MU-NLPC/Calc-aqua_rat huggingface dataset:
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:	Choose the correct answer:  A) 1:2  B) 4:5  C) 1:3  D) 1:1  E) 1:4

Solution: Let the third number be x.   Then, first number = 120% of x = 120x/100 = 6x/5   Second number = 150% of x = 150x/100 = 3x/2   Therefore, Ratio of first two numbers = (6x/5 : 3x/2)   = 12x : 15x = 4 : 5.   Answer is 4:5.
Answer: B
12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 16 cm height. What is the diameter of each sphere? Choose one:
A) 4 cm  B) 6 cm  C) 8 cm  D) 10 cm  E) 12 cm

Solution: Volume of cylinder = pi*r^2*h   Volume of a sphere = 4*pi*R^3 / 3   12*4*pi*R^3 / 3 = pi*r^2*h   R^3 = r^2*h / 16 = 64 cm^3   R = 4 cm   D = 8 cm   The answer is 8 cm.
Answer: C
X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
Select the correct option.
A) 3  B) 4  C) 6  D) 9  E) 5

Solution: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000   Let investment period of Z be x months.   Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)   = 240 : 300 : 30x = 8 : 10 : x   The share of Z in the annual profit of Rs. 50000 is Rs. 14000.   => [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7   => 25x = 7x + (18 * 7) => x = 7 months.   Z joined the business after (12 - 7) months. i.e., 5 months.   Answer:5
Answer: E
Two members of a certain club are selected to speak at the next club meeting. If there are 15 different possible selections of the 2 club members, how many members does the club have?	Select the correct option
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Method-1   Total No. of Selection of r out of n objects are defined by nCr = n! / [(r!)(n-r)!]   i.e. If total member = n   then nC2 = n! / [(2!)(n-2)!] = 15   i.e. n*(n-1)*n-2!/ [(2!)n-2!] = 15   i.e. n*(n-1) = 30   (for Positive Values of n)   therefore, n*(n-1) = 30   i.e. n= 6   Answer: Option 6
Answer: B
Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 2000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?	Choose the correct choice from the following answers:
A) 100000  B) 12500  C) 42000  D) Data inadequate  E) None of these

Solution: Let the investment of X in 1995 be x.   ∴ Profit = x⁄5   ∴ Income = (x + x⁄5) = 6⁄5x   Investment of company X in 1996 would be (x – 2000) From the question,   (x - 2000) × 126⁄100 = 6⁄5x ⇒ x = 42000   Answer 42000
Answer: C
If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King and other will be 10?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit Choose the correct choice from the following answers:  A) 8/2652  B) 18/2652  C) 1/2652  D) 12/2652  E) 16/2652

Solution: 2 possible cases:   King - 10 or 10 -King (4 kings and 4 10).   Either way,   the total probability = 2( King -10) = 2 (4/52 * 4/51) = 18/2652. 18/2652 is the correct answer.
Answer: B
Ayesha's father was 35 years of age when she was born while her mother was 30 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? Select
A) 2 years
B) 4 years
C) 6 years
D) 8 years
E) 9 years

Solution: Mother's age when Ayesha's brother was born = 30 years.   Father's age when Ayesha's brother was born = (35 + 4)= 
(35 + 4) = 39
39 years.   Required difference= (39 - 30)= 
(39 - 30) = 9
9 years. Answer: Option 9 years
Answer: E
sale of Rs 6835, Rs. 9927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6700 ?  Choose the correct answer:
A) 4966	B) 6191	C) 2877	D) 2676	E) 1881

Solution: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.   Required sale = Rs.[(6700 x 6) - 34009]   = Rs. (40200 - 34009)   = Rs. 6191   Answer: 6191
Answer: B
In one can of mixed nuts, 10% is peanuts. In another can of mixed nuts that is one-half the size of the first one, 40% is peanuts. If both cans are emptied into the same bowl, what percentage of the mixed nuts in the bowl is peanuts? Pick.
A) 16 2/3%  B) 20%  C) 25%  D) 33 1/3%  E) 35%

Solution: Can 1: size 1; 10% nuts   Can 2: size 0.5 and 40% nuts   (1x0.1+0.5x0.4)/1.5=33.33   33 1/3%
Answer: D
There is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save. Auggie was very curious to test this theory.
Auggie spent all of his money in 5 stores. In each store, he spent Rs.4 more than one-half of what he had when he went in. How many rupees did Auggie have when he entered the first store?	Choose the correct answer: A) 248 B) 120 C) 252 D) 250 E) 350

Solution: Amount left = 0.5x−4   For fifth store this is zero. So x = 8. That means he entered fifth store with 8.   Now for fourth store, amount left = 8 so 0.5x−4=8⇒ x = 24   For third store, amount left = 24 so 12x−4=24⇒ x = 56   For Second store, amount left = 56 so 0.5x−4=56⇒ x = 120   For first store, amount left = 120 so 0.5x−4=120⇒ x = 248   So he entered first store with 248.   248NSWER:248
Answer: A
What is the sum of the odd integers from 25 to 55, inclusive? Select.
A) 495
B) 550
C) 555
D) 600
E) 640

Solution: The mean is 40.   Sum=Mean(# of elements)   There are 16 odd numbers between 25-55 inclusive. 16*40=640   640
Answer: E
A farmer is having a total of 20 fruits (apples or oranges). He made two type packets with these fruits. All the fruits are in either apple packets of orange packets. Apple Packets contain 3 apples each and Orange packets contain 2 oranges each.
If |apple packets| < 4
Then How many packets of apples the farmer can have. When number of apple and orange packets are both positive integers above zero.
Choose the correct choice from the following answers
A) 2
B) 3
C) 4
D) 7
E) 6

Solution: Let us start by understand the meaning of 4 > |Number of Apples|   1) when we write |-x| this means the same as |x|.   2) Mod is very easy concept if you solve mod question by considering as a distance. when a mod is written as |x-(a)| = b, this means the distance from point 'a' (both side left and right of 'a' on number line) is b. |x-(a)| < b means the distance is between the two extreme distance(left and right side of 'a' on number line, considering the max distance is 'b' from 'a' - as per this scenario.....hence the value of 'a' must be between these two extremes. |x-(a)| > b means the distance is greater than the distance of 'b'..i.e the value of a could be anywhere more than 'b'.   Now come to the question. Let number of apple packets be ‘a’ and number of oranges packets be ‘b’. First its given |a| < 4 ==> |a-0| < 4 ==> the distance from zero is less than 4. So the point ‘a’ will be -3,-2,-1,0,1,2,3 as distance from 0 to these values is less than 4. Number of apple packets is above zero so possible values of ‘a’ left are 1,2,3.   As per the given information there are total of 20 fruits and they are in packets (3 per packet for apples and 2 per packets for oranges) so we can write it as follows:   3a + 2b = 20 ==> b = 10 – (3*a)/2. If b is an integer then ‘a’ must be divisible by 2. If we take only those values of ‘a’ that are divisible by 2 then we are left with 2 only. So there are two packets of apples. If there are two packets of apples then b = 10 – (3*2)/2 ==> b = 7. So we have 7 packets of oranges and 2 packets of apples. So A is the answer. 7 packets (2 orange each) and 2 packets of apples (3 apples each) make 20 fruits in total.
Answer: A
A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60?
Pick.
A) 20 B) 10 C) 60 D) 50 E) 40

Solution: Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above.   [sum(Xi) + sum(Yi)] / 20 = 70 : class average   sum(Xi) / n = 50 : average for less that 60   sum(Yi) / N = 75 : average for 60 or more   50n + 75N = 1400 : combine the above equations   n + N = 20 : total number of students   n = 4 and N = 16 : solve the above system   correct answer 20
Answer: A
The average (arithmetic mean)R of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.
Choose the correct choice from the following.
A) I only
B) II only
C) III only
D) II and III only
E) None of the above

Solution: Given :   p + q = EVEN (odd + odd =even)   p + q + s + t = EVEN (even + even = even) nothing more....   (p + q + s + t) / 4 = x   I.   x may or may not be integer, we only know sum of 4 variables is even not necessarily multiple of 4. I is out.   II.   Similarly, x an integer if sum of 4 variables is multiple of 4 but not an integer if it is not multiple of 4, we only know it is even. II is out.   III.   As in II, if X is integer 2x is Even, if X has decimal part (a.5), 2x is odd. III is out.   Answer None of the above, None.
Answer: E
A grocer stacked oranges in a pile. The bottom layer was rectangular with 4 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer? Choose the correct choice from the following answers
A) 6
B) 4
C) 3
D) 2
E) 1

Solution: Bottom Layer = 5 x 4 = 20   IInd Layer = (5-1) x (4-1) = 12   IIIrd Layer = (4-1) x (3-1) = 6   6nswer = 6 = 6
Answer: A
A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? Choose the correct answer
A) 3 1/5 Km B) 4 Km C) 4 1/5 Km D) 3 2/5 Km E) 3 3/5 Km

Solution: Formula = S1*S2/S2-S1 * T1+T2/60   = 4*6/2 * 16/6   = 24/2 * 16/60   = 8 * 2/5   = 16/5 = 3 1/5 Km   3 1/5 Km
Answer: A
Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 23 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?  Choices:
A) 64	B) 72	C) 86	D) 98	E) 102

Solution: Use the options.   The options which after getting added to 23 shows a cube of a number could be right.   Here    64+23= 
 64+23 = 87
87   72+23= 
72+23 = 95
95   86+23= 
86+23 = 109
109   98+23= 
98+23 = 121
121   102+23= 
102+23 = 125
125 ---(5*5*5)   So we have 102 as the answer!   102
Answer: E
A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
Pick one
A) 10.36 B) 10.39 C) 10.3 D) 10.34 E) 10.31

Solution: D = 70 * 1 ½ = 105 km   RS = 85 – 70 = 15   T = 105/15= 
105/15 = 7
7 h     3.30 + 7= 
  3.30 + 7 = 10.3
10.30 p.m.   Answer:10.3
Answer: C
An entry in an unshaded square is obtained by adding the entries connected to it from the row above (11 is one such number). Write the value of n ?  Choose one:
A) 10  B) 11  C) 12  D) 9  E) 8

Solution: see the values row wise   5 6 n 7   11 6+n 7+n   11+6+n 6+n+7+n   60   hence 11+6+n+6+n+7+n =60   n= 10   10NSWER:10
Answer: A
The population of a town is 10000. It increases annually at the rate of 40% p.a. What will be its population after 2 years?
Choose the correct choice:
A) 14000 B) 14400 C) 19600 D) 14600 E) 14700

Solution: Formula :   10000 × 140/100 × 140/100 = 19600   Answer : 19600
Answer: C
Length of a rectangular plot is 20mtr more than its breadth. If the cost of fencing theplot at 26.50 per meter is Rs.5300, what is the length of the plot in mtr? Choose the most appropriate option.
A) 40 m  B) 60 m  C) 70 m  D) 77 m  E) 80 m

Solution: Let breadth = x metres.   Then, length = (x + 20) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 20) + x] = 200   2x + 20 = 100   2x = 80   x = 40.   Hence, length = x + 20 = 60 m   60 m
Answer: B
How much interest will $10,000 earn in 9 months at an annual rate of 4%?
Select:
A) $300
B) $350
C) $450
D) $550
E) $650

Solution: Soln:-   9 months = 3/4 of year;   4% = 4/100=1/25;   $10,000(principal)*1/25(interest rate)*3/4(time)=$300.   $300NSWER:$300
Answer: A
What is the remainder when 8^714 is divided by 5 ?  Choose the correct choice from the following options:
A) 2	B) 3	C) 1	D) 0	E) 4

Solution: 8^0 = 1   8^1 = 8   8^2 = 64   8^3 = 512   8^4 = 4096   8^5 = .....8   and so on after ignoring the first last-digit of 8^0 = 1, in a recurring last-digit pattern of 8,4,2,6,8,4,2,6....   715/4 = 178 (with a remainder 2) so the last number is a 4.   so when 8^714 is divided by 5 the remainder is 4, ANS = 4
Answer: E
A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 40 inches. Find b. Choose the correct choice from the following answers:  A) 8  B) 6  C) 24  D) 32  E) 48

Solution: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.   From the second premise, we know that the LCM of 12 (2^2*3) andbis 40 (2^3*5), sob=2^3 or 2^3*5 (8 or 40).   Combining 2 premises shows the answer is 6(6).
Answer: B
The edge of a cube is 5a cm. Find its surface?
Choose the most appropriate option: A) 150a2 cm2 B) 170a2 cm2 C) 125a2 cm2 D) 175a2 cm2 E) 120a2 cm2

Solution: 6a2 = 6 * 5a * 5a = 150a2   150a2 cm2nswer:150a2 cm26 * 5  * 5= 
6 * 5  * 5 = 150
150a2   150a2 cm2nswer:150a2 cm2
Answer: A
Of the 65 cars on a car lot, 45 have power steering, 25 have power windows, and 17 have both power steering and power windows. How many of the cars on the lot have neither power steering nor power windows? Choose the correct option:  A) 2  B) 8  C) 12  D) 15  E) 18

Solution: Total -Neither = All power steering + All Power Windows - Both   or 65 - Neither = 45 + 25 -17= 
45 + 25 -17 = 53
53.=> Neither = 12, hence C.   Answer : 12
Answer: C
If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?
I.	x > y>z
II.	x > y
III. x = z  Options:
A) I and II	B) I only	C) II only	D) III only	E) None

Solution: 3x-3y=-3z   x-y=-z   Since z<0; -z>0   x-y>0   x>y   II correct.   We can't say much about z though;   x=-5; y=-100; z=-95   I and III incorrect.   Ans:II only
Answer: C
To create paint with a certain shade of gray, one must combine 2.116 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?	Select the correct option:
A) 165.4	B) 176.4	C) 347.1	D) 694.4	E) 705.6

Solution: Since the ratio of Black to White is 2.016 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.   Now between A and B:   Black:White = 2.116:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. B is more than half so can not be the answer, A fits the criteria hence should be the correct answer. No calculation needed whatsoever.
Answer: A
Statements: The old order changed yielding place to new.
Assumption:
1) Change is the law of nature.
2) Discard old ideas because they are old. Choose the correct choice from the following options.
A) Only conclusion I follows  B) Only conclusion II follows  C) Either I or II follows  D) Neither I nor II follows  E) Both I and II follow

Solution: Clearly, I directly follows from the given statement. Also, it is mentioned that old ideas are replaced by new ones, as thinking changes with the progressing time. So, II does not follow.   Only conclusion I follows
Answer: A
A man is 24 years older than his son.In two years, his age will be twice the age of his son.The present age of the son is :
Choose the most appropriate option
A) 22
B) 25
C) 45
D) 32
E) 15

Solution: Let the son's present age be x years. Then, man's present age =(x+24) years.   (x+24)+2=2(x+2)   x+26=2x+4   x=22.   22nswer is 22
Answer: A
The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?  Choose the correct choice from the following answers
A) 10 and 20	B) 12 and 18	C) 30 and 16	D) 21 and 63	E) 22 and 44

Solution: 16 has only the prime 2 (16=2^4) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.   The answer is 30 and 16.
Answer: C
In how many R ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.  Pick one
A) 288  B) R=144  C) R=12  D) R=48  E) 96

Solution: 4 white chess pieces can be arranged in 4! ways and 4 black pieces can be arranged in 3 ! ways.   W_ W_W_W   Number of ways = 4!*3! = 24 * 6= 
24 * 6 = 144
144   Answer R=144
Answer: B
If 25% of x is 20 less than 15% of 1500, then x is? Choose the most appropriate option
A) 872 B) 820 C) 837 D) 840 E) 83

Solution: 25% of x = x/4 ; 15% of 1500   = 15/100 * 1500= 
15/100 * 1500 = 225
225   Given that, x/4= 225 - 20   => x/4 = 205 => x = 820.   Answer:820
Answer: B
Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?	Choose the correct choice from the following.
A) 29%p.a
B) 28%p.a
C) 20%p.a
D) 24%p.a
E) 26%p.a

Solution: Rs.1440 - 1200   = Rs.240 is the interest on Rs.1200 for one year.   Rate of interest   = (100 * 240) / (100 * 1) = 20%p.a   Answer:20%p.a
Answer: C
Which of the following functions does not intersect with E = 3x^2 + 2x + 1  Choose the most appropriate option:	A) E = 3x^2 + 3x + 1	B) E = 2x^2 + 3x + 1	C) E = 3x^2 + 2x + 3	D) E = 4x^2 + 2x - 3	E) E = x^2 + 2x + 3

Solution: Let’s find the actual intersecting point of given function and each choice E.   A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0   B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1   C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.   D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2   E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.   So only choice (C) has no intersecting point. The answer is (E = 3x^2 + 2x + 3).
Answer: C
Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?	Pick.
A) 12	B) 14	C) 27	D) 53	E) 86

Solution: In this series, each number is repeated, then 13 is subtracted to arrive at the next number.   Answer: 14
Answer: B
A fast food truck spends one third of its monthly budget for truck rent and half of the rest for food and beverages. What percentage of the budget does the fast food truck spend for food and beverages? Choose the correct choice from the following answers.
A) 23.5%
B) 32.5%
C) 33.33%
D) 30%
E) 75%

Solution: Spend on rent = 1/3   Spend on food and beverage= 1/2 of remaining = 1/2*2/3= 2/6=1/3   So 1/3= 33.33%   33.33% is the answer
Answer: C
In a apartment, 30% of the people speak English, 20% speak Hindi and 12% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?  Choose the correct option:
A) 1/30
B) 2/30
C) 19/50
D) 12/90
E) 3/70

Solution: P (E) = 30 / 100 , P (H) = 20 / 100 and P (E âˆ© H) = 12 / 100 =   P (E or H) = P (E U H)   = P (E) + P (H) - P (E âˆ© H)   = (30 / 100) + (20/100 - (12 / 100) = 38/100 = 19/50   19/50
Answer: C
Difference of two numbers is 1760. If 7.5% of the number is 12.5% of the other number , find the number ?
Choose one.
A) 2640, 1000
B) 3660, 4400
C) 3000, 4160
D) 2490, 4150
E) 4660, 3000

Solution: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y   X = 125*y/75 = 5*y/3.   Now, x-y =1760   5*y/3 –y =1760   2*y/3= 1760   y =[ (1760*3)/2= 
(1760*3)/2 = 2_640
2640.   One number= 2640, Second number =5*y/3 =4400.   Answer 3660, 4400.
Answer: B
A student multiplied a number by 3/5 instead of 5/3.
What is the percentage error in the calculation?
Choose the correct answer.
A) 34% B) 44% C) 54% D) 64% E) None

Solution: Let the number be x   Then error = 5/3x - 3/5x = 16/15x   Error%= (16x/15 x 3/5x x 100)% = 64%   Answer: Option 64%
Answer: D
If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 222 responses are needed, what is the minimum number of questionnaires that should be mailed? Select the correct option.
A) 280	B) 370	C) 460	D) 550	E) 640

Solution: Let x be the minimum number of questionnaires to be mailed.   0.6x = 222   x = 370   The answer is 370.
Answer: B
A fruit salad mixture consists of apples, peaches, and grapes. There are 2 times as many pounds of apples as grapes and 3 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 12 pounds per fruit, how many more pounds of apples than grapes does the mixture have?  Pick one:
A) 15  B) 12  C) 9  D) 6  E) 4

Solution: A+P+G= 12*2   A=2G   P=3G   3G+2G+G= 12*2   G= 12*2/6= 
12*2/6 = 4
4   A= 4*2= 
4*2 = 8
8   Difference= 8-4= 
8-4 = 4
4   '4' is the answer
Answer: E
34 is related to 12 in the same way as 59 is related to  Pick.
A) 45  B) 66  C) 77  D) 88  E) 61

Solution: Explanation:   The second number is the product of the digits of the first.   45nswer: 45) 45
Answer: A
Evaluate 28% of 450 + 45% of 260
Pick
A) 232
B) 243
C) 252
D) 262
E) 282

Solution: Explanation:   = (28/100) * 450 + (45/100) * 260   = 126 + 117= 
126 + 117 = 243
243   Answer: Option 243
Answer: B
Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 25 in two years, at the same percent rate per annum?	Choose the correct choice from the following answers:
A) s. 40	B) s. 48	C) s. 49	D) s. 20	E) s. 60

Solution: Explanation:   SI in 2 years = Rs. 20, SI in 1 year = Rs. 10   CI in 2 years = Rs. 25   % rate per annum = [(CI – SI) / (SI in 1 year)] *100   = [(25 – 20) / 20] * 100   = 25 % p.a.   Let the principal be Rs. X   Time = T = 2 years   % rate = 25% p.a.   SI = (PRT/100)   20 = (X*25*2) / 100   X = Rs. 40   s. 40NSWER: s. 40
Answer: A
What is the largest 4 digit number exactly divisible by 88?
Choose the correct answer.
A) 9999	B) 9944	C) 9988	D) 9900	E) 9991

Solution: Largest 4 digit number = 9999   9999 ÷ 88 = 113, remainder = 55   Hence largest 4 digit number exactly divisible by 88 = 9999 - 55= 
9999 - 55 = 9_944
9944   Answer is 9944
Answer: B