MU-NLPC/Calc-aqua_rat huggingface dataset:
A number when divided by 4, gives 40 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 3 Choose the correct choice
A) A)1 B) B)3 C) C)4 D) D)6 E) E)7

Solution: Explanation:   P ÷ 4 = 40   => P = 40 * 4= 
40 * 4 = 160
160   P / 3= 160/ 3 = 53, remainder = 1   1nswer: Option 1
Answer: A
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?  Choose the correct choice from the following answers.
A) 3	B) 6	C) 8	D) 9	E) 6

Solution: M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 6   T = 6/2= 
6/2 = 3
3   3nswer:3
Answer: A
The salary of a person was reduced by 28%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?  Choose the correct option:
A) 10%
B) 15%
C) 20%
D) 25%
E) 38.9%

Solution: Let the original salary be $100   new salary = $72   increase on 72 = 28   increase on 100 = [(28/72)100]% = 38.9%   Answer is 38.9%
Answer: E
In honor of the year 2014, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive? Choose one:
A) 18
B) 36
C) 42
D) 55
E) 56

Solution: All options other than 'D' are factors of 2014. Hence, '55' is the answer
Answer: D
The ratio of Gomati’s and Rashmi’s ages is 3 : 5 respectively. After ten years this ratio will become 2 : 3. What is Rashmi’s age in years? Choose the correct choice from the following.
A) 50  B) 40  C) 60  D) Cannot be determined  E) None of these

Solution: Quicker Method : After 10 years, the ratio of Gomati and Rashmi’s ages is 2 : 3. We can also write 2 : 3 as 4 : 6. Now, difference in the ratio is I in both the cases.   Therefore, 1 = 10   ∴ 5 → 5 × 10 = 50 years.   50nswer 50
Answer: A
a man leaves office daily at 7 pm, a driver with car comes from his home to pick up him from office and bring back home.one day he gets free at 5:30 pm....,instead of waiting for car ,he starts walking towards his home,on the way he meets the car and returns home by car,he reaches home 20 minutes earlier than usual. In how much time does he reach home usually ?  Choices:  A) 1 hr and 20 mins  B) 1 hr and 30 mins  C) 1 hr and 40 mins  D) 1 hr and 10 mins  E) 1 hr and 50 mins

Solution: Since the car has met the person 20 minutes before hand, it has actually saved 10 mins of journey (to and fro)   since the man has started 1.30 hrs before and car has met him 10 mins before actual time he takes to reach daily is 1 hr and 20 mins   1 hr and 20 minsNSWER:1 hr and 20 mins
Answer: A
How many positive integers I less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ? Pick.
A) 19
B) 18
C) 17
D) 16
E) 15

Solution: We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?   The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?   1, 3, 5, 7   None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = 15
Answer: E
In Richie's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?  Choose the correct choice from the following:
A) 43.0 B) 45.5 C) 46.0 D) 49.0 E) 50.0

Solution: In Richie's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 50 and 51 employee will be each 43K. hence median = (43K+43k)/2=43.0(43 +43 )/2= 
(43 +43 )/2 = 43
43.0
Answer: A
Souju's age is 1/4th of her father's age. Souju's father's age will be twice Tharak's age after
10 years. If Tharak's eight birthdays was celebrated two years before, then what is Souju's present age.  Select:
A) 6.5	B) 7.5	C) 8.5	D) 8	E) 9

Solution: tharak's present age =8+2= 
8+2 = 10
10   souju's father's age after 10 years=2(10+10)=40   souju's father's present age =40−10=30   tharak's present age =1/4 *30= 
1/4 *30 = 15/2 = around 7.5
7.5   ANSWER:7.5
Answer: B
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 choices:  A) 150  B) 781  C) 767  D) 277  E) 266

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
Price of a book increases 15% successively (2times) what is the new price of the book more compared to that of the old price: Select the correct option:
A) 32.25% B) 23.34% C) 36% D) 39% E) 29%

Solution: New price is 1.15*1.15*old price = 1.3225 *old price   Increase in price = 0.3225 * old price   % increase = 100* 0.3225 * old price /old price = 32.25 %   32.25%NSWER:32.25%
Answer: A
A is 16th position and 29th from down of the people who passed. 5 failed , 6 didn't give . how many boys are there in the class? Choose the correct choice from the following answers:
A) 52	B) 53	C) 54	D) 55	E) 56

Solution: A is 16th position, means = 15 + A   29th from down, means = A + 28   Total passed = A + 15 + 28 = 44   Total failed = 5   55idn't give = 6   Therefore, total boys = 44 + 5 + 6= 
44 + 5 + 6 = 55
55   ANSWER:55
Answer: D
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Choose the correct choice from the following
A) 2 : 3
B) 4 : 3
C) 6 : 7
D) 9 : 16
E) None of these

Solution: Let us name the trains as A and B. Then,   (A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.   Answer 4 : 3
Answer: B
9 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio  Choose the correct choice from the following options
A) 1:2	B) 1:3	C) 2:1	D) 2:5	E) None of these

Solution: Explanation:   Let 1 man 1 day work = x   1 boy 1 day work = y   then 9x + 2y = 4(x+y)   => 5x = 2y   => x/y = 2/5   => x:y = 2:5   Option 2:5
Answer: D
The speed of a car is 90 km in the first hour and 42 km in the second hour. What is the average speed of the car? Select
A) 89 kmph  B) 92 kmph  C) 75 kmph  D) 65 kmph  E) 66 kmph

Solution: S = (90 + 42)/2= 
(90 + 42)/2 = 66
66 kmph   66 kmph
Answer: E
How many five digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 12, without any of the digits repeating?
Answers:
A) 100
B) 98
C) 81
D) 96
E) 72

Solution: 0,1,2,3,4,5   One digit will have to remain out for all 5 digit numbers;   if 0 is out; Leftover digits will be 1,2,3,4,5 = Sum(1,2,3,4,5)=15. Ignore   if 1 is out; Leftover digits will be 0,2,3,4,5 = Sum(0,2,3,4,5)=14. Ignore   if 3 is out; Leftover digits will be 0,1,2,4,5 = Sum(0,1,2,4,5)=12.   4*4! = 4*24= 
4*24 = 96
96   if 4 is out; Leftover digits will be 0,1,2,3,5= Sum(0,1,2,3,5)=11. Ignore   if 5 is out; Leftover digits will be 0,1,2,3,4 = Sum(0,1,2,3,4)=10. Ignore   Total count of numbers divisible by 12 = 96   Ans:96
Answer: D
6 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?	Pick: A) 30 B) 21 C) 18 D) 15 E) 10

Solution: the formula to count handshakes is n(n−1)2n(n−1)2   Where n is the number of people   => 6(6-1)/2 = 6*5/2 = 30/2= 
30/2 = 15
15=> the answer is 15(15)
Answer: D
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?  Choose the correct choice from the following choices:	A) 10	B) 5	C) 15	D) 20	E) 25

Solution: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.   The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.   The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.   Required number of numbers = (1 x 5 x 4) = 20.   Answer is 20.
Answer: D
Which of the following correctly lists the data sets in order of greatest to least standard deviation?
I. 4, 12, 15, 17, 19, 25
II. 42, 42, 42, 42, 42, 42
III. 57, 58, 59, 50, 51, 52  Choose the correct choice from the following options:
A) II, I, III  B) I, III, II  C) I, II, III  D) II, III, I  E) III, II, I

Solution: out of three given sets,   II has all numbers same, so it has zero standard deviation hence it is Least   only answer choices C and D have II in least position.   Out of I ans III   III has consecutive numbers , hence all are closedly spaced hence std deviation will be less   while in I,numbers are spread widely hence std deviation should be more than III   hence order should be II, III, I   IMO I, II, III
Answer: C
If Rs. 782 be divided into three parts, proportional to 1/2:2/3 :3/4, then the first part is: Select the correct option.
A) 202  B) 201  C) 205  D) 206  E) 204

Solution: Given ratio = 1/2: 2/3:3/4   = 6 : 8 : 9.   Therefore, 1st part = Rs. (782 x 6/23)= Rs. 204.   Answer is 204.
Answer: E
X, Y, and Z are consecutive numbers and X > Y > Z. Also, 2X + 3Y + 3Z = 5Y + 11. What is the value of Z?	Choose the correct choice
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.   2X + 3Y + 3Z = 5Y + 11   2Z+4+3Z+3+3Z = 5Z+5+11   3Z = 9   Z = 3   The answer is 3.
Answer: B
The population of a town increased from 1,75,000 to 2,97,500 in a decade. The average percent increase of population per year is	Choose the correct choice from the following:
A) 4.37%
B) 5%
C) 6%
D) 8.75%
E) 7%

Solution: Solution   Increase in 10 years	= (297500 - 175000)= 
(297500 - 175000) = 122_500
122500   Increase%= (122500/175000Ã—100)%   = 70%.   Required average	= (70/10)= 
(70/10) = 7
7%.   Answer 7%
Answer: E
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1600 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?  Choose the correct choice from the following answers.
A) 140 B) 99 C) 88 D) 160 E) 12

Solution: Given that the area of the square = 1600 sq.units   => Side of square = √1600 = 40 units   The radius of the circle = side of the square = 40 units Length of the rectangle = 2/5 * 40= 
2/5 * 40 = 16
16 units   Given that breadth= 10 units   Area of the rectangle = lb = 16 * 10= 
16 * 10 = 160
160 sq.units   Answer: 160
Answer: D
If a tap could fill entire tank in 20 hrs due to leakage, then in how much time
tank can be emptied by leakage if tap can fill entire tank in 16 hrs without leakage	Options:	A) 12hrs	B) 24hrs	C) 36hrs	D) 80hrs	E) 52hrs

Solution: time take to fill[withleakage] =20hrs so workdone in 1hr=1/20   time tkae to fill[without leakage]=16hrs so workdone in 1hr=1/16   if u subtract both u'll get time taken by leakage to empty...   1/20-1/16=1/80 so 80hrs   ANSWER:80hrs
Answer: D
A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 20 km in 10 hours. How much time he would have saved if the direction of tide has not changed? Select the correct option
A) 2 B) 8 C) 1 D) 6 E) 5

Solution: Explanation:   He covered 5 km in 1 hour , so he might cover 20 km in 4 hours.   But he took 10 hours.   He would have saved 10 – 4 = 6 hours.   Answer: 6
Answer: D
Look at this series: 544, 509, 474, 439, 404, 369 ... What number should come next?  Choose the correct choice from the following choices.
A) 334	B) 408	C) 306	D) 507	E) 404

Solution: 334   This is a simple subtraction series. Each number is 35 less than the previous number.   334
Answer: A
The cost of type 1 rice is Rs 15 per Kg and type 2 rice
is Rs 20 per Kg. If both type1 and type 2 are mixed in the
ratio of 2:3,then the price per Kg of the mixed variety
of rice is?
Choose the most appropriate option
A) 15 B) 17 C) 19 D) 18 E) 16

Solution: Let the price of the mixed variety be Rs x per Kg.   Cost of 1 Kg of type 1 rice Rs 15 Cost of 1 Kg of type 2 rice Rs 20   Mean Price Rs x   20-x x-15   (20-x) /( x-15) = 2/3   => 60-3x = 2x-30   5x = 90=>x=18.   ANSWER : 18 18
Answer: D
The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?  Options:
A) 3% decrease
B) 5% decrease
C) 9% decrease
D) 4% decrease
E) 8% decrease

Solution: (30 * 30)/100= 
(30 * 30)/100 = 9
9% decrease   Answer:9% decrease:
Answer: C
A money lender lent Rs. 1000 at 4% per year and Rs. 1400 at 5% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.
Select the correct option.
A) 3.2	B) 3.75	C) 4	D) 4.25	E) 4.5

Solution: (1000xtx4/100) + (1400xtx5/100) = 350 â†’ t =3.2 answer 3.2
Answer: A
If d is the standard deviation x, y, and z, what is the standard deviation of x + 4, y + 4, z + 4 ?  Choose the correct choice:
A) 4d
B) d
C) 5d
D) d+4
E) d+16

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 4 is added in each term of set {x, y, z} then the new set {x+4, y+4, z+4} will remain same as the previous standard deviation i.e. d   Answer: d
Answer: B
A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.	Select
A) 40  B) 50  C) 62  D) 45  E) 56

Solution: Let the average after 11th inning = x   Then, average after 10th inning = x-5   10(x-5)+100 = 11x   x = 100-50= 
100-50 = 50
50   Answer is 50
Answer: B
At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time.If the finance charges= 40 percent of the remainder the cost, how much less would 2 machines of type A cost than 1 machine of type B? Choose the correct choice from the following answers:
A) $10,000 B) $11,200 C) $12,000 D) $12,800 E) $13,200

Solution: 1 machine of type B will cost: 20% down payment of 50,000 = 10,000 plus remaining sum (50,000-10,000=40,000) with 40% of finance charges 40,000*1.4=56,000 --> 10,000+56,000=66,000;   2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000 plus remaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;   Difference = 66,000 - 52,800 = 13,200.   Answer: $13,200.
Answer: E
If simple interest on a certain sum of money for 8 years at 4% per annum is same as the simple interest on Rs. 560 for 8 years at the rate of 12% per annum then the sum of money is  Choose the correct choice from the following:  A) Rs.1820  B) Rs.1040  C) Rs.1120  D) Rs.1680  E) None of these

Solution: Explanation:   Let the sum of money be x   then   (x × 4 × 8)/100 = (560 × 12 × 8)/100   x × 4 × 8 = 560 × 12 × 8   x × 4 = 560 × 12x = 560 × 3 = 1680   Answer: Option Rs.1680
Answer: D
The average age of a group of persons going for tour is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for tour is:
Choose the correct choice from the following answers:  A) 5  B) 10  C) 20  D) 30  E) 40

Solution: Explanation :   Let the initial number of persons be x. Then,   => 16x + 20 x 15 -15.5 (x + 20)   => 0.5x = 10   => x = 20   Answer : 20
Answer: C
A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture?  Choose the correct choice from the following options:  A) 8  B) 7  C) 5  D) 2  E) 1

Solution: 70 * (10/100)= 
70 * (10/100) = 7
7   Wine Water   87 1/2% 12 1/2%   87 1/2% ------- 63   12 1/2% -------?=> 9-7= 
9-7 = 2
2   Answer: 2
Answer: D
Which of the following are roots of an equation (x^-2)-(x^-1)-30=0
Choose the correct choice from the following answers:
A) 1/5 and -1/6
B) -1/5 and 1/6
C) 1/5 and 1/6
D) -1/5 and -1/6
E) -5/2 and -1/6

Solution: Given: (x^-2) - (x^-1) - 30 = 0   Rewrite as: 1/(x²) - 1/x - 30 = 0   Remove fractions by multiplying both sides by x² to get: 1 - 1x - 30x² = 0   Rearrange to get: 30x² + x - 1 = 0   Factor to get: (5x + 1)(6x - 1) = 0   So, EITHER 5x + 1 OR 6x - 1 = 0   If 5x + 1 = 0, then x = -1/5   If 6x - 1 = 0, then x = 1/6   So, the roots (solutions) are -1/5 and 1/6   The answer is -1/5 and 1/6.
Answer: B
A drink vendor has 80 liters of Mazza, 144 liters of Pepsi, and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required? Select:	A) 35	B) 36	C) 37	D) 38	E) 39

Solution: If we want to pack the drinks in the least number of cans possible, then each can should contain the maximum numbers of liters possible.As each can contains the same number liters of a drink, the number of liters in each can is a comman factor for 80,144 and 368; and it is also the highest such factor, as we need to store the maximum number of liters in each can.   So, the number of liters in each can = HCF of 80,144 and 368 = 16 liters.   Now, number of cans of Maaza = 80/16= 
80/16 = 5
5   Number of cans of Pepsi= 144/16= 
144/16 = 9
9   Number of cans of Sprite= 368/16= 
368/16 = 23
23   Thus, the total number of cans required= 5 + 9 + 23= 
5 + 9 + 23 = 37
37 Answer: 37
Answer: C
Two trains move in the same direction at speeds 50 kmph and 32 kmph respectively. A man in the slower train observes that 15 seconds elapse before the faster train completely passes by him. What is the length of faster train?  Select.
A) 100m B) 75m C) 120m D) 50m E) 70m

Solution: since both trains move in same direction so:   average speed=50-32= 
50-32 = 18
18kmph=5mps   speeed=length of train /time   length of train=5*15= 
5*15 = 75
75m   ANSWER:75m
Answer: B
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:  Choose the correct choice from the following answers:
A) 39, 30	B) 41, 32	C) 42, 33	D) 43, 34	E) 42, 34

Solution: Let their marks be (x + 9) and x.   Then, x + 9 = 56/100(x + 9 + x)   25(x + 9) = 14(2x + 9)   3x = 99   x = 33   So, their marks are 42 and 33.   answer :42, 33
Answer: C
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 60 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Choose the correct option.
A) 21 B) 88 C) 40 D) 99 E) 22

Solution: Relative speed = 60 + 30= 
60 + 30 = 90
90 km/hr.   90 * 5/18= 
90 * 5/18 = 25
25 m/sec.   Distance covered= 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 *1/25= 
1000 *1/25 = 40
40 sec   Answer: 40
Answer: C
There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of n? Select the correct option:
A) 11 B) 12 C) 15 D) 18 E) 22

Solution: Combinations of two persons, in which Michael was not selected = 55   number of ways two persons can be selected from m people = m*(m-1)/2   Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11   Thus, n = m + 1(Michael) = 12   option 12
Answer: B
Jim is now twice as old as Fred, who is nine years older than Sam. Six years ago, Jim was six times as old as Sam. How old is Jim now?  Choose the correct option:
A) 30	B) 34	C) 38	D) 42	E) 46

Solution: J = 2F = 2(S+9) = 2S+18   J-6 = 6*(S-6)   (2S+18)-6 = 6S-36   S = 12 and so J = 42   The answer is 42.
Answer: D
The average of 11 numbers is 9.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is  Choices:
A) 71.5
B) 11.5
C) 81.5
D) 11.5
E) 22.5

Solution: Explanation:   Middle numbers = [(10.5 x 6 + 11.4 x 6) - 9.9 x 11] = 22.5.   Answer: 22.5
Answer: E
A man has Rs. 80 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?	Choose the correct option:	A) 15	B) 60	C) 75	D) 90	E) 105

Solution: Answer : A   Let number of notes of each denomination be x.   Then, x + 5x + 10x = 80   16x = 80   x =5.   Hence, total number of notes = 3x = 15.
Answer: A
(128.5 x 32) + (13.8 x 30) = ? x 25  Select:
A) 524.48
B) 556.02
C) 574.36
D) 181.04
E) 595.46

Solution: Explanation :   ? = (128.5 x 32) + (13.8 x 30)/25   = 4112 + 414/25 = 181.04   Answer : Option 181.04
Answer: D
Two pipes A and B can fill a cistern in 37 ½ min and 45 minutes respectively. Both the pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after Choices:
A) 6 minutes
B) 9 minutes
C) 45 minutes
D) 3 minutes
E) 4 minutes

Solution: If pipe 9 minutes is turned off after x mins, then   (2*30)/75 + x/45 =1   x/45 = 1-60/75 = 1/5   x= 45/5= 
45/5 = 9
9 mins   ANSWER:9 minutes
Answer: B
If a(a - 6) = 27 and b(b - 6) = 27, where a ≠ b, then a + b =?  Pick.
A) −48  B) 6  C) −2  D) 46  E) 48

Solution: i.e. if a =-3 then b = 9   or if a = 9 then b =-3   6ut in each case a+b = -3+9= 
-3+9 = 6
6   Answer: option 6
Answer: B
Nine persons went to a hotel for taking their meals. Eight of them spent 14 each on their meals and the ninth spend 8 more than the average expenditure of all the nine. What was the total money spent by them? Pick
A) 115 B) 117 C) 119 D) 122 E) 135

Solution: Let the average expenditure of all the nine be x.   Then, 14 × 8 + (x + 8) = 9x or 8x = 120 or x = 15.   ∴ Total money spent = 9x = (9 × 15) = 135.   Answer 135
Answer: E
What is the greater of the two numbers whose product is 2048, given that the sum of the two numbers exceeds their difference by 64?	Choices
A) A)90  B) B)32  C) C)64  D) D)70  E) of these

Solution: Let the greater and the smaller number be g and s respectively.   gs = 2048   g + s exceeds g - s by 64 i.e., g + s - (g - s) = 64   i.e., 2s = 64 => s = 32.   g = 2048/s = 64.   ANSWER:64
Answer: C
For an upcoming charity event, a male vocalist has agreed to sing 5 out of 8 “old songs” and 3 out of 7 “new songs.” How many ways can the singer make his selection?
Choices.
A) 25	B) 50	C) 150	D) 217.78	E) 600

Solution: =8C5*7C3   =8*7/3*7*5/3   =217.78   Ans = 217.78
Answer: D
On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
Choices.
A) Saturday
B) Friday
C) Monday
D) Tuesday
E) Surday

Solution: Explanation:   The year 2006 is an ordinary year. So, it has 1 odd day.   So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.   But, 8th Dec, 2007 is Saturday   S0, 8th Dec, 2006 is Friday.   Answer: Friday) Friday
Answer: B