MU-NLPC/Calc-aqua_rat huggingface dataset:
The parameter of a square is equal to the perimeter of a rectangle of length 40 cm and breadth 20 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?  Choose the correct answer
A) 47.14	B) 45.15	C) 43.23	D) 41.44	E) 41.51

Solution: Let the side of the square be a cm.   Parameter of the rectangle = 2(40 + 20) = 120 cm Parameter of the square = 120 cm   i.e. 4a = 120   a = 30   Diameter of the semicircle = 30 cm   Circimference of the semicircle   = 1/2(âˆ)(30)   = 1/2(22/7)(30) = 660/14 = 47.14 cm to two decimal places   47.14nswer: 47.14
Answer: A
The average of marks obtained by 120 boys was 35. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?	Pick
A) 100	B) 110	C) 120	D) 130	E) 140

Solution: Let the number of boys who passed = X.   Then, 39 x X + 15 x (120 - X) = 120 x 35   24X = 4200 - 1800   => X = 2400/24= 
2400/24 = 100
100.   Hence, the number of boys passed= 100.   100NSWER:100
Answer: A
The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (8,0) and (8,4). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line? Choose the correct choice from the following answers:  A) 1/3  B) 2/5  C) 4/7  D) 1  E) 7/4

Solution: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.   The center of the rectangle is the point (4,2).   The slope of line passing through points (1,1) and (4,2) = (2-1)/(4-1) = 1/3   The answer is 1/3.
Answer: A
The speed of a train is 72 kmph. What is the distance covered by it in 20 minutes?
Choose the correct choice from the following options
A) 20 kmph B) 28 kmph C) 25 kmph D) 22 kmph E) 24 kmph

Solution: 72 * 20/60= 
72 * 20/60 = 24
24 kmph   Answer: 24 kmph
Answer: E
The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 1 shirts each of them then average number of shirt each of them now has Choose the correct answer
A) 66	B) 63	C) 62	D) 64	E) 61

Solution: Required average   = Old average + New average   = 60 + 1= 
60 + 1 = 61
61   answer :61
Answer: E
What is the missing number in the series?
4,9,20,43,90,?	Options
A) 175	B) 185	C) 195	D) 205	E) 215

Solution: 4*2+1= 
4*2+1 = 9
9   9*2+2= 
9*2+2 = 20
20   20*2+3= 
20*2+3 = 43
43   43*2+4= 
43*2+4 = 90
90   similarly  90*2+5= 
 90*2+5 = 185
185   ANSWER:185
Answer: B
The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?	Select the correct option.
A) 12  B) 76  C) 97  D) 16  E) 19

Solution: (12 + B) - (B + C) = 12   12 - C = 12   12nswer:12
Answer: A
The largest natural number which exactly divides the product of any four consecutive natural numbers is:	Select the correct option:
A) 65
B) 12
C) 24
D) 120
E) 6

Solution: Required number   = 1*2*3*4= 
1*2*3*4 = 24
24   ANSWER:24
Answer: C
In how many ways 4 boys and 4 girls can be seated in a row so that they are alternate. Choose the correct choice from the following:
A) 144 B) 288 C) 12 D) 576 E) None

Solution: Solution: Let the Arrangement be,   B G B G B G B G   4 boys can be seated in 4! Ways.   Girl can be seated in 4! Ways.   Required number of ways,   = 4!*4! = 576.   Answer: Option 576
Answer: D
Pipe P can fill a tank in 3 hours, pipe Q in 9 hours and pipe R in 24 hours. If all the pipes are open, in how many hours will the tank be filled? Select
A) 2 hours  B) 2.1 hours  C) 3 hours  D) 3.5 hours  E) 4.5 hours

Solution: Explanation:   Part filled by (P + Q + R) in 1 hour = (1/3 + 1/9 + 1/24) = 35/72   All the three pipes together will fill the tank = 72/35 = 2.1 hours   ANSWER 2.1 hours
Answer: B
Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 25% vinegar, dressing P comprises what percentage of the new dressing? Choose the most appropriate option
A) 75%
B) 60%
C) 40%
D) 25%
E) 20%

Solution: Let x be the percentage of dressing P in the new dressing.   0.3x + 0.1(1-x) = 0.25   0.2x = 0.15   x = 0.75 = 75%   The answer is 75%.
Answer: A
Find value of x: 3x^2+5x+2 = 0  Select the correct option:
A) -1	B) 1	C) 2	D) 3	E) 4

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
What percent is 150 of 90?  Options:
A) 133 1/3 %  B) 166 2/3 %  C) 135 1/3 %  D) 140 1/3 %  E) 143 1/3 %

Solution: 150/90 = 5/3   5/3 × 100 = 500/3 = 166 2/3 %   166 2/3 %
Answer: B
The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.	Options:
A) Rs. 19828.87  B) Rs. 19828.80  C) Rs. 19828.81  D) Rs. 19828.89  E) Rs. 19828.83

Solution: Explanation:   Let the sum be Rs.P   P{ [ 1 + 8/100]2 - 1 } = 2828.80   P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08= 
1360/0.08 = 17_000
17000 Principal + Interest= Rs. 19828.80   Answer: Rs. 19828.80
Answer: B
There has been successive increases of 15% and then 10% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?	Options
A) 12% B) 15% C) 18% D) 21% E) 24%

Solution: Let P be the original price per unit of gas.   Let x be the original gas consumption.   Let y be the reduced gas consumption.   y*1.1*1.15*P = x*P   y = x / (1.1*1.15) which is about 0.79x which is a decrease of about 21%.   The answer is 21%.
Answer: D
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. Choose the correct choice from the following answers
A) 150  B) 388  C) 266  D) 299  E) 261

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 9= 
  (50/3) * 9 = 150
150 meter.150nswer: 150
Answer: A
22 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
Choose one: A) 21 B) 22 C) 44 D) 45 E) 46

Solution: n for cyclic hand shake and n-1 for linear handshake.   so here no of hand shake is 22.   ANSWER:22
Answer: B
a dealer buys 4 varieties of rice costing rs. 40,rs.42,rs.54 and rs.50 per kg in the ratio 6:5:10:9 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of rice?  Select the correct option: A) 68 B) 70 C) 72 D) 75 E) 77

Solution: 72P = 40*6+42*5+54*10+50*9= 
40*6+42*5+54*10+50*9 = 1_440
1440   SP= 1.5*1440= 
1.5*1440 = 2_160
2160   Total no.of kgs=6+5+10+9= 
6+5+10+9 = 30
30   SP per kg=2160/30= 
2160/30 = 72
72   ANSWER:72
Answer: C
The population of a town is 7500. It decreases annually at the rate of 10% p.a. What was its population 2 years ago?
Options
A) 9300 B) 8000 C) 8500 D) 9500 E) 10000

Solution: Formula :   ( 9300fter =100 denominator   9300go = 100 numerator)   7500 Ã— 100/90 Ã— 100/90 = 9259   9300)
Answer: A
In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 12 percent of revenues. The profits in 1999 were what percent of the profits in 1998? Choose the correct choice:  A) 80%  B) 105%  C) 96%  D) 124.2%  E) 138%

Solution: 0,096R = x/100*0.1R   Answer 96%
Answer: C
5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are?  Choose one:
A) 6Rs  B) 7Rs  C) 8Rs  D) 4Rs  E) 2Rs

Solution: 5M = xW = 8B   5M + xW + 8B ----- 90 Rs.   5M + 5M + 5M ----- 90 Rs.   15M ------ 90 Rs. => 1M = 6Rs.   6Rsnswer: 6Rs
Answer: A
There were two candidates in an election. Winner candidate received 75% of votes and won the election by 500 votes. Find the number of votes casted to the winning candidate?
Choose the correct choice.
A) 228 B) 744 C) 750 D) 199 E) 231

Solution: W = 75% L = 25%   75% - 25% = 50%   50% -------- 500   75% -------- ?  75  - 25= 
 75  - 25 = 50
50%   50% -------- 500   75% -------- ?=> 750   Answer: 750
Answer: C
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007  Choose the correct choice from the following answers:
A) 1056787	B) 1076658	C) 1079767	D) 1079977	E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 1083875   1083875
Answer: E
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer T that must divide n is?
Choose the correct answer
A) 6  B) 12  C) 24  D) 36  E) 48

Solution: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer T that must divide n is:   A 6, B 12, C 24, D 36, E 48   n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.12
Answer: B
A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?  Choices:
A) 2 a.m
B) 6 a.m
C) 9 a.m
D) 5 a.m
E) 1 a.m

Solution: 9 a.m.   Answer:9 a.m
Answer: C
Mr. Hernandez, who was a resident of State X for only 10 months last year, had a taxable income of $22,500 for the year. If the state tax rate were 4 percent of the year’s taxable income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’s State X tax for last year?  Choose the correct choice.
A) $900  B) $750  C) $600  D) $300  E) $60

Solution: Total tax for the year = 22,500 x 4% = 900   As stated Annual tax is prorated as per the duration of stay.   Prorated Tax = 900 (10/12) = 750   Answer $750
Answer: B
Nicole cycles at a constant rate of 18 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her? Pick.
A) x/3
B) 2x/3
C) x
D) 3x/2
E) 2x

Solution: In x minutes, Jessica travels (x/60)*30 = x/2 miles   The time it takes Nicole to travel x/2 miles is (x/2) / 18 = x/36 hours = 5x/3 minutes   Jessica needs to wait 5x/3 - x = 2x/3 minutes.   The answer is 2x/3.
Answer: B
For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 115 units raises the average to 55 units per day, what is the value of n?
Choose the correct option:  A) 8  B) 10  C) 12  D) 14  E) 16

Solution: The daily production was raised by 5 units for n days, which has a weighting of 5n.   5n = 115-55= 
115-55 = 60
60   n= 12   The answer is 12.
Answer: C
What is the 23th digit to the right of the decimal point in the decimal form of 1/11?  Choose the correct choice from the following choices.
A) 1 B) 6 C) 3 D) 5 E) 0

Solution: To solve ,we first have to use some long division.Long division allows us to get 1/11 in decimal form, which is 0.090909… where “09” is repeating.   We see that the 1st, 3rd, 5th digit to the right of the decimal point is a 0 and that the 2nd, 4th, 6th digit to the right of the decimal point is a 9. In other words, each odd-positioned digit is a 0, and each even-positioned digit is a 9.   Then the 23th digit to the right of the decimal point and we see that 23 is odd, then 23th digit is a 0.   Answer 0.
Answer: E
A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 100 shares of the company's stock? Choose the correct choice from the following answers.
A) $92 B) $96 C) $52 D) $120 E) $240

Solution: EPS Actual> EPS expected.   each gets and additional .12 per share.   Thus .52*100 --> $52   answer is $52
Answer: C
How many integers from 0 to 48, inclusive, have a remainder of 1 when divided by 3 ? Choose the most appropriate option
A) 15
B) 16
C) 17
D) 18
E) 19

Solution: My ans is also C.17.   Explanation:   1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.   Hence we have an arithmetic progression: 1, 4, 7, 10,..... 46, which are in the form 3n+1.   Now we have to find out number of terms.   tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.   so, 46 = 1+(n-1)3   or, (n-1)3 = 45   or, n-1 = 15   or, n = 16   16
Answer: B
Of the five numbers in a sequence, the first term is 18,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?	Select the correct option
A) 19,375.00  B) 19,750.90  C) 19,975.25  D) 17,984.50  E) 17,971.20

Solution: 1st number= 18,000   2nd number = 20% of 18,000= 3600   3rd number= 20% of 3600= 720   4th number = 20% of 720= 144   5th number= 20% of 144= 28.8   Range = 18,000-28.8= 17971.20   17,971.20 is the answer
Answer: E
If x^2 + 1/x^2 = 9, what is the value of x^4 + 1/x^4 ?  Choose the correct answer:
A) 10  B) 72  C) 79  D) 16  E) 18

Solution: IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 9 andSQUAREboth sides:   (x² + 1/x²)²= 81   So, (x² + 1/x²)(x² + 1/x²) = 81   Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 81   Simplify: x⁴ + 1/x⁴ = 79   Answer: 79
Answer: C
Which of the following must be subtracted from 2^96 so that the resulting integer will be a multiple of 3?
Select
A) 2
B) 5
C) 3
D) 1
E) 4

Solution: {4^1} / 3 =4/3 remainder 1   {4^2} / 3 = 16/3 remainder 1   {4^3} / 3 = 64/3 remainder 1   {4^4} / 3 = 256/3 remainder 1   Actually the same remainder keeps repeating .....   Try with a diff no, say 2   {2^1}/3 = remainder 2   {2^2}/3 = remainder 1   {2^3}/3 = remainder 2   {2^4}/3 = remainder 1   Answer : 1
Answer: D
list of salaries of 8 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $34,000	Choose the most appropriate option.
A) $28,000
B) $28,500
C) $32,500
D) $30,800
E) $31,500

Solution: Ordering the data from least to greatest, we get:   $27,000, $29,000, $30,000, $31,000, $34,000, $35,500, $40,000, $43,000   Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.   $31,000 + $34,000 = $65,000   The median salary is $32,500.   Answer : $32,500
Answer: C
A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 30% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?
Select the correct option:
A) 21%
B) 22.5%
C) 25%
D) 30%
E) 40%

Solution: 1st year Income= I   1st year savings= S   1st year Expense= E1   2nd year Income = 1.3I   2nd year savings= 2S (100% increase)   2nd Year expense= E2   E1+ E2= 2E1   E2=E1   That means Expenses are same during both years. With increase of 30% income the savings increased by 100%.   or S= .3I   or S= 30% of Income   30% is the answer
Answer: D
A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same color? Choose the correct choice from the following choices:
A) 7/15
B) 7/17
C) 8
D) 8/15
E) 9

Solution: Let S be the sample space   Then n(S) = no of ways of drawing 2 balls out of   (6+4)= 
  (6+4) = 10
\inline {\color{Black}10C_{2}}= =45   Let E = event of getting both balls of same colour   Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)   =\inline {\color{Black}6C_{2}+4C_{2}} = = 15+6= 
15+6 = 21
21   Therefore, P(E)= n(E)/n(S) = 21/45 = 7/15   7/15)
Answer: A
The average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?	Choose the correct choice from the following choices
A) 27	B) 55	C) 31	D) 34	E) 35

Solution: The total of seven numbers = 7X22 = 154   The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99   So, the middle number is  (154 - 99 )= 
 (154 - 99 ) = 55
55   55
Answer: B
Tough and Tricky questions: Absolute Values.
If |a| = 1/3 and |b| = 1/2, which of the following CANNOT be the result of a + b?	Choose the correct choice from the following answers:
A) -5/6
B) -1/6
C) 1/6
D) 2/3
E) 5/6

Solution: |a| = 1/3   Absolute value of 'a' can have two values = 1/3 and -(1/3)   |b| = 1/2   Absolute value of 'b' can have two values = 1/2 and -(1/2)   Now different combinations of a + b are as follows:   a + b = (1/3) + (1/2) = 5/6   - a - b = -(1/3) - (1/2) = -5/6   a - b = (1/3) - (1/2) = -(1/6)   -a + b = -(1/3) + (1/2) = 1/6   Cross verifying with the given options, left over option is 2/3.
Answer: D
A boat goes 100 km downstream in 10 hours, and 200 Km upstream in 25 hours. The speed of the stream is?  Choose the correct choice from the following answers:
A) 1
B) 22 1/7
C) 2
D) 22 1/2
E) 3

Solution: 100 --- 10 DS = 10   ? ---- 1   200 ---- 30 US = 8   ? ----- 1 S = (10 - 8)/2= 
(10 - 8)/2 = 1
1 kmph.   1nswer:1
Answer: A
The highest score in an inning was 3/11 of the total and the next highest was 3/11 of the reminder . If the score differ by 9, the total score was :
Choose one.
A) 110	B) 121	C) 132	D) 143	E) None of these

Solution: Explanation:   Let the score be x. Then the highest score = 3x/11.   Reminder = (x - 3x/11) = 8x/11 .Next the highest score = 3/11 of 8x/11 = 24x/121.   3x/11 - 24x/11 = 9 <=> 33x - 24x = 9 × 121 <33  - 24= 
33  - 24 = 9
9 × 121 <=> x = 121..   Answer: 121
Answer: B
Avg cost of 6 pencils and 8 pens is Rs. 70.The avg cost of 8 pencils and 10 pens is Rs.90. Find the total cost of 25 pencils and 25 pens?
Choose the correct choice from the following.
A) 100 B) 125 C) 130 D) 80 E) 90

Solution: Avg cost of 6 pencils and 8 pens is Rs. 70   (6 pencil + 8 pens) 14=70   therefore 1 pencil cost is  70/14= 
 70/14 = 5
5, so 6 pencil cost is 6x5=30 and 8 pens cost is 8x5=40   Again, avg cost of 8 pencils and 10 pens is Rs.90   (8 pencil + 10 pens) 18=90   therefore 1 pencil cost is  90/18= 
 90/18 = 5
5, so 8 pencil cost is 8x5=40 and 10 pens cost is 10x5=50   So 25 pencil cost is (25/a)=125 and 25 pens cost is (25x5)=125   ANSWER:125
Answer: B
In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?  Pick one.
A) 30% B) 70% C) 100% D) 250% E) 120%

Solution: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420   New C.P. = 125% of Rs. 100 = Rs. 125.   New S.P. = Rs. 420   Profit = 420 - 125 = Rs. 295   Required percentage = 295/420 * 100 = 1475/21 = 70%   ANSWER:70%
Answer: B
On the Richter scale, which measures the total amount of energy released during an earthquake, a reading of x-1 indicates one-tenth the released energy as is indicated by a reading of x. On that scale, the frequency corresponding to a reading of 7 is how many times as great as the frequency corresponding to a reading of 5? Options: A) 10^2 B) 10^3 C) 10^4 D) 10^5 E) 10^6

Solution: If Richter scale reading goes from X-1 to X it will be 10   if Richter scale reading goes from 5 to 6 it will be 10   Similarly if Richter scale reading goes from 6 to 7 it will be 10   so it will from 5 to 7 i.e 6,7 = 10*10 = 10^2   10^2nswer is 10^2
Answer: A
In a group of 100 people,50 like reading books,20 like both reading books and listening songs. How many like listening songs?  Options:
A) 40 B) 50 C) 70 D) 60 E) None

Solution: Make a Venn diagram, and enter your data.   Let the number of people who like Listening Songs be x   x + 20 + 30 = 100   x = 50   so number who like Listening Songs = 20+50= 
20+50 = 70
70   Answer 70
Answer: C
There are 6 baskets numbered from 1 to 6 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end? Choices.
A) 90  B) 91  C) 210  D) 790  E) 910

Solution: Total number of apples in the basket initially = 1000   Each child picks up = 1+2+3+4+5+6 = 6*7/2= 
6*7/2 = 21
21   Total number of apples picked up by 10 children= 21*10= 
21*10 = 210
210   Number of apples left in the end= 1000-210= 
1000-210 = 790
790   Answer is 790
Answer: D
A man whose bowling average is 12.4, takes 3 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
Pick.
A) 23	B) 24	C) 25	D) 26	E) 27

Solution: 12.4*x+26=(3+x)12   solve equation x=25   ANSWER:25
Answer: C
Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6358, how much amount did Raghu invest ?	Choices
A) 1287	B) 2200	C) 2000	D) 1129	E) 1192

Solution: Let money invested by Raghu = Rs. x   Money invested by Trishul = 9/10= 
9/10 = 9/10 = around 0.9
0.9x   Money invested by Vishal= 9/10x * 110/100 = 0.99x   Also, x+0.9x+0.99x 9/10  * 110/100= 
9/10  * 110/100 = 99/100 = around 0.99
0.99x   Also, x+0.9x+0.99x= 6358   = x= 6358/2.89= 
6358/2.89 = 2_200
2200   Therefore, amount invested by Raghu is Rs. 2200.   Answer: 2200
Answer: B
For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *7 + 3 and *7 + 7, inclusive?  Choose the correct choice:	A) None	B) One	C) Two	D) Three	E) Four

Solution: 7! = 720 * 7= 
720 * 7 = 5_040
5040   # in question= 5043, 5044, 5045, 5046, 5047   none of these are prime   Nonenswer - None
Answer: A
What is the ratio of 6/7 to the product 3*(7/3)?	Choose the correct option:
A) 3:7  B) 1:3  C) 3:21  D) 6:49  E) 3:49

Solution: 6/7 / 21/3 = 6/49...   IMO option 6:49.
Answer: D
Mars travels around the Sun at an approximate speed of 14.4 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)  Choose the correct choice from the following options: A) 64,200 B) 75,300 C) 86,400 D) 97,500 E) 108,600

Solution: The speed is 14.4 miles/s. Then 14.4/0.6= 
14.4/0.6 = 24
24 km/s   24*3600= 86,400 kph   The answer is 86,400.
Answer: C
If -1 < h < 2, which of the following has the greatest value?	Select.
A) a) 1-h
B) b) 1+h
C) c) 1+h^2
D) d) 1-1/h
E) e) 1-1/(h^2)

Solution: easiest way of solving this would be to substitute a value.   lets say h= - 1/2   a) 3/2   b) 1/2   c) 5/4   d) 3   e) - 3   the value you chose is wrong . h cannot be 0.9 as -1<h<0. if you chose -0.9 answer will still be D.   Answer is c) 1+h^2.
Answer: C