MU-NLPC/Calc-aqua_rat huggingface dataset:
A man spends Rs. 1700 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
Options:
A) 2025
B) 2125
C) 2225
D) 2325
E) 2425

Solution: Explanation:   Total expenditure for the first 3 months = 3 Ã— 1700 = 5100   Total expenditure for 4 months = 4 Ã— 1550 = 6200   Total expenditure for 5 months = 5 Ã— 1800 = 9000   Total expenditure and saving (which is income for one year)   = 5100 + 6200 + 9000 + 5200 = Rs. 25500   So, Average monthly income = 25500/12 = Rs. 2125   Answer 2125
Answer: B
Peter rolls two dice at the same time. What is the probability that he will not roll a double?	Choose the correct choice from the following options:  A) a) 1/12  B) b) 1/36  C) c) 1/6  D) d) 1/6  E) e) 5/6

Solution: We can have 6 different outcomes on a dice.   Total outcomes on two dices = 6*6   We need only the cases when Peter rolls a double, that means only the outcomes in which the numbers on both the dices are same   They can be {1, 1}, {2, 2}, {3, 3}, {4, 4}, {5, 5}, {6, 6}.   A total of 6 outcomes   Number of outcomes where he will not roll a double = 36-6= 
36-6 = 30
30   Probability= favorable outcomes/ total outcomes = 30/36 = 5/6.   Option e) 5/6
Answer: E
Length of a rectangular plot is 50 mtr more than its breadth. If the cost of fencin g the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?  Select.
A) 46 m  B) 60 m  C) 58 m  D) 75 m  E) 80 m

Solution: Let breadth = x metres.   Then, length = (x + 50) metres.   Perimeter = 5300/26.5= 
5300/26.5 = 200
200 m.   2[(x + 50) + x]= 200   2x + 50 = 100   2x = 50   x = 25.   Hence, length = x + 50 = 75 m   75 m
Answer: D
The simple interest on a sum in 2 years is Rs. 96 and the compound interest on the same sum for the sametime is Rs. 99. Find the sum and the rate.
Choose the correct option:
A) 3.25%	B) 5.25%	C) 6.25%	D) 4.25%	E) 7.25%

Solution: P(r/100)^2 =3, ie) pr^2 =30000 S.I =P*2*R/100=96 ie) pr =4800 pr^2/pr =30000/4800= 
30000/4800 = 25/4 = around 6.25
6.25% Answer : 6.25%
Answer: C
The no of revolutions a wheel of diameter 40cm makes in traveling a distance of 176m is Choose the correct choice from the following answers.
A) 122	B) 140	C) 287	D) 128	E) 112

Solution: distance covered in 1 revolution =   = 2 *(22/7) *20 = 880/7 cm   required no of revolutions = 17600 *(7/880)= 
17600 *(7/880) = 140
140   Answer: 140
Answer: B
A and B can do a work in 6 days.They both started the work and after three days A left the work.B finished the remaining work in 15 days.In how many days will A finish the work?  Select:
A) 7 days
B) 7.5 days
C) 8.5 days
D) 9.5 days
E) 6.5 days

Solution: A and B'S 1 DAY WORK i.e A+B =1/6   WORK COMPLETED AFTER THREE DAYS=3*1/6=1/2   REMAINING WORK 1/2 i.e 50 percentage completed by B in 15 days,so B can finish work in 30 days.. b's 1 day work 1/30   a's 1 day work=1/6-1/30=4/30   so a can finish work 30/4= 
30/4 = 15/2 = around 7.5
7.5 days   ANSWER:7.5 days
Answer: B
Rs.1600 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?  Choose the most appropriate option
A) 1100
B) 1200
C) 1300
D) 1400
E) 1700

Solution: (x*5*1)/100 + [(1600 - x)*6*1]/100 = 85   5x/100 + (9600 – 6x)/100 = 85   => x = 1100   1100NSWER:1100
Answer: A
A pharmaceutical company received $4 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?	Choices
A) 8% B) 15% C) 45% D) 52% E) 58%

Solution: Solution:   This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.   We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales, and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.   First 20 Million   royalties/sales = 4/20= 1/5   Next 108 Million   royalties/sales = 9/108 = 1/12   Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents.   First 20 Million   royalties/sales = (4/20) x 60 = 12   Next 108 Million   royalties/sales = 9/108 = (1/12) x 60 = 5   We can plug 12 and 5 into our percent change formula:   (new – old)/old x 100   [(5 – 12)/12] x 100   -175/3 x 100   At this point we can stop and consider the answer choices. Since we know that 175/3 is just a bit less than ½, we know that -175/3 x 100 is about a 58% decrease.   Answer 58%.
Answer: E
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is:  Choose the correct answer.
A) 276 B) 299 C) 322 D) 345 E) 395

Solution: Clearly, the numbers are (23 x 10) and (23 x 12).   Larger number = (23 x 12) = 276.   276nswer: Option 276
Answer: A
How many ways can 7 friends be arranged around a circular dinner table? Select the correct option:  A) 120  B) 720  C) 3280  D) 5040  E) 5660

Solution: The number of ways to order 7 people is 7!   However, around a circular table, each pattern would be repeated 7 times.   So the number of ways to seat 7 friends around a circular table is 6! = 720   The answer is 720.
Answer: B
A bat is bought for Rs.400 and sold at a gain of 30% find its selling price. Choose the correct choice from the following choices.
A) A)Rs.460/-  B) B)Rs.470/-  C) C)Rs.480/-  D) D)Rs.500/-  E) E)Rs.520/-

Solution: 100 % ------> 400 (100 * 4 = 400)   130 % ------> 520 (130 * 4 = 520)   Selling price = Rs.520   Answer : Rs.520/-
Answer: E
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 9 p.c?	Choose the correct choice from the following choices.
A) 36400	B) 29000	C) 37000	D) 38000	E) 40000

Solution: Option B   Explanation:   CP + CP/8 = 45000   CP = 40000   SP = 40000*(91/100)= 
40000*(91/100) = 36_400
36400   Option 36400
Answer: A
Think of a number, divide it by 5 and add 8 to it. The result is 61. What is the number thought of?  Select the correct option:
A) 24
B) 77
C) 297
D) 265
E) 29

Solution: Explanation :   61-6 = 53   53 x 5 = 265   Answer : 265
Answer: D
At what price must an article costing Rs.51.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? Choose the correct choice from the following options:
A) 60.5 B) 69.5 C) 67.5 D) 67.7 E) 22.5

Solution: CP = 51.50   SP = 51.50*(125/100)= 
51.50*(125/100) = 64.375
64.375   MP*(95/100)= 64.375   MP = 67.7   Answer:67.7
Answer: D
If the salary of an employee is first increased by 20% and the decreased by 12%, then what is the change in his salary in percent? Choices.
A) 5.9 % increase
B) 5.6 % increase
C) 4.6 % increase
D) 1.6 % increase
E) 5.7 % increase

Solution: Explanation:   Let the first change be denoted by ‘x’ and the second by ‘y’.   The net change is given by {x + y + (x*y)/100}%   Therefore, the net change in salary is {20 + (-12) + (20*(-12))/100}   = 8 – 2.4   = 5.6% (as the sign is +ve, the change is increase)   ANSWER: 5.6 % increase
Answer: B
Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?  Pick
A) 7.19
B) 7.17
C) 7.19
D) 7.15
E) 7.11

Solution: T = (121 + 165)/ (80 + 65) * 18/5   T = 7.15   Answer:7.15
Answer: D
Reena took a loan of 1500 with simple interest for as many years as the rate of interest. If she paid 735 as interest at the end of the loan period, what was the rate of interest?
Pick
A) 3.6	B) 7	C) 18	D) Cannot be determined	E) None

Solution: Explanation: Let rate = R% and time = R years.   Then, (1500 x R x R)/100 = 735   15RÂ² = 735   RÂ² = 49   R = 7.   Answer: Option 7
Answer: B
A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $65,000, what is the average income of the other 40 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations?  Options
A) $27,500	B) $35,000	C) $37,500	D) $40,000	E) $50,000

Solution: let x be the average of 40 customers   40*x + 10* 65000 = 50*45000   solving this we have x= 40000   Answer is $40,000.
Answer: D
If 20% of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together .	Select.
A) 11 1/9
B) 10 1/9
C) 12
D) 15
E) Source: TIME material.

Solution: Use algebra:   0.2/11 1/9 + 0.8/B = 20   1/11 1/9 + 4/B = 100   0.8/11 1/9 + 0.2/B = 30   4/11 1/9+ 1/B = 150   15/B = 250   B = 3/50 work per day   11 1/9 = 3/100 work per day   Combined rate = 3/40 + 3/100 = 9/100   Time taken when working together = 100/9 = 11(1/9) days   11 1/9nswer (11 1/9)
Answer: A
The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $55,000?
Choose the correct choice from the following
A) $38,796.
B) $40,000.
C) $38,976.
D) $39,679.
E) $53,592.

Solution: 55,000 *1.16*.84= 53,592   Answer $53,592.
Answer: E
The integer n is formed by writing the integers 1 through 333 in order as shown below.
n=123456789101112.......331332333
counting from the left, what is the 333rd digit of n?
Choose the correct choice from the following answers:
A) 0	B) 1	C) 3	D) 7	E) 8

Solution: the other way you can approach this is:   add zeroes as follows:   123456789....   make a pair of 3 by making each number a 3 digit number   000   001   002   003   004   005   006   007   008   009   010.... and so on   ....by doing this we can make that every other 30th digit will be a 9   and for doing this we are adding 1*3+2*9+1*90=112 zeroes...therefore 333rd digit now will be 333+111= 
333+111 = 444
444 th digit   now 30*15=450....therefore 450th digit will be 9   and 15 th series will be of 141,142....149   so ........147148149.....in this 9 is the 450th digit therefore 444 th will be 7   hence the answer is 7 answer is 7
Answer: D
Four friends, Peter, John, Quincy, and Andrew, are pooling their money to buy a $1600 item. Peter has twice as much money as John. Quincy has $40 more than Peter. Andrew has 10% more than Quincy. If they put all their money together and spend the $1600, they will have $14 left. How much money does Peter have?
Choose the correct answer:
A) $400
B) $560
C) $425
D) $380
E) $455

Solution: P= 2J ; Q= P+40 ; A= 1.1(Q)   P+J+Q+R-1600=14   P+0.5P+P+40+1.1(P+40) = 1614   P+0.5P+P+40+1.1P+44=1614   P+0.5P+P+1.1P+84=1614   P+0.5P+P+1.1P=1530   3.6P=1530   P=425   Answer:$425
Answer: C
Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 80% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount?
Options:
A) $1000  B) $1100  C) $1200  D) $1300  E) $1400

Solution: 0.8(x-600)=0.6(x-400)   0.2x=480-240   x=1200   The answer is $1200.
Answer: C
Calculate the percentage gain if a trader bought a bicycle for Rs.440 and sold it for Rs.610?  Choose the correct choice from the following.
A) 38.64%	B) 39.64%	C) 31.64%	D) 35.64%	E) 34.64%

Solution: C.P. = 440   S.P. = 610   Gain = 610-440 ---- 170   % Gain => 170/440*100 => 38.64%   38.64%nswer:38.64%
Answer: A
A ladder 22 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 3 feet, how many feet will the bottom of the ladder slip?
Pick one:
A) 12.86
B) 15
C) 18
D) 19
E) 25

Solution: 22^2-7^2=435   it means that the height is equal to 20.85.   since the top of the ladder slips down 4 feet, then the height of the wall =20.85-3= 
20.85-3 = 17.85
17.85   the bottom=sqrt(22^2-17.85^2)=sqrt(484-318.62)=12.86   ans is 12.86
Answer: A
A circular mat with diameter 14 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?  Choose one:
A) 5/12  B) 2/5  C) 1/5  D) 3/4  E) 5/6

Solution: SO we are looking for the area of the cloth over the area of the table   Area of the 1/5loth = (pi)(r)^2 which is about (3)(7)(7)   Area of the Table = (24)(24)   So the quick way to estimate is looking at the fraction like this: (3/24)(41/24)   I hope this is easy to follow, so with some simplification i get (1/8)(12/7) =3/14= (1/5) Answer is 1/5
Answer: C
Which part of an atom has no electrical charge?  Choose the correct answer:
A) q1  B) 22  C) 72  D) 27  E) 28

Solution: Answer: Option 22
Answer: B
The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?	Choices: A) Rs. 2400 B) Rs. 2200 C) Rs. 2300 D) Rs. 2500 E) Rs. 2600

Solution: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.   Then, 2x + 4y = 1600 .... (i)   and x + 6y = 1600 .... (ii)   Divide equation (i) by 2, we get the below equation.   => x + 2y = 800. --- (iii)   Now subtract (iii) from (ii)   x + 6y = 1600 (-)   x + 2y = 800   ----------------   4y = 800   ----------------   Therefore, y = 200.   Now apply value of y in (iii)   => x + 2 x 200 = 800   => x + 400 = 800   Therefore x = 400   Solving (i) and (ii) we get x = 400, y = 200.   Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.   Rs. 2400
Answer: A
A company sells two products, L and M. Last year, seventy percent of the units sold were product L, and the price of product L was 25 percent greater than the price of product M. Approximately what percent of the total revenue the company received last year was from the sale of product L?
Choose the correct choice from the following.
A) 15% B) 25% C) 35% D) 65% E) 74%

Solution: Percentage of total units that is product L = 70 %   Price of product L = 25 percent greater than price of product M.   Now , we can consider this as a weighted average scenario .   If the price of both the products L and M was equal , then contribution of product L to total sales would be = 70%   But since , price of product L is greater than M , then contribution of product L to total sales will be greater than 70%   The only option is 74%   Answer 74%
Answer: E
Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 5. The numbers are Select:
A) 12, 24, 30
B) 12, 24, 38
C) 12, 24, 362
D) 5, 10, 15
E) 12, 24, 321

Solution: Explanation:   Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 5   \inline \fn_jvn \therefore The numbers are 5, 10, 15   Answer: 5, 10, 15) 5, 10, 15
Answer: D
In how many no. between 10 and 40 exactly Two of the digits is 4?
Choose the correct choice from the following answers:
A) 10
B) 15
C) 35
D) 1
E) 45

Solution: It's simple can be solved by elimination of answer choices.   Option B and C are too large, not possible. Even AE are large to have correct choice.   Ans : 1
Answer: D
From given equation find the value of x: 2x² + 9x − 5 Select the correct option: A) 1 B) 1/2 C) 1/3 D) 2/3 E) 2/5

Solution: That quadratic is factored as follows:   2x² + 9x − 5 = (2x − 1)(x + 5).   Lesson 17.   Now, it is easy to see that the second factor will be 0 when x = −5.   As for the value of x that will make   2x − 1 = 0,   we must solve that little equation. (Lesson 9.)   We have:   2x = 1   x = 1   2   The solutions are:   x = 1/2 or −5   1/2
Answer: B
A garrison of 2000 men has provisions for 40 days. At the end of 20 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement?	Select the correct option
A) 1888
B) 2766
C) 2999
D) 2000
E) 1712

Solution: 2000 ---- 40   2000 ---- 20   x ----- 10   x*10 = 2000*20   x = 4000   2000   -------   2000   Answer: 2000
Answer: D
What is the total number of positive integers that are less than 200 and that have no positive factor in common with 200 other than 1?  Choose the correct choice from the following answers.
A) 60  B) 70  C) 80  D) 90  E) 100

Solution: Since 200=2^3*5^2 then a number can not have 2 and/or 5 as a factor.   The odd numbers do not have 2 as a factor and there are 100 odd numbers from 1 to 200.   We then need to eliminate the 20 numbers that end with 5, that is 5, 15, 25,...,195.   There are a total of 100 - 20= 
100 - 20 = 80
80 such numbers between 1 and 200.   The answer is 80.
Answer: C
P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 4), the remainder is also D. If P/Q = 1020.75 and P/(Q + 4) = 816.6, then which of the following gives the correct set of {D, Q}? Choose the correct option:
A) {6, 12}
B) {6, 15}
C) {12, 16}
D) {9, 15}
E) {15, 24}

Solution: p/q= d=p/q+4   d= .75 q   d= .6(q+4)   we get d = 12 and q = 16. Answer = {12, 16}.
Answer: C
A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance T between the two cities?  Answers.
A) 48  B) 72  C) 96  D) 120  E) 192

Solution: Hmmm I did this question a while ago and got it wrong so trying again   Rate x time = distance.   For the initial trip lets the distance T to the midpoint be represented by P.   EQN1: R x 2 = P   For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:   Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5   EQN2: R x 2.5 = P + 24   EQN2-EQN1 : 0.5R=24   R=48   So the distance is rate x time = 48 x 4 = 192.   ANS = 192
Answer: E
The H.C.F. of two numbers is 12 and their L.C.M. is 520. If one of the numbers is 480, then the other is:
Choose the correct option.
A) 13  B) 18  C) 21  D) 24  E) 38

Solution: Other number =	(12 x 520)/480 = 13.   13NSWER :13
Answer: A
Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?	Pick:
A) 19
B) 18.7
C) 19.9
D) 21.7
E) 22.8

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 36 Paise is given as tax   => Total tax incurred = 36 Paise = Rs.36/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−36/100−x)6/100 = 36/100   ⇒ 6(25 −0.36 −x) = 36   ⇒ (25 − 0.36 − x) = 6   ⇒ x = 25 − 0.36 − 6 = 18.7   18.7)
Answer: B
In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 3% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year?
Options.
A) 4 : 11  B) 5 : 4  C) 2 : 3  D) Data inadequate  E) None of these

Solution: Let the population of males = x; then the population of females = 9000 – x   Now, 3% of x + 8% of (9000 – x)   = (9600 – 9000 ) = 600   or 0.03x + 720 – 0.08x = 600   or 720 – 600 = 0.08x – 0.03x   or, 120 = 0.05x   x = 2400   Reqd ratio of population of males and females   2400/9000−2400=2400/6600=4:11   4 : 11nswer 4 : 11
Answer: A
Find 3486/189 Choose one:
A) 18.44  B) 18.48  C) 18.42  D) 18.49  E) 18.41

Solution: First we make the denominator 200. i.e., we are introducing an error of 11 which is 11189=11711189=117 th of the denominator.   Now 3486200=17.433486200=17.43   But this answer is less than actual answer. So we have to increase it by 1/17th part of it.   117×17.43≃1117×17.43≃1   So final answer = 17.43 + 1= 
17.43 + 1 = 18.43
18.43   18.44ctual answer= 18.44   18.44nswer:18.44
Answer: A
If you write down all the numbers from 1 to 50, then how many times do you write 3 ?	Choose the correct choice:
A) A)11 B) B)15 C) C)20 D) D)21 E) E)22

Solution: Explanation:   Explanation:   Clearly, from 1 to 50, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.   So, required number = 5 + 10= 
5 + 10 = 15
15.   Answer:15
Answer: B
Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 500 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
Options
A) 15.502%
B) 25.7014%
C) 12.502%
D) 21.7014%
E) none

Solution: Only trick n this question is to ignore 60% information as farm tax is levied uniformly in the village and that includes Mr William's land.   What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (500/3840)x100 =13.02083%in percentage terms.   But the question asks ratio between his total land to total cultivated land. Hence the answer is 13.02083%x (100/60) = 21.7014% and the answer is not there in the options.   The correct answer is (21.7014%).
Answer: D
If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 1 year would be  Choose one:  A) (1.5)^4  B) 4(1.5)  C) (1.05)  D) 1 + (0.05)^4  E) 1 + 4(0.05)

Solution: f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 1 year would be   1(1.05)^1   1.05^1   C. (1.05)
Answer: C
x, y, and z are positive integers. The average (arithmetic mean) of x, y, and z is 11. If z is two greater than x, which of the following must be true?
I. x is even
II. y is odd
III. z is odd
Choose the correct answer
A) I only B) II only C) III only D) I and II only E) I and III only

Solution: Given that:   x+y+z = 33 and z=x+2   using both equations   2x(Even) + y = 31 (Odd)   Since the sum is Odd 'y' has to be odd. Hence , only options (B) and (D) to be verified.   To check for 'x'.   x+y+z=33   x+z= 33- Odd   x+z= Even   Even + Even = Even   Odd+Odd = Even   ANSWER:II only
Answer: B
If you write down all the numbers from 1 to 100, then how many times do you write 1 ? Choose one.
A) A)11  B) B)18  C) C)20  D) D)21  E) E)22

Solution: Explanation:   Explanation:   Clearly, from 1 to 100, there are ten numbers with 1 as the unit's digit- 1, 11, 21, 31, 41, 51, 61, 71, 81, 91; and ten numbers with 1 as the ten's digit - 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100   So, required number = 10 + 11= 
10 + 11 = 21
21.   Answer: 21
Answer: D
If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B?  Choose the correct option:
A) 41
B) 42
C) 43
D) 44
E) 45

Solution: A two-digit number "cd" can be expressed algebraically as 10c+d.   The sum of A + B = (10c+d)+(10d+c)=11(c+d).   The only answer that is a multiple of 11 is 44.   The answer is 44.
Answer: D