MU-NLPC/Calc-aqua_rat huggingface dataset:
Sam bought 50 candles and 3 lighters costing 2 dollars each. How was Sam's total?  Choose the correct option:
A) 300
B) 103
C) 56
D) 106
E) 55

Solution: For this we need to add all items and multiple all items together   2x(50+3)=2x50+2x3=100+6= 
100+6 = 106
106   correct answer is 106)106
Answer: D
2 identical circles intersect so that their centre and point at which they intersect form a square of 1 cm.the area of portion that is common two circles is
4 Choose the correct option.
A) π2-1	B) 4	C) √2-1	D) √5	E) π/2-1

Solution: the area of the sector is pi*r^2*90/360 (as it is a square, so the angle is 90)   =pi*r^2/4   =pi/4 (as the area of the square is 1cm^2, so the sides are 1 cm each. the sides of the square are the radii of the circle)   now, the area of the triangle formed by two radii and a line which joins the point of intersection of the two circles = 0.5*1*1= 
0.5*1*1 = 0.5
0.5   So, half of the portion of our desired area= (pi/4 - 0.5)   therefore, the area of our desired portion is 2* (pi/4 - 0.5)   = pi/2 - 1   ANSWπ/2-1R:π/2-1
Answer: E
In the first week of last month, Company X realized an average wholesale profit of $1428 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit?	Choose the correct choice
A) $3	B) $4	C) $7	D) $13	E) $51

Solution: The key operator that everyone seems to have missed is the average. The average profit of $1428 per day is equivalent to a total profit of $9996 for the whole week.   Therefore, the difference between sale price and cost per unit is equal to $9996, which is divisible by all of the answer choices, except for 13.   So, $13 is the answer.
Answer: D
Ritesh and Co. generated revenue of Rs. 1,500 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?	Choose the correct choice from the following choices
A) 12.5% B) 20.83% C) 25% D) 50% E) None of these

Solution: Explanation :   Given, Ritesh and Co. generated revenue of Rs. 1,500 in 2006 and that this was 12.5% of the gross revenue.   Hence, if 1250 is 12.5% of the revenue, then 100% (gross revenue) is:   =>(100/12.5)×1500.   =>12,000.   Hence, the total revenue by end of 2007 is Rs. 12,000. In 2006, revenue grew by Rs. 2500. This is a growth of:   =>(2500/12000)×100.   =>20.83%.   Answer : 20.83%
Answer: B
Two trains of equal lengths take 12 sec and 24 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? Choose the correct choice from the following answers:
A) 18 sec
B) 12 sec
C) 17 sec
D) 21 sec
E) 16 sec

Solution: Speed of the first train = 120/12= 
120/12 = 10
10 m/sec.   Speed of the second train= 120/24= 
120/24 = 5
5 m/sec.   Relative speed= 10 + 5= 
10 + 5 = 15
15 m/sec.   Required time= (120 + 120)/15= 
(120 + 120)/15 = 16
16 sec.   Answer: 16 sec
Answer: E
A student is ranked 17th from right and 5th from left. How many students are there in totality ?  Choose the most appropriate option
A) 18	B) 19	C) 20	D) 21	E) 22

Solution: From right 17 , From left 5   Total = 17+5-1= 
17+5-1 = 21
21   ANSWER:21
Answer: D
An ant walks an average of 500 meters in 60 minutes. A beetle walks 15% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?  Select the correct option.
A) 1.0	B) 0.5	C) 0.75	D) 0.425	E) 0.3

Solution: the ant walks an average of 500 meters in 60 minutes   500 meters in 1 hours   the beetle walks 15% less distance = 500-75= 
500-75 = 425
425 meters in 60 minutes   0.425 km in 1 hours   speed= 0.425*1= 
0.425*1 = 0.425
0.425 km/h   I guess option 0.425 should be 0.425
Answer: D
log42 - log82 + log16 2 -…. to ∞ is  Select the correct option.
A) e2	B) ln2+1	C) ln2-1	D) 1-ln2	E) None of these

Solution: Required sum = 1/2 - 1/3 +1/4 - … to ∞   Now, loge(1 + X) = X - X2/2 + X3/3 - …   Therefore, loge2 = 1-1/2 + 1/3 - … to ∞   =>1/2 - 1/3 + 1/4 .. to ∞ = 1 - loge2 = 1- ln2.   ANSWER:1-ln2
Answer: D
A man wants to cross a home, which has 2 doors on one side and 1 door on other site. He has 2 x 1=2 ways for it.
Choose the correct choice from the following options.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: The product of first ‘n’ natural numbers is denoted by n!.   n! = n(n-1) (n-2) ………………..3.2.1.   Ex. 5! = 5 x 4 x 3 x 2 x 1 =120   Note 0! = 1   Proof n! =n, (n-1)!   Or (n-1)! = [n x (n-1)!]/n = n! /n   Putting n = 1, we have   O! = 1!/1   or 0 = 1   1
Answer: A
A candidate appearing for an examination has to secure 42% marks to pass paper I. But he secured only 42 marks and failed by 22 marks. What is the maximum mark for paper I? Select: A) 110 B) 120 C) 130 D) 152 E) 150

Solution: he secured 42 marks nd fail by 22 marks so   total marks for pass the examinatn=64   let toal marks x   x*42/100=64   x=152   ANSWER:152
Answer: D
In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"? Choose the correct choice:
A) 25	B) 13	C) 40	D) 20	E) 30

Solution: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.   3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3 = 30 ways.   ANSW30R:30
Answer: E
A person was asked to state his age in years. His reply was , "Take my age 3 years hence, multiply it by 3 and subtract 3 times my age 3 years ago and you will know how old I am." What was the age of the person ? Pick:
A) 18  B) 20  C) 24  D) 30  E) 35

Solution: Explanation:   Let the present age of person be x years.   Then, 3(x + 3) - 3(x - 3 ) = x <=> (3x + 9) - (3x - 9) = x <=> x = 18   18NSWER IS 18
Answer: A
At a particular pizza shop, a pizza can be created from any combination of 5 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?
Options
A) 6 B) 35 C) 120 D) 450 E) 750

Solution: Number of possible ways to select 1 type of spice = 5c1 = 5   Number of possible ways to select 2 types of cheese = 4c2 = 6   Number of possible ways to select 4 types of meat but without pepperoni and anchovies together   = Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together   = 7c4 - 5c2   =35 - 10= 
35 - 10 = 25
25   Possible ways to garnish the pizza are available to the customer= 5*6 * 25= 
5*6 * 25 = 750
750   Answer 750
Answer: E
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train? Choose the correct choice:
A) 27 7/6
B) 27 7/5
C) 27 7/2
D) 27 7/9
E) 27 7/1

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 5 = 250/9   = 27 7/9 m.   Answer:27 7/9
Answer: D
If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.41 then sum is  Choose one
A) s.5000 B) s.5100 C) s.5800 D) s.6000 E) s.4100

Solution: p(r/100)^2=C.I-S.I   P(10/100)^2=41   4100   ANSWs.4100R:s.4100
Answer: E
The average temperature of Haridwar in the first four days of a month was 58 degrees C. The average for the second, third, fourth and fifth days was 60 degrees. If the temperature of the first and fifth days were in the ratio 7:8, then what is the temperature on the fifth day of Haridwar? Choose the correct option.
A) 240 degree B) 64 degree C) 232 degree D) None of these E) Cannot be determined

Solution: Explanation :   Suppose Temperature on 1st day = 7K   Suppose Temperature on 5st day = 8K   So, temperature on T + w + Th + F = 240   232 - 7K = 240 - 8K => K = 8   Temperature on 5th day = 64 degree.   Answer : 64 degree
Answer: B
Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and K. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of K if J is negative?  Select the correct option:  A) -2  B) K=0  C) 1  D) 2  E) 5

Solution: since j is negative, therefore median of the set will be 3. which is an odd number. also, we know that odd^n will always be odd. now since 34 is even, therefore 3^w will have only one factor with 34 for w=0.   mode of the set is a number which occurs maximum number of time in the set. now, since K is the mode of the set. therefore K=0. hence answer is K=0
Answer: B
x=9^10–3^17 and x/n is an integer. If n is a positive integer that has exactly two factors, how many different values for n are possible? Select the correct option.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: The expression can be rewritten as (3^2)^10 - 3^17.   Factoring the above we get: 3^17*[(3^3)-1)] = 3^17(26) = 3^17*13*2   The question asks us to find the number of prime factors (number with exactly two factors) of the expression.   From it's factored form we can find that only 2, 3 and 13 will satisfy the above conditions.   Hence Option 3
Answer: C
The sum of two numbers is 22. Five times one number is equal to 6 times the other. The smaller of the two numbers is:
Choose the correct answer
A) 10
B) 11
C) 16
D) 12
E) 24

Solution: Sol.   Let the numbers be x and (22 - x).   Then, 5x = 6(22 - x)   ⇔ 11x = 132⇔ x = 12.   So, the numbers are 12 and 10.   10nswer 10
Answer: A
In Town X, 64 percent of the population are employed, and 46 percent of the population are employed males. What percent of the employed people in Town X are females?
Select:
A) 16% B) 25% C) 28% D) 40% E) 52%

Solution: We are asked to find the percentage of females in employed people.   Total employed people 64%, out of which 46 are employed males, hence 18% are employed females.   (employed females)/(total employed people)=18/64=28%   Answer: 28%.
Answer: C
If a^x = b^3y, then  Choose the correct choice from the following answers:	A) log a/b= x/y	B) log a/ log b = x/y	C) log a/ log b = 3y/x	D) log b/a = x/y	E) log b/a = y/x

Solution: a^x = b^3y => log a^x = log b^3y => x log a = 3y log b   => log a/ log b = 3y/x   ANSWER:log a/ log b = 3y/x
Answer: C
A, B, C, D and E are 5 consecutive points on a straight line. If BC = 2CD, DE = 5, AB = 5 and AC = 11, what is the length of AE?  Pick one:
A) 19  B) 21  C) 23  D) 25  E) 27

Solution: AC = 11 and AB = 5, so BC = 6.   BC = 2CD so CD = 3.   The length of 19E is 19B+BC+CD+DE = 5+6+3+5= 
5+6+3+5 = 19
19   The answer is 19.
Answer: A
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:  Select the correct option
A) 3500 B) 3200 C) 3900 D) 3400 E) 3800

Solution: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.   Then, 10x = 4y or y = 5/2 x.   Therefore, 15x + 2y = 4000   =15x + 2 x 5/2x = 4000   =20x = 4000   Therefore, x = 200.   So, y =(5/2 x 200) = 500.   Hence, the cost of 12 chairs and 3 tables = 12x + 3y   = Rs. (2400 + 1500)   = Rs. 3900.   Answer is 3900.
Answer: C
A man buys a cycle for Rs.1400 and sells it at a loss of 25%. What is the selling price of the cycle?	Choose the correct choice from the following:  A) Rs.1090  B) Rs.1160  C) Rs.1190  D) Rs.1050  E) NONE

Solution: Solution   S.P	= 75% of Rs.1400   = Rs.(75/100×1400)   Rs.1050.   Answer Rs.1050
Answer: D
A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 6 large photos they could use for those three slots, and 22 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?	Choose the correct choice from the following.
A) 3,150
B) 4,200
C) 5,040
D) 30,800
E) 84,000

Solution: MAGOOSHOFFICIAL SOLUTION:   For the large photos, we need 6C3, which we calculated in the article:   6C3 = 20   For the smaller photos, we need 22C19, which by symmetry must equal 22C3, and we have a formula for that. In fact, in the article above, we already calculated that 22C3 = 1540.   Now, by the FCP, we just multiply these: total number of possible albums = 20*1540= 
20*1540 = 30_800
30800.   Answer= 30,800
Answer: D
Anintegratedteam consists of 2 members from the engineering team and 2 members from the design team. If the engineering team has 7 members and the design team has 5 members, how manyintegratedteam formations are possible?
Pick:
A) 36
B) 54
C) 176
D) 210
E) 312

Solution: 2 out of 7 times 2 out of 5 => 7*6/2*1 * 5*4/2*1= 
7*6/2*1 * 5*4/2*1 = 210
210   210
Answer: D
An unbiased cubic die is thrown.What is the probability of getting a multiple of 4?
Select.
A) 1/6
B) 1
C) 2/6
D) 3/6
E) 1/12

Solution: S={1,2,3,4,5,6}   P(E)=n(E)/n(S)   n(s)=Total numbers in a die=6   Let E be the event of getting the multiple of 4   then ,E={4}   P(multiple of 4) = 1/6   ans 1/6
Answer: A
Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 10 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone? Choose the correct option:  A) 4  B) 5  C) 6  D) 12  E) None of these

Solution: The part of job that Suresh completes in 9 hours   = 9⁄15 = 3⁄5   Remaining job = 1 - 3⁄5 = 2⁄5   Remaining job can be done by 4shutosh in 2⁄5 × 10 = 4 hours   4nswer 4
Answer: A
If 2 and 3 are positive integers, then 2*3 + 2 is	Pick.
A) 8
B) 10
C) 12
D) 12
E) 16

Solution: 8nswer : 8
Answer: A
If a - b = 5 and a2 + b2 = 31, find the value of ab.
Answers
A) 9
B) 2
C) 3
D) 7
E) 12

Solution: 2ab = (a2 + b2) - (a - b)2   = 31 - 25= 
31 - 25 = 6
6   ab= 3.   Answer: 3
Answer: C
x and y are positive integers. When x is divided by 12, the remainder is 5, and when x is divided by 13, the remainder is 3. When y is divided by 14, the remainder is 5, and when y is divided by 7, the remainder is 5. What is the least possible value of x + y?
Answers:
A) 24
B) 12
C) 64
D) 48
E) 25

Solution: When x is divided by 12, the remainder is 5: So, the possible values of x are: 5, 17, 29, 41, etc.   When x is divided by 13, the remainder is 3: So, the possible values of x are: 3,16,29... STOP. Since both lists include 29, the smallest possible value of x is 29.   When y is divided by 14, the remainder is 5: So, the possible values of y are: 5, 19, 33,47 etc.   When y is divided by 7, the remainder is 5: So, the possible values of y are: 5, 19 ...STOP. Since both lists include 19, the smallest possible value of y is 19   Since the smallest possible values of x and y are 29 and 19 respectively, the smallest possible value of x + y is 48. So,48 is the correct answer to the original question.
Answer: D
Arun, Akash, Amir and Aswanth go for a picnic. When Arun stands on a weighing machine, Akash also climbs on, and the weight shown was 132 kg. When Akash stands, Amir also climbs on, and the machine shows 130 kg. Similarly the weight of Amir and Aswanth is found as 102 kg and that of Akash and Aswanth is 116 kg. What is Aswanth’s weight? Select the correct option:
A) 78 kg B) 44 kg C) 62 kg D) 50 kg E) None of these

Solution: Explanation :   Let weight of arun,akash,amir and aswanth be a,b,c and respectively.   a+b=132.......(1)   b+c=130.......(2)   c+d=102.......(3)   b+d=116.......(4)   Evaluating 3 and 4 we get   2b=144   b=72   From (4) we have d=116-72= 
116-72 = 44
44.   Therefore weight of aswanth is 44 kg...   Hence (B) is the correct answer.   Answer : 44 kg
Answer: B
A 24" x 24" square metal plate needs to be fixed by a carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 25 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use?
Choose the correct answer
A) 94  B) 95  C) 96  D) 97  E) 98

Solution: every corner will have one,4 corners will have 4+ and for 4 sides 23   no of nails=4+(4*23)= 
4+(4*23) = 96
96   ANSWER:96
Answer: C
Two persons start running simultaneously around a circular track of length 200 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?  Answers
A) 16 seconds	B) 18 seconds	C) 19 seconds	D) 27 seconds	E) 10 seconds

Solution: Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 200 / (15 + 25)5/18 = 200* 18 / 40 * 5   = 18 seconds.   Answer:18 seconds
Answer: B
A taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 10 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.  Choose the correct answer.
A) 20  B) 24  C) 32  D) 16  E) 40

Solution: Let the speed of bus be v - 10, speed of taxi be v   The bus travelled a total of 8 hrs and taxi a total of 3 hrs.   Hence 8 * (v-10) = 3v   8v - 80 = 3v   5v = 80   16
Answer: D
A train running at the speed of 60 km/hr crosses a pole in 15 seconds. What is the length of the train?
Choose the correct answer
A) 120 metres B) 180 metres C) 324 metres D) 250 metres E) 150 metres

Solution: Speed= 60 x	5/18	m/sec	= 50/3	m/sec.   Length of the train = (Speed x Time).   Length of the train = 50/3	x 15 m = 250 m.   Option 250 metres
Answer: D
UNO plans a gathering.
However there is threat of terrorist attack. So security guard who is a mathematical plans somethings to secure the place.
A terrorist stands nearby the door where
1st ambassador comes , the security guard said 'twelve' and ambassador replied with 'six'.
2nd ambassador comes , the security guard said 'six' and ambassador replied with 'three'.
The terrorist thinks its enough and walks to the door.
The security person said 'eight' , terrorist replied 'four' and get immediately arrested.
why ? Select the correct option:
A) Five
B) Three
C) Two
D) Eight
E) Seven

Solution: Five   'five'   Its the count of alphabet
Answer: A
A cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 6 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ? Answers:  A) 4.5 hrs  B) 5 hrs  C) 6.5 hrs  D) 7.2 hrs  E) 30 hrs

Solution: Net part filled in 1 hour= 1/5 -1/6= 1/30   Therefore the cistern will be filled in 30 hours .   ANSW30 hrsR:30 hrs
Answer: E
Molly's age in 18 years will be four times her age eighteen years ago. What is Molly's present age?
Select:
A) 20	B) 21	C) 24	D) 30	E) 36

Solution: Let x be Molly's present age.   x + 18 = 4(x-18)   x = 30   The answer is 30.
Answer: D
An investor bought two shares of stock, which he sold for $72 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had: Options.
A) a profit of $10 B) a profit of $6 C) a loss of $6 D) a loss of $10 E) neither a profit nor a loss

Solution: The cost of the first stock was 72/1.2= 
72/1.2 = 60
60, so the profit from it is 12.   The cost of the second stock was 72/0.8= 
72/0.8 = 90
90, so loss from it is 18.   Overall the loss is $6.   The answer is a loss of $6.
Answer: C
How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 7?
Pick one:
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: The numbers should be of the form 7c+3.   The minimum is 3 when c=0.   The maximum is 45 when c=6.   There are 7 such numbers.   The answer is 7.
Answer: C
One out of five employees are capable of doing a certain task. 80 percent of the five employees, including the one who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable?  Choose the correct choice from the following answers
A) 43.33%
B) 33.33%
C) 13.33%
D) 75%
E) 23.33%

Solution: Given 80% of 4 employees including 1 who are capable of doing task.   80% of 5 employeees   = 80/100 * 5= 
80/100 * 5 = 4
4 employees===> 1 employees who are capable of doing the task and three employee who is not capable.   percentage of employees assigned who are not capable   = 3/4 * 100= 
3/4 * 100 = 75
75%   ANSWER:75%
Answer: D
A group consists of 4 men, 6 women and 1 child. In how many ways can 2 men , 3 women and 1 child selected from the given group?	Answers:
A) 400  B) 120  C) 287  D) 278  E) 281

Solution: Explanation:   Two men, three women and one child can be selected in â´Câ‚‚ * â¶Câ‚ƒ * âµCâ‚ ways   = (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 1= 
(4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 1 = 120
120 ways.   Answer:120
Answer: B
Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $4 per page each time a page is revised. If a certain manuscript has 100 pages, of which 30 were revised only once, 20 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?  Choose the correct choice from the following:  A) $760  B) $750  C) $810  D) $800  E) $780

Solution: 50 pages typed 1x   30 pages typed 2x (original + one revision)   20 pages typed 3x (original + two revisions)   50(5)+30(5+4)+20(5+4+4)=250+270+260= 
250+270+260 = 780
780   Answer - $780
Answer: E
How many such pairs of digits are there in the number '5391246' in both forward and backward directions, each of which has as many digits between them in the number as when the digits are arranged in ascending order with in the number? Choose the correct choice from the following options.
A) 1	B) 2	C) 0	D) 3	E) More than 3

Solution: Answer: Option More than 3
Answer: E
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. 64.50, his capital is?
Pick.
A) 24,602  B) 28,888  C) 25,800  D) 24,628  E) 24,6012

Solution: Let the capital be Rs. x. Then,   (x * 8 * 1)/100 - (x * 31/4 * 1/100) = 64.50   32x - 31x = 6450 * 4   x = 25,800.   Answer: 25,800
Answer: C
x and y are integers. x + y < 11 and x > 6. What is the smallest possible value of x - y ?	Choose the most appropriate option.
A) 1
B) 2
C) 4
D) -2
E) -4

Solution: Focus on the transition points and plug in the values.   x > 6 so x could be 7, 8, 9, 10, 11 etc   Look at x = 7   7 + y < 11   y < 4   y could be 3, 2, 1, 0, -1 etc   When y is 3, we get x - y = 4   This must be the smallest value because as x increases, y reduces so x - y increases.   Take another example. x = 11 so y < 0.   x - y will give a value greater than 11.   Answer (4).
Answer: C
The rate of Interest on a sum of money is 2% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is Pick:
A) 2,200
B) 2,000
C) 2,100
D) 2,250
E) 2,540

Solution: Explanation:   I1 = (P x 3 x 2)/100 = 3P/50   I2 = (P x 4 x 4)/100 = 4P/25   I3 = (P x 1 x 5)/100 = P/20   3P/50 + 4P/25 + P/20 = 540   The L.C.M of 50, 25, 20 = 100   (6P + 16P + 5P)/100 = 540   27P/100 = 540   27P = 54000   P = 54000/27= 
54000/27 = 2_000
2000   Answer: Option 2,000
Answer: B
The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?  Choices.
A) Rs.4098
B) Rs.4078
C) Rs.4097
D) Rs.4096
E) Rs.4028

Solution: Principal   = [4913 / (1 + 25/(4 * 100))3]   = 4913 * 16/17 * 16/17 * 16/17   = Rs.4096.   Answer:Rs.4096
Answer: D
Each of the 55 points is placed either inside or on the surface of a perfect sphere. If 60% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere? Choices:
A) 7  B) 11  C) 13  D) 16  E) 38

Solution: Maximum number of points on the surface is 60%*55 = 33   Now note that if two points form a diameter, they cannot be part of any other diameter.   So in the best case we can pair up the points   We have 33 points, so at best we can form 16 pairs (32).   So, answer is (16)
Answer: D