MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 21 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.
How many are Bare Feet ?  Select:  A) 1  B) 2  C) 4  D) 5  E) 7

Solution: 12 kids wear socks   8 kids wear shoes   6 wear both.   12 â€“ 6 = 6 (wear only socks)   8 â€“ 6 = 2 (wear only shoes)   6 (wear both)   hence, 21 -14 = 7   7 kids are with bare feet.   7
Answer: E
A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
Choices.
A) 250	B) 277	C) 299	D) 266	E) 292

Solution: CP1 = 100 SP1 = 90   CP2 = 80 SP2 = 80 * (140/100)= 
80 * (140/100) = 112
112   22 ----- 100   55 ----- ?=> Rs.250.250nswer: 250
Answer: A
The perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 70, then how long is the base of isosceles triangle?  Choose the correct choice from the following options:
A) 15	B) 20	C) 25	D) 30	E) 35

Solution: The base of the isosceles triangle is 70-20-20= 
70-20-20 = 30
30 units   The answer is 30.
Answer: D
In a firm there are men and cows. In all, there are 21 heads and 64 feet. How many men and how many cows are in the firm?  Choose one:	A) 8 men and 13 cows.	B) 10 men and 11 cows.	C) 6 men and 15 cows.	D) 5 men and 16 cows.	E) 11 men and 10 cows.

Solution: 10 men and 11 cows.   Let M = men and C = cows. We can come up with 2 equations.   M + C = 21   2M + 4C= 64   Solving the 2 equations will give 10 men and 11 cows.   Answer 10 men and 11 cows.
Answer: B
In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 80% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that an advanced Trigonometry student is selected?
Choose the correct choice: A) 8% B) 12% C) 16% D) 20% E) 24%

Solution: Let x be the number of students in calculus.   Then the number of students in trigonometry is 1.5x   The number of students on beginner calculus is 0.8x   The number of students in beginner trigonometry is 4/5*(2.5x) - 0.8x = 1.2x   The number of students in advanced trigonometry is 0.3x   The percentage in advanced trigonometry is 0.3x / 2.5x  4/5*(2.5 ) - 0.8= 
 4/5*(2.5 ) - 0.8 = 1.2
1.2x   The number of students in advanced trigonometry is 0.3x   The percentage in advanced trigonometry is 0.3x / 2.5x= 12%   The answer is 12%.
Answer: B
If a and b are different positive integers and a + b = a(a + b+1), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b	Choose the most appropriate option:
A) I only
B) II only
C) III only
D) I and II
E) I and III

Solution: Number picking might not be the best way to solve MUST BE TRUE questions.   The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.   So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).   As forCOULD BE TRUEquestions:   The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.   III only
Answer: C
Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $450, what were her original savings? Pick one
A) $1500
B) $1600
C) $1700
D) $1800
E) $1900

Solution: If Linda spent 3/4 of her savings on furnitute, the rest   4 / 4 - 3 / 4 = 1 / 4 on a TV   But the TV cost her $450. So 1 / 4 of her savings is $450. So her original savings are 4 times $450 = $1800   correct answer $1800
Answer: D
A is thrice as good a work man as B and together they finish a piece of work in 16 days.The number of days taken by B alone to finish the work is : Choose the correct answer: A) 64 days. B) 24 days. C) 52 days. D) 35 days. E) 28 days.

Solution: Solution   (A’s 1 day’s work): (B’s 1 day’s work)= 3 : 1.   (A + B)'s 1 day’s work = 1/16   Divide 1/14 in the ratio 3 : 1.   ∴ B’s 1 day’s work = (1/16 x1/4)= 1/64   Hence,B alone can finish the work in 64 days.   64 days.nswer 64 days.
Answer: A
Sunil invested $ 2300 fir 3 years and $ 800 for 4 years at the same rate of Simple Interest. If the total interest from these investments is $ 1350, what is the rate of interest?	Choose one
A) 12 3/4% B) 15 1/3% C) 15 1/2% D) 16% E) 13 1/4%

Solution: (2300x3xR)/100+(800x4xR)/100=1350   101R=1350   R= 13 1/4%   Answer is 13 1/4%
Answer: E
A cylindrical water tower with radius 15 m and height 4 m is 3/4 full at noon. Every minute, .08π m3 is drawn from tank, while .03π m3 is added. Additionally, starting at 1pm and continuing each hour on the hour, there is a periodic drain of 4π m3. From noon, how many hours will it take to drain the entire tank?  Choose the correct choice from the following answers.
A) 20 2/7 B) 90 6/7 C) 91 D) 91 3/7 E) 97

Solution: initial volume = (3/4)×∏×15²×4= 675∏   Relative Drain/ min = .08∏ - .03∏ = .05∏ m³/min drain   Relative drain / hour .08  - .03= 
.08  - .03 = 0.05
.05∏ m³/min drain   Relative drain / hour= .05∏×60 = 3∏ m³/ hr   Every one hour starting from 1pm, 4∏ m³ of water is drained. It means that only at the hour the water is drained and NOT “in that 1 hour“   So after 1 hr the relative drain would be 3∏ + 4∏ = 7∏m³ of water drain   What i did initially was formed an equation 675∏   3  + 4= 
  3  + 4 = 7
7∏m³ of water drain   What i did initially was formed an equation 675∏= 7∏×n (n is the number of hrs) so ended up with 96.42. This wrong   Look at this way   after 96 hrs the amount of water drain will be 96×7∏ = 672∏ m³   Left over water in the tank after 96 hrs = 3∏ m³   From above we know that it take 1 more hour to drain that 3∏ m³.   So ans is 97hrs
Answer: E
The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?
Select the correct option.
A) 16 B) 12 C) 17 D) 15 E) 71

Solution: 63 + 83 + 103 = a3   => a = 12   Answer: 12
Answer: B
Thirty five percent of the portfolios managed by the Crocodile Brokers company (C.B.C.) hold Hatsopoulos stocks. Forty percent of the portfolios managed by C.B.C. hold McQuarrie stocks and do not hold Hatsopoulos stocks. Fifteen percent of the portfolios managed by C.B.C. hold Hatsopoulos stocks and do not hold McQuarrie stocks. What percent of the portfolios managed by C.B.C. do NOT hold McQuarrie stocks?
Choose the correct choice from the following answers:  A) 20  B) 25  C) 40  D) 60  E) 65

Solution: H represent those portfolios holding Hatsopoulos stocks   M represent those portfolios holding McQuarrie stocks   35% hold H => z+x=35z+x=35   40% hold M and do not hold H => y = 40   15% hold H and not M => z = 15   We have , x = 20   x+y+z=20+40+15= 
20+40+15 = 75
75 x+y+z=20+40+15= 
20+40+15 = 75
75   There are 25% portfolios holding neither H nor M.   Portfolios that do not hold M= z+(neither H nor M)z+(neither H nor M)   = 15+25= 
15+25 = 40
40   ANSWER:40
Answer: C
The population of a town increased from 1,75,000 to 2,45,000 in a decade. The average percent increase of population per year is	Choose the correct choice.
A) 4%
B) 5%
C) 6%
D) 8.75%
E) None

Solution: Solution   Increase in 10 years	= (245000 - 175000)   = 87500.   Increase%	= (70000/175000Ã—100)%   = 40%.   Required average	= (40/10)= 
(40/10) = 4
4%.   4%nswer 4%
Answer: A
Find the value of x from the below equation? : 3x^2+5x+2 = 0  Choices
A) -1 B) -2 C) 1 D) 2 E) 3

Solution: a = 3, b = 5, c = 2   x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6   x1 = (-5 + 1)/6 = -4/6 = -2/3   x2 = (-5 - 1)/6 = -6/6 = -1   -1
Answer: A
3 candidates in an election and received 3000, 5000 and 20000 votes respectively. What % of the total votes did the winningcandidate got in that election?	Choose one.
A) 45.12% B) 50% C) 57% D) 71.42% E) 65%

Solution: Total number of votes polled = (3000 + 5000 + 20000)= 
(3000 + 5000 + 20000) = 28_000
28000   So, Required percentage= 11628/20400 * 100 = 71.42%   71.42%
Answer: D
C and D started a business by investing Rs.1000/- and Rs.1500/- respectively. Find the D’s share out of a total profit of Rs.500:  Choose the most appropriate option:  A) 400  B) 300  C) 200  D) 100  E) 150

Solution: C = Rs.1000/-   100 = Rs.1500/-   C share 2 parts & 100 share 3 parts   Total 5 parts -----> Rs.500/-   ----> 1 part -------> Rs.100/-   100 share = 3 parts -----> Rs.300/-   100
Answer: D
x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 7 will be equal to: Choose the correct option.
A) 3  B) 6  C) 1/9  D) 1/3  E) 9/49

Solution: Explanation :   Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.   .'. x = 9/y^2   => x =9 /7^2 = 9/49   Answer : 9/49
Answer: E
Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?	Choices:
A) 2 years
B) 4 years
C) 6 years
D) 8 years
E) None

Solution: EXPLANATION   Mother’s age when Ayesha’s brother was born = 36 years.   Father’s age when Ayesha’s brother was born = (38 + 4)= 
(38 + 4) = 42
42 years.   Required difference= (42 – 36) years = 6 years.   Answer 6 years
Answer: C
If x,y and z are positive integers, and 30x=35y=42z, then which of the following must be divisible by 3?
I. x
II. y
III. z Choose the correct choice.
A) I B) II C) III D) I & III E) I, II & III

Solution: 30X=35y=42z   x=35y/30---now check whether x is divisible by 3--35y/30 is not divisible by 3   y=30X/35---divisible by 3   z=35y/42----not divisible by 3   hence y is only divisible by 3.   Answer:II
Answer: B
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 6 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?	Choose the correct choice:
A) 13:1	B) 13:3	C) 13:8	D) 13:5	E) 13:2

Solution: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres   Quantity of alcohol in vessel Q = 87.5/100 * 6 = 21/4 litres   Quantity of alcohol in the mixture formed = 5/4 + 21/4 = 13/2= 
13/2 = 13/2 = around 6.5
6.5 litres   As 8 litres of mixture is formed, ratio of alcohol and water in the mixture formed= 6.5 : 1.5 = 13:3.   Answer: 13:3
Answer: B
The dairy condensed milk has only 20% water while the cow milk has 90% water. How many litres of milk maid will be obtained from 72 litres of milk? Choose the most appropriate option
A) 2  B) 7  C) 6  D) 9  E) 8

Solution: Explanation:   In this question, Pure milk in condensed milk = Pure milk in cow milk   80% (x) = 10% (72)   Therefore, x = 9 Liters.   Answer:9
Answer: D
The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?  Options.
A) 399  B) 665  C) 998  D) 2771  E) 22

Solution: 8 * 84= 
8 * 84 = 672
672 – 7= 665   Answer:665
Answer: B
A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, white,blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?	Answers
A) 12	B) 15	C) 21	D) 36	E) 28

Solution: Since the order in which we select the socks does not matter (e.g., selecting a red sock and then a blue sock is the same outcome as selecting a blue sock and then a red sock), we can usecombinations.   We can select 2 socks from 8 socks in 8C2 ways.   8C2 = 28   Answer : 28
Answer: E
In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?	Select
A) 234 B) 255 C) 278 D) 289 E) 290

Solution: Andrew can select one or more than one of his 8 gang.   => Required number of ways = 28 – 1= 255.   255
Answer: B
11 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
Choose one:
A) 84 m B) 88 m C) 14 m D) 137 m E) None

Solution: Sol.   Let the length of the wire b h.   Radius = 1/2 mm = 1/20 cm. Then,   22/7 * 1/20 * 1/20 * h = 11 ⇔ = [11 * 20 * 20 * 7 / 22= 
11 * 20 * 20 * 7 / 22 = 1_400
1400cm= 14 m.   Answer 14 m
Answer: C
A solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally q% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar? Choose the correct choice:
A) 100q/(1-q)	B) 80q/(1-q)	C) 75q/(1-q)	D) 100q/(80-0.2q)	E) 100q/(80+0.2q)

Solution: We'll go for the ALTERNATIVE approach since there are variables in all the answers (which means that any number could work). Since the question deals with percents, the easiest number to use is X = 100. Now let's say that q = 10. Before the evaporation we had 10 pound of sugar and 90 pounds of water. Since only water evaporated, after the evaporation the 10 pounds of sugar remained the same, but the water reduced by 20% of 90 (18 pounds), so we have only 72 pounds of water. 10 out of 82 is the fraction of sugar, so if we multiply it by 100 we get the percents. The correct answer is 100q/(80+0.2q): 100q/(80+0.2q) >>> 100x10 / 82
Answer: E
A man rows down stream 40 km and upstream 21 km taking 4 hrs each time. what is the velocity of current?	Select the correct option:  A) 2.735 Kmph  B) 2.375 kmph  C) 2. 573 kmph  D) 2 kmph  E) None of these

Solution: Explanation:   Man's rate downstream = 40/4= 
40/4 = 10
10 Kmph   Man's rate upstream= 21/4= 
21/4 = 21/4 = around 5.25
5.25 Kmph   Velocity of current= 1/2( 10 - 5.25)   = 2.375 Kmph   Answer: Option 2.375 kmph
Answer: B
If eight numbers are randomly selected without replacement from set {1, 2, 3, 4, 5, 6, 7, 8}, what is the probability that the numbers are selected in ascending order?
Choose the correct option.
A) 1/25600 B) 1/36240 C) 1/48360 D) 1/24120 E) 1/40320

Solution: The total number of ways to arrange 8 numbers is 8! = 40320.   There is only one way to arrange the numbers in ascending order.   P(ascending order) = 1/40320   The answer is 1/40320.
Answer: E
Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on friday. They were very happy. What day of the week would come on 14 Feb. 2010?  Choose the most appropriate option:
A) monday	B) tuesday	C) sunday	D) wednesday	E) thursday

Solution: feb 14 2005 - friday   feb 14 2006 - saturday   feb 14 2007 - sunday   feb 14 2008 - monday   feb 14 2009 - wednesday[since 2008 is leap year , 2 days ll go forward]   feb 14 2010 - thursday   ANSWthursdayR:thursday
Answer: E
Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 20 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?  Choose the correct answer:
A) A) 6.24
B) B) 8
C) C) 10
D) D) 19.1
E) E) 24

Solution: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9   New time in minutes to cross 10 miles stretch = 10*60/20 = 10*3= 
10*3 = 30
30   Time difference= 19.1   Ans:19.1
Answer: D
In how many ways can 5 boys and 2girls be arranged at a table if 2girls are never together?
Choose the correct choice from the following answers.
A) 329
B) 350
C) 378
D) 390
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
A car covers a distance of 624 km in 3 hours. Find its speed? Select the correct option:
A) 104	B) 277	C) 298	D) 269	E) 208

Solution: 624/3= 
624/3 = 208
208 kmph   Answer:208
Answer: E
A and B can do a piece of work in 50 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?
Pick:
A) 30days
B) 35days
C) 40days
D) 44days
E) 45days

Solution: Explanation:   (30days+B)’s 10 days work = 10[1/50+1/50]=10[1+1/50]= 2/5   30days complete remaining work in   2/5*50= 
  2/5*50 = 20
20   Total work= 10+20= 
10+20 = 30
30days   30daysnswer: Option 30days
Answer: A
Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements E. Answers:
A) a) E=48 B) b) E=144 C) c) E=240 D) d) 288 E) e) 120

Solution: One specific boy is seated to either of end seat, lets call him b1   One specific girl is seated in the middle, lets call her g1   Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.   b1 can be seated 2 different seats : 2!   g1 is seated on the seat #4, fixed (no other alternative) : 1   the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!   2! x 1 x 5! = 240   Answer c) E=240
Answer: C
An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of?  Choose the correct choice from the following choices
A) 600km/hr B) 720km/hr C) 710km/hr D) 510km/hr E) 480km/hr

Solution: Distance = 240*5= 
240*5 = 1_200
1200 km   Required speed= 1200 * 3/5= 
1200 * 3/5 = 720
720km/hr   Answer is 720km/hr
Answer: B
If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 30  Choose the correct option
A) 11
B) 13
C) 15
D) 17
E) 18

Solution: P Ã· 44 = 432   => P = 432 * 44= 
432 * 44 = 19_008
19008   P / 30= 19008 / 30 = 633, remainder = 18   18
Answer: E
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 8 women and 12 children take to complete the work? Options:  A) 4  B) 5  C) 7  D) 8  E) 2

Solution: 1 women's 1 day work = 1/70   1 child's 1 day work = 1/140   (8 women + 12 children)'s 1 day work   = (8/70 + 12/140) = 1/5   8 women and 4 children will complete the work in 5 days.   5
Answer: B
In a kilometer race, A beats B by 40 meters or 10 seconds. What time does A take to complete the race? Choose the correct choice from the following: A) 180 sec B) 190 sec C) 290 sec D) 490 sec E) 240 sec

Solution: Time taken by B run 1000 meters = (1000 * 10)/40= 
(1000 * 10)/40 = 250
250 sec.   Time taken by A= 250 - 10= 
250 - 10 = 240
240 sec.   Answer:240 sec
Answer: E
If d is the standard deviation x, y, and z, what is the standard deviation of x +3, y + 3, z + 3 ?  Select:
A) 3d B) 3d+3 C) d D) 3d+9 E) 3d-3

Solution: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.   1) It depends on the separation between the successive terms of the set   2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant   e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}   3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number   e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}   When 3 is added in each term of set {x, y, z} then the new set {x+3, y+3, z+3} will remain same as the previous standard deviation i.e. d   Answer: d
Answer: C
Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 30 years. What is Molly's age right now?
Choose the correct choice from the following:  A) 12  B) 14  C) 16  D) 18  E) 20

Solution: Now, Sandy is  30 - 6= 
 30 - 6 = 24
24   Molly's age is (3/4) * 24= 
(3/4) * 24 = 18
18   The answer is 18.
Answer: D
A person lent a certain sum of money at 6% per annum at simple interest and in 8 years the interest amounted to $572 less than the sum lent. What was the sum lent? Choose the correct option
A) 1000	B) 1100	C) 1200	D) 1300	E) 1400

Solution: P - 572 = (P*6*8)/100   P = 1100   The answer is 1100.
Answer: B
The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, What is the the speed of the first train?  Pick one
A) 87.0
B) 87.5
C) 87.2
D) 87.1
E) 87.4

Solution: Speed and time are inversely proportional (when distance is constant) ⇒Speed ∝ 1Time (when distance is constant)   Here distance is constant and hence speed and time are inversely proportionalSpeed ∝ 1Time⇒Speed1Speed2=Time2Time1⇒78=4Time1⇒Time1 = 4×87 hr⇒Speed of the first train = DistanceTime1=400(4×87)=100×78=12.5×7=87.5 km/hr   Answer :87.5
Answer: B
The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 20 kmph?  Choose the correct option:
A) 21.21  B) 20.25  C) 32.25  D) 75.75  E) 62.61

Solution: distance covered in 1 min=(20*1000)/60=333.33m   circumference of the wheel=(2*(22/7)*.70)= 
(2*(22/7)*.70) = 4.4
4.4m   no of revolution per min=333.33/4.4=75.75   ANSWER:75.75
Answer: D
6, 11, 21, 36, 56, ?  Answers
A) 51 B) 71 C) 81 D) 61 E) 91

Solution: The pattern is + 5, + 10, + 15, + 20,....   Answer : 81.
Answer: C
Salaries of A, B and C were in the ratio 3 : 5 : 7 respectively. If their salaries were increased by 50 per cent, 60 per cent and 50 per cent respectively, what will be the new ratio of their respective salaries?	Choices:
A) 4 : 5 : 7
B) 3 : 6 : 7
C) 4 : 15 : 18
D) 9 : 16 : 21
E) 8 : 16 : 21

Solution: New ratio will be 3 x (150/100) : 5 x (160/100) : 7 x (150/100) = (9/2) : 8 : (21/2)   = 9 : 16 : 21   ANSWER:9 : 16 : 21
Answer: D
How many terms are there in 2, 4, 8, 16,..., 2048?
Choose the correct choice.
A) 14 B) 11 C) 12 D) 10 E) 8

Solution: 2, 4, 8, 16, ...,2048 is a G.P with a =2   and r =4/2= 
4/2 = 2
2   Let the number of terms be n. Then   2 x 2 ^n-1= 2048   or 2^n-1 = 1024= 2^10   Thus n - 1 =10   n= 11   ANSWER:11
Answer: B
Which of the following is the product of two integers whose sum is 12?	Choose the correct choice from the following options.
A) -42  B) -28  C) 12  D) 26  E) 32

Solution: I solved this Question like this,   Let the two integers are x,y   x+y=12 (Given)   xy=? (Needed)   instead of solving this algebraically, Test the Answer choices   B. -28   Do the factorization : (-1,28)----> There sum is not 12--eliminate   (-2,14)---->There sum is 12 Bingo!!!!   So, my answer is B...   As the answer is in B, it took me very less time to answer the question. but i think this method is be simple and efficient.
Answer: B
In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by?
Options:
A) 4
B) 8
C) 1
D) 1/8
E) 1/64

Solution: Say r=2 => V1 = 1/16   when r=1; V2 = 1/4   V2 = 4*V1.   4nswer : 4
Answer: A
Mrs. Napier has 38 stickers to give to 5 students for a reward. How many
stickers will each student get? Will there be any stickers left over?
Choose the correct choice from the following answers.
A) 2-5 B) 2-4 C) 7-6 D) 2-3 E) 2-8

Solution: 38/5 = 7 R 6 Mrs. Napier will give each student 7 stickers and there   will be 6 left over.   correct answer 7-6
Answer: C