing costs for sets of horseshoes include a $12,450 initial outlay, and $20.75 per set. They can sell the sets $50. If profit is revenue from sales minus manufacturing costs, and the company producessells 950 sets of horseshoes, what was their profit?  Choose one:  A) $15300  B) $14300  C) $15337.50  D) $16300  E) $15800

Solution: Total Manufacturing cost = 12,450+950*20.75 = 32162.5   Total Selling cost = 950*50= 
950*50 = 47_500
47500   Profit= 47500-32162.50= 
47500-32162.50 = 15_337.5
15337.50   Answer : $15337.50
Answer: C
During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 40 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip? Choose the correct choice from the following choices
A) 400/x%  B) 50%  C) x/12%  D) 60/x%  E) 500/x%

Solution: Say x = 5 miles (so no remainder of the trip).   Time to cover x = 5 miles at 30 miles per hour = (time) = (distance)/(rate) = 5/30 = 1/6 hours = 10 minutes.   Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/40 = 1/8 hours = 5 minutes.   (Or simply, half rate will result in doubling the time.)   So, we can see that the time to cover x = 4 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 4 miles at 60 miles per hour (5 minutes).   Now, plug x = 4 miles into the answer choices to see which one yields 100%. Only answer E works.   400/x%nswer: 400/x%.
Answer: A
The area of a parallelogram is 98sq m and its altitude is twice the corresponding base. Then the length of the base is?
Choose the correct choice from the following answers:
A) 8  B) 9  C) 7  D) 6  E) 5

Solution: 2x * x = 98 => x= 7   Answer: 7
Answer: C
A train 630 m long, running with a speed of 63 km/hr will pass a tree in? Choose the correct choice from the following options:
A) 35	B) 36	C) 37	D) 38	E) 39

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 630 * 2/35= 
630 * 2/35 = 36
36 sec   Answer: Option 36
Answer: B
Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 30 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 70 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered? Choose the correct choice from the following choices:  A) 36  B) 72  C) 122  D) 144  E) 180

Solution: 1st part: - In 1hr, Bus A covers 30 miles.   Relative speed of bus ABus B is   (80-30)= 
  (80-30) = 50
50mph.   So time required for Bus B to cover the exact distance as A is   50*t= 30   t=3/5 = 36min   2nd part   80*t=2d - B has to cover twice the distance   30*(t+1) = d - A traveled 1hr more and has to travel only only d   so   d/30 - 2d/80 = 1   D=120   T= 3hrs = 180 min   Question asks for +ve difference between part 1 and part 2 in minutes   = 180-36 = 122min   122
Answer: C
total no. of players is 99 other than me.50 plays soccer,45 plays basket ball,50 play valley ball.15 play all three. How many will play only 2 games?	Options.
A) 40
B) 50
C) 60
D) 70
E) 80

Solution: let A=soccer players..B=basket ball players..C=vollyball players   n(A U B U C)=n(A) + n(B) + n(C) - n(A INTERSECTION B) - n(A INTERSECTION C) - n(C INTERSECTION B) + n(A INTERSECTION B - INTERSECTION C)   therefore..   100=50+45+50-intersections+15   hence..intersections=145-100+15= 
145-100+15 = 60
60 play only 2 games..   ANSWER:60
Answer: C
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:	Select the correct option: A) 16 km/hr B) 50 km/hr C) 19 km/hr D) 15 km/hr E) 87 km/hr

Solution: Speed of the train relative to man   = (125/10) m/sec   = (25/2) m/sec. [(25/2) * (18/5)] km/hr   = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed   = (x - 5) km/hr. x - 5 = 45 ==> x   = 50 km/hr.   Answer: 50 km/hr
Answer: B
The speed of a car is 80 km in the first hour and 60 km in the second hour. What is the average speed of the car? Choose the correct choice from the following choices.
A) 50 kmph
B) 60 kmph
C) 70 kmph
D) 80 kmph
E) 85 kmph

Solution: S = (80 + 60)/2= 
(80 + 60)/2 = 70
70 kmph   ANSWER:70 kmph
Answer: C
If the positive integer X is divisible by 3, 6, and 12, then which of the following must X be divisible by?
I. 12
II. 35
III. 46  Choose the most appropriate option
A) III B) II only C) I and II only D) II and III only E) I only

Solution: Answer = I only   LCM of 3, 6, 12 = 12   Answer = 12   Answer : I only
Answer: E
A monkey ascends a greased pole 22 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?	Choose the correct choice from the following
A) 40th minute
B) 41st minute
C) 43rd minute
D) 42nd minute
E) 45th minute

Solution: The money is climbing 1meter in 2min. This pattern will go on till he reaches 20meters. I mean this will continue for first  20*2= 
 20*2 = 40
40mins. he would have reached 20meters. After that he will climb 2meters and he will reach the pole. So total time taken= 40 + 1= 
40 + 1 = 41
41mins.   So, asnwer will be 41st minute
Answer: B
Raghav borrows Rs.2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be ?	Choose the correct choice from the following answers
A) Rs.1275	B) Rs.1283	C) Rs.1352	D) Rs.1377	E) Rs.1577

Solution: Let the value of each instalment be Rs.x.   x/(1+4/100) + x/(1+4/100)2 = 2550 = 25x/26 + 625x/676 = 2550   1275x = 2550 *676   x = (2550*676)/1275= 
(2550*676)/1275 = 1_352
1352.   ANSWER:Rs.1352
Answer: C
If the number 761 * 829 is completely divisible by 9, then the smallest whole number in place of * will b	Select
A) 4	B) 5	C) 3	D) 8	E) 9

Solution: Sum of digits = (7 + 6 + 1 + x + 8 + 2 + 9) = (33 + x), which must be divisible by 9.   x = 3.   3)
Answer: C
b.	Last Night lottery winning numbers followed this pattern: 25, 22, 20, 19, 16, 14, 13, 10, 8, 7, ? What is the last winning number? Options
A) 6  B) 3  C) 4  D) 5  E) 7

Solution: The sequence progresses -3, -2, -1 repeated; The last winning number is 4.   Ans 4 = 4
Answer: C
Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
Options:	A) 21	B) 35	C) 36	D) 60	E) 65

Solution: The total number of the people in the room must be a multiple of both 7 and 12 (in order 3/7 and 5/12 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 12, which is 84.   Since, the total number of the people in the room is greater than 50 and less than 100, then there are 84 people in the room.   Therefore there are   3/7*84= 
  3/7*84 = 36
36 people in the room under the age of 21.   Answer: 36.
Answer: C
The ratio of numbers is 5:6 and their H.C.F is 4. Their L.C.M is:  Pick one:  A) 12  B) 16  C) 24  D) 48  E) 120

Solution: Let the numbers be 5x and 6x.   Then their H.C.F = x. So, x = 4.   So, the numbers are 20 and 24.   L.C.M of 20 and 24 = 120.   ANSW120R:120
Answer: E
The number '7' is the prime followed by a cube.
Is there any other number sharing the same quality? Select:  A) No  B) Yes  C) May be  D) None of above  E) Do know

Solution: A   No   7 is the only prime followed by a cube.   Assume that n3-1 is a prime for some n.   N3-1 will be equal to (n−1)(n2+n+1)   Now, n-1 divides n3-1.   If n-1>1, then we will have a contradiction to n3-1 being a prime.
Answer: A
A man sells an article at 15% loss. Had he sold it for Rs. 350/- more he could have gained 20%. What is the cost price of the article?  Pick:
A) Rs.420/-	B) Rs.400/-	C) Rs.460/-	D) Rs.1000/-	E) None of these

Solution: Explanation:   Short cut method:   Loss =====> 15 %   Profit ====> 20 %   ~   ----------------   35 % ---------> Rs. 350/-   100 % --------> Rs. 1000/-   Answer: Option Rs.1000/-
Answer: D
If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?  Choose the correct choice from the following:
A) 44
B) 48
C) 45
D) 47
E) 49

Solution: Let the required length be x meters   More men, More length built (Direct proportion)   Less days, Less length built (Direct Proportion)   Men 20:35 and Days 6:3::56:x   Therefore (20 x 6 x (X))=(35 x 3 x 56)   x=(35x3x56)/120=49   Hence, the required length is 49 m.   Answer is 49.
Answer: E
X does a work in 20 days. Y does the same work in 30 days. In how many days they together will do the same work?	Choose the most appropriate option:
A) 10	B) 12	C) 20	D) 30	E) 15

Solution: X's 1day's work= 1/20   Y's 1 day's work=1/30   (X+Y)'s 1day's work= (1/20+1/30)=1/12   both together will finish the work in 12 days.   correct option is 12
Answer: B
The average age of a class is 15.8 years. The average age of the boys in the class is 16.4 years and that of the girls is 15.4 years. What is the ratio of boys to girls in the class?  Choose the correct choice from the following choices:
A) 1 : 2  B) 3 : 4  C) 2 : 3  D) 3:2  E) None of these

Solution: Let number of boys = x ; Let number of girls = y   Total numbers of students = x + y   (x + y) × 15.8 = 16.4x + 15.4y   0.6x = 0.4y   x/y = 0.4/0.6 = 2/3   ANSWER:2 : 3
Answer: C
Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 50 years. What will be the age of the B ten years hence?	Choose one.
A) 39
B) 23
C) 28
D) 96
E) 100

Solution: Let the present ages of A, B and C be a, b and c respectively.   Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)   (b + c)/2 = 50 => b + c = 100 --- (2)   Answer: 100
Answer: E
What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?	Choose the correct choice.
A) 1 : 3	B) 2 : 3	C) 1 : 2	D) 3 : 2	E) 1 : 4

Solution: Let the principal be P and rate of interest be R%.   Required ratio =   (P x R x 6)/100 DIVIDED BY	(P x R x 9)/100   =	6PR/9PR	=	6/9	= 2 : 3.   ANSWER : 2 : 3   100   9PR 9
Answer: B
A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit? Choose the correct option.
A) 2205
B) 2888
C) 2669
D) 2770
E) 2771

Solution: 2205 = 2000(21/20)2 = 2205   2205nswer: 2205
Answer: A
Taylor is making a bracelet. He Starts with 4 blue knots, 5 red knots, and 2 yellow knots, in that order, and repeats the pattern until there is no more string. If the last Knot is yellow which of the following could be the total number of knots on the bracelet.
Pick: A) 87 B) 90 C) 95 D) 97 E) 102

Solution: Repeating sequence = 4 + 5 + 2= 
4 + 5 + 2 = 11
11.   87s the pattern ends in Y this could be the 10th thread or 11 thread (both are yellow)   Out of the answer choices, correct on should be a multiple of 11(since 11 threads are repeating) and if not, multiple of 11 + 10 (since 11 threads are repeating and last sequence end at first yellow)   none of the options is a direct multiple of 11 and only option that is multiple of 11; + 10 is 87 (11*7) + 10   Hence, answer is 87
Answer: A
Last year Jackie saved 5% of her annual salary. This year, she made 10% more money than last year, and she saved 8% of her salary. The amount saved this year was what percent of the amount she saved last year?
Answers
A) 56%	B) 76%	C) 158%	D) 176%	E) 188%

Solution: Assuming Annual salary of last year = 100   5 % Salary Saving (last year) would give = (5/100) * 100= 
(5/100) * 100 = 5
5   she made 10% more money than last year= 110 (This year Salary)   8 % Salary saving this year = (8/100) * 110 = 88/10= 
88/10 = 44/5 = around 8.8
8.8   (Amount saved this year/Amount saved last year) * 100= (8.8/5) * 100 = 8.8 * 20= 
8.8 * 20 = 176
176 %   ANSWER:176%
Answer: D
Using all the letters of the word "BUTTON", how many words can be formed, which begin with B and end with N? Choose the most appropriate option.
A) 9 B) 24 C) 7 D) 5 E) 3

Solution: There are five letters in the given word.   Consider 6 blanks ....   The first blank and last blank must be filled with B and N all the remaining three blanks can be filled with the remaining 4 letters in 4! ways.   The number of words = 4! = 24.   Answer:24
Answer: B