MU-NLPC/Calc-aqua_rat huggingface dataset:
y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?  Pick:
A) -512
B) -257
C) -256
D) -513
E) 128

Solution: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.   For the quadratic equation is in the form of ax^2+bx+c=0,   The product of the roots =c/a= 512/1=256 and the sum of the roots =-b/a=-b   512 can be expressed as product of two numbers in the following ways:   1 * 512   2 * 256   4 * 128   8 * 64   16 *32   The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512= 
1 + 512 = 513
513.   The least value possible for b is therefore -513.   -513
Answer: D
75 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor?  Choose the correct option:	A) 48	B) 180/7	C) 50.4	D) 60	E) 90

Solution: 75% of Area of the floor = 4*9= 
4*9 = 36
36 square feet   i.e. 100% 48rea of Floor= (36/75)*100= 
(36/75)*100 = 48
48 square feet   48nswer: Option 48
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Choose the correct choice from the following answers:  A) 120 metres  B) 110metres  C) 90 metres  D) 150 metres  E) 100 metres

Solution: Answer: Option 150 metres   Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9)= 
(50/3 * 9) = 150
150 m.
Answer: D
A person has 12 friends and he wants to invite 8 of them to a birthday party. Find how many times 3 particular friends will always attend the parties. Choose one: A) 126 B) 95 C) 130 D) 155 E) None

Solution: Explanation :   No. of times 3 particular friends will attend the party always.   Hence the number of ways of selection is :-   => n-kCr-k, where n= 12, r=8 and k=3.   => No. of combinations = 12-3C8-3 .   => 9C5.   => 126.   Hence, the number of combinations with 3 particular friends present in each combination (party) is 126.   126nswer : 126
Answer: A
852.68 âˆ’ 4.5 + 108.90 = ? âˆ’ 2132.54	Select.
A) 6078.58
B) 5225.9
C) 6258.58
D) 6078.5
E) None

Solution: Option '6078.5'
Answer: D
An officer was appointed on maximum daily wages on contract money of Rs. 4956. But on being absent for some days, he was paid Rs. 3894. For how many days was he absent?  Choose the correct answer:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Explanation:   HCF (4956, 3894) = 354   Here 354 are the maximum daily wages.   The officer was appointed on contract money of Rs. 4956 = 354 × 14.   i.e., he was appointed for 14 days.   But he was paid Rs. 3894 = 354 × 11,   i.e., he was present for 11 days.   Hence he was absent for 3 days.   Answer: 3
Answer: C
Pamela bought an electric drill at 85% of the regular price.
She paid $32.89 for the drill. What was the regular price?
(Round to the nearest cent)	Choose the correct option.
A) $28.69	B) $18.69	C) $38.69	D) $58.69	E) $48.69

Solution: we know   85/100=32.89/x   Multiply the opposites:   100 x 32.89 = 3289   Divide by the remaining number:   38.694/3289 .000   85   $38.69   correct answer $38.69
Answer: C
The average (arithmetic mean) of 7 numbers is 7. If 3 is added from each of 5 of the numbers, what is the new average?  Choose the correct choice from the following choices
A) 7.3	B) 5.6	C) 4.6	D) 9.1	E) 8.9

Solution: Sum of 8 numbers = 7*7= 
7*7 = 49
49   If 3 is added from each of five of the numbers , we added  3*5= 
 3*5 = 15
15 from the total sum   Sum of 7 number after adding 3 from each of five of the numbers=49+15= 
49+15 = 64
64   New average=64/7=9.1   Answer (9.1)
Answer: D
In a basket the number of cherries is 20% of the number of apples. Express the number of apples as a percentage of cherries in the basket?	Choose the correct choice from the following: A) 2% B) 7% C) 12% D) 5% E) 15%

Solution: The number of cherries is 20% the number of apples.   If apples=10   cherries=2   We are asked for the number of apples as a percentage of cherries   A/C=10/2= 
10/2 = 5
5%   Answer is 5%
Answer: D
An analyst will recommend a combination of 4 industrial stocks, 3 transportation stocks, and 4 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 5 utility stocks, how many different combinations of 11 stocks are possible?
Choose the correct choice from the following
A) 12  B) 19  C) 60  D) 100  E) 720

Solution: 5C4 * 4C3 * 5C4 = 5*4*5= 
5*4*5 = 100
100.   Answer: 100
Answer: D
The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 70 respectively. The sum is:	Choose the correct choice from the following answers.
A) 1360  B) 1450  C) 1600  D) 1800  E) None

Solution: Sol.   Sum = S.I. * T.D. / (S.I)-(T.D.) = 85 * 70 / (85 - 70) = Rs.396.7.   Answer None
Answer: E
The average age of 18 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is? Pick
A) 9  B) 31  C) 56  D) 72  E) 90

Solution: Age of the 15th student = 18*15 - (14*5+16*9) = 270-214= 
270-214 = 56
56 years   Answer is 56
Answer: C
In store A there are 10 pairs of pants for every 50 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned? Answers:
A) 4:15.
B) 2:3.
C) 1:3.
D) 3:4.
E) 2:5.

Solution: 1st statement : ratio of pants   Store 4:15. : Store B   10x : 50x   X:5X   Price :   4y:3y   Total revenue   4xy : 15xy   4:15   4:15.nswer is 4:15.
Answer: A
A sum of money is sufficient to pay B's wages for 12 days and C's wages for 24 days. The same money is sufficient to pay the wages of both for?  Choose the correct choice from the following choices:
A) 6	B) 7	C) 8	D) 9	E) 10

Solution: Let the total money be $x   B's 1day work = $ x/12   8's 1day work = $ x/24   A+B 1day work = $ x/8   Money is sufficient to pay the wages of both for 8days   Answer is 8
Answer: C
The ratio of number of boys and girls in a class is 3 : 2. In the 1st semester exam 20% of boys and 25% of girls get more than or equal to 90% marks. What percentage of students get less than 90% marks ?  Choose the correct choice:
A) 56	B) 70	C) 78	D) 80	E) 85

Solution: Let boys =3x and girls =2x.   Number of those who get less than 90% mark =(80% of 3x) + (75% of 2x)   =(80/100 )*3x +(75/100 *2x) =39x/10   Required percentage = (39x/10 *1/5x *100)% = 78%.   ANSWER:78(39 /10 *1/5  *100)= 
(39 /10 *1/5  *100) = 78
78%.   ANSWER:78
Answer: C
If six persons sit in a row, then the probability that three particular persons are always together is? Choose the correct choice from the following:
A) 1/9	B) 1/6	C) 1/5	D) 1/2	E) 1/3

Solution: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5   Answer: 1/5
Answer: C
Find the odd number. 15, 25, 30, 51, 85, 90, 115
Choose one:
A) 12
B) 42
C) 46
D) 47
E) 51

Solution: All numbers are multiples of 5 except 51   so answer is 51   answer 51
Answer: E
If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+4) for all positive integers n, what is the third term of the sequence? Pick.
A) 3	B) 4	C) 6	D) 8	E) 9

Solution: Tn = nth term   T1 = 1st term   T2 = 2nd term   and so on...   Sn = Sum of first n terms of the sequence   Sn = 1st term + 2nd term + 3rd term + ... + nth term   Sn = T1 + T2 + T3 + ....Tn   You are given here thatSn is the SUM of first n terms...So you have   Sn = T1 + T2 + T3 + ....Tn = n(n+1)   So S1 = T1   S2 = T1 + T2   S3 = T1 + T2 + T3   and so on   S1 = T1 = 1*(1+1)= 
1*(1+1) = 2
2   S2= T1 + T2 = 2 + T2 = 2*(2+1)= 
2*(2+1) = 6
6   So T2= 4   S3 = T1 + T2 + T3 = 2 + 4 + T3 = 3*(3+1)= 
3*(3+1) = 12
12   So T3= 9   (This is what we wanted)   The third term is 9.   9
Answer: E
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?	Options:	A) 567	B) 564	C) 645	D) 735	E) 756

Solution: we have 3m and 2w   or   4m and 1w   or   5m   no of ways =(7C3 x 6C2) + (7C4 x 6C1) + (7C5)=	= (525 + 210 + 21)= 
(525 + 210 + 21) = 756
756.   ANSW756R:756
Answer: E
2/5 of the fish in an aquarium are red and 1/4 of the fish are brown. 1/2 of the red fish and 1/5 of the brown fish are male. If the rest of the fish in the aquarium are female, what is the probability that a fish randomly picked from the aquarium is male? Select the correct option:
A) 3/20	B) 7/30	C) 5/16	D) 1/4	E) 2/5

Solution: 1/2*2/5 + 1/5*1/4 = 1/4   The answer is 1/4.
Answer: D
Venus travels around the Sun at an approximate speed of 21 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)	Choose the correct answer:	A) 84,000	B) 126,000	C) 135,000	D) 148,000	E) 162,000

Solution: The speed is 21 miles/s. Then 21/0.6= 
21/0.6 = 35
35 km/s   35*3600= 126,000 kph   The answer is 126,000.
Answer: B
Find the product of the localvalue and absolutevalue of 3 in 20368?
Options
A) 1000 B) 1100 C) 1200 D) 900 E) 10000

Solution: Local value of 3 = 3 x 100 = 300   Place value of 3 = 3   There fore = 3 x 300 = 900   900
Answer: D
A number when divided by 17 leaves 11 as a remainder. This number is greater than fifty but less than seventy. What will be the remainder if the number is divided by 10?
Select.
A) 5
B) 8
C) 2
D) 17
E) 11

Solution: Let 17 + 11= 
17 + 11 = 28
28 be the smallest number divisible by 17 with a remainder of 11.   Since 17 is prime, we need only add 17 to 28 until we enter the specified range.   17 + 17+ 11= 
17 + 17+ 11 = 45
45 That doesn't fit.   17 +17 +17 +11= 
17 +17 +17 +11 = 62
62 Bingo!   Now, 62 divided evenly into tens leaves a remainder of 2.   The answer is 2.
Answer: C
At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 42 years. What is the age of Deepak at present?  Choose the correct option:
A) 77 years B) 15 years C) 66 years D) 88 years E) 27 years

Solution: Let the present ages of Arun and Deepak be 4x and 3x years respectively.   Then, 4x + 6 = 42 => x = 9   Deepak's age = 3x = 27 years.   Answer: 27 years
Answer: E
Two dogsled teams raced across a 700-mile course in Alaska. Team A finished the course in 7 fewer hours than team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour?	Choose the correct choice from the following choices
A) 12	B) 15	C) 18	D) 20	E) 25

Solution: Let v be team B's average speed.   Time = Distance/Rate and the time difference was 7 hours.   700/v - 700/(v+5)= 7   700v + 3500 - 700v = 7(v)(v+5)   500 = (v)(v+5)   (20)(25) = (v)(v+5)   v = 20 mph   The answer is 20.
Answer: D
Find the invalid no.from the following series 3, 7, 15, 31, 61, 127, 255 Choose the correct choice from the following choices:
A) 3  B) 61  C) 27  D) 63  E) 127

Solution: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 61 is wrong.   61
Answer: B
Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 25 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?  Choose the correct choice from the following options.
A) 10.5 B) 0.5 C) 25.5 D) 30 E) 60

Solution: The time it takes Darcy to walk to work is (1.5/3)*60= 
(1.5/3)*60 = 30
30 minutes   The time it takes Darcy to take the train is (1.5/20)*60 + x= 4.5 + x minutes   It takes 15 minutes longer to walk, so 30 = 4.5 + x + 25   x=0.5 minutes   Answer: 0.5
Answer: B
A freight train starts from Los Angeles and heads for Chicago at 40 mph. Two hours later a
passenger train leaves the same station for Chicago traveling 60 mph. How long before the
passenger train overtakes the freight train?  Choose the correct choice from the following answers.
A) 6hours
B) 5hours
C) 9ours
D) 2hours
E) 4 hours

Solution: Read the problem. It is a time, rate, and distance problem. (Use D=r*t)   The question asks, “how long?” (which means time) for the passenger train.   Let t=the time it takes the passenger train to overtake the freight train   t+2=the number of hours the freight train had traveled when overtaken.   Draw a sketch and make a table.   Time Rate Distance   Freight t+2- 40 mph- 40(t+2)   Passengert- 60 mph-60t   Equation: When the passenger train overtakes the freight train, they have both traveled   the same distance. Write each of their distances in terms of ratetime (as seen in the   table above), then set them equal to each other to create an equation. Then solve the   equation.   40(t+2)=60t   40t+80=60t   80=20t   t=4   The answer: It takes the passenger train 4 hours to overtake the freight train.   Check by substituting 4 into the original equation.   40(4+2)=60(4)   40(6)=240   240=240   true   Thus, 4 hours is the correct answer.   correct answer 4 hours
Answer: E
Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?	Choose the correct choice from the following:
A) 9680  B) 96288  C) 26667  D) 1662  E) 2882

Solution: (8000*3*2)/100= 
(8000*3*2)/100 = 480
480   9200   --------   9680   9680nswer:9680
Answer: A
The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:	Pick.
A) Rs. 1800 B) Rs. 1450 C) Rs. 1360 D) Rs. 6800 E) Rs. 7800

Solution: sum=si*td/(si-td)   sum=80*85/(85-80)= 
80*85/(85-80) = 1_360
1360   ANSWER:Rs. 1360
Answer: C
A car drove from Town A to Town B without stopping. The car traveled the first 90 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 70 miles if the car’s average speed for the entire trip was 40 miles per hour? Choose the correct choice from the following choices:  A) 128  B) 148  C) 150  D) 155  E) 175

Solution: KAPLANOFFICIAL SOLUTION:   To solve this problem, you must remember that average speed means total distance divided by total time over an entire journey. This should not be confused with the average of the speeds. The total distance in this problem is 160 miles, but we will need to express the total time in a more complex way.   For the first 90 miles, the car traveled at 25 miles per hour. Therefore, we can say that the time this took was 90/25, because distance divided by rate equals time.   For the last 70 miles, we are trying to solve for the rate, so we can call this speed R. Thus, the time for the final 70 miles is 70/R.   If we put all of this together, knowing that the average speed over the entire journey is 40 miles per hour, we get the equation 160/(90/25 + 70/R) = 40. We can now solve for R and reach our answer.   160/(90/25 + 70/R) = 40   R = 175 is choice (175) and that’s our correct answer.
Answer: E
3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate gotin that election?	Choose the correct answer.
A) 40%	B) 55%	C) 57%	D) 60%	E) 62%

Solution: Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400   So, Required percentage= 11628/20400 * 100= 
11628/20400 * 100 = 57
57%   57%
Answer: C
Which among the following fractions below has the highest value?
Choose the correct choice from the following options.
A) A)23/77  B) B)23/78  C) C)23/84  D) D)23/87  E) E)23/27

Solution: 23/27.   Now, all options have the same numerator 23. If numerator is same, the fraction with the highest value will be the one with the lowest denominator.   Answer (23/27).
Answer: E
What is the value of 3x^2 − 2.4x + 0.3 for x = 0.6?  Choose one: A) −0.3 B) 0 C) 0.06 D) 1.08 E) 2.46

Solution: 3x^2-2.4x+0.3 for x=0.6   =3(0.6*0.6)-4*0.6*(0.6)+0.3   =-0.6*0.6+0.3   =0.06   0.06orrect Option : 0.06
Answer: C
Aman started a business investing Rs. 60,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?	Choose the correct choice from the following answers:
A) 12:15:18	B) 72:105:112	C) 52:105:112	D) 62:105:112	E) 12:105:112

Solution: Explanation:   Aman : Rakhi : Sagar = (60000 * 36) : (105000 * 30) : (140000 * 24)   = 72:105:112   Answer: 72:105:112
Answer: B
A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 42 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?	Choose the correct choice from the following answers: A) 229 B) 288 C) 787.5 D) 888 E) 121

Solution: D = 30 * 5= 
30 * 5 = 150
150   RS= 42 – 30 = 8   T = 150/8= 
150/8 = 75/4 = around 18.75
18.75   D= 42 * 18.75= 
42 * 18.75 = 787.5
787.5 km   Answer: 787.5
Answer: C
What is the sum of all 3 digit positive integers that can be formed using the digits 1, 4, and 8, if the digits are allowed to repeat within a number?
Answers:
A) 12,987
B) 13,876
C) 14,765
D) 15,654
E) 16,543

Solution: The number of these 3-digit numbers is   3*3*3= 
  3*3*3 = 27
27   Each digit 1, 4, and 8 will appear in the ones, tens, and hundreds place 9 times each.   The sum equals 9(111) + 9(444) + 9(888)= 12,987   The answer is 12,987.
Answer: A
What is the unit digit in the product (245 x 122 x 431)?  Choose the correct choice from the following choices
A) 2  B) 3  C) 0  D) 1  E) Can't be determined

Solution: Explanation:   Product of unit digits = 5 x 2 x 1 = 10   Required digit = 0   Answer: Option 0
Answer: C
A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?	Options.
A) 8	B) 24	C) 58	D) 80	E) 210

Solution: 6!/3!(6-3)! = 20   4!/1!(4-1)!=4   so number of different committees equals   20*4= 
  20*4 = 80
80   ANS:80
Answer: D
One fourth of a solution that was 10 percent RICE by weight was replaced by a second solution resulting in a solution that was 16 percent RICE by weight. The second solution was what percent RICE by weight ?  Select the correct option.
A) 34%
B) 24%
C) 22%
D) 18%
E) 8.5%

Solution: EQ can be written as ...   let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of RICE in 2nd sol)=34%=34%
Answer: A
The H.C.F. of two numbers is 25 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is: Choose the most appropriate option
A) 276	B) 299	C) 322	D) 345	E) 350

Solution: Clearly, the numbers are (25 x 13) and (25 x 14).   Larger number = (25 x 14) = 350.   Answer: Option 350
Answer: E
In racing over a given distance d at uniform speed, A can beat B by 20 meters, B can beat C by 6 meters, and A can beat C by 23 meters. What is the distance d in meters?	Choose the correct choice from the following answers:
A) 32
B) 36
C) 40
D) 48
E) 60

Solution: When A is at the finish line, B is 20 meters back, and C is 23 meters back.   When B runs another 20 meters to the finish line, C is 6 meters back.   So B gains 3 meters every 20 meters covered.   To gain a final difference of 6 meters, B runs a total of 40 meters.   The answer is 40.
Answer: C
A company decreased the price of its main product by 10%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?
Choose one.
A) 4.3 B) 5.6 C) 6.2 D) 10.0 E) 12.0

Solution: For the total revenue to remain the same when the price is 1/10, the number of products sold must 1/10 times. Therefore increase in the number of products sold is 100%   => The required ratio = 100%/10% = 10.0   Answer : 10.0100 /10= 
100 /10 = 10
10.0   Answer : 10.0
Answer: D
At Deluxe paint store, Fuchsia paint is made by mixing 6 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 24 liters of Fuchsia to change it to Mauve paint?
Choose the correct choice from the following choices:
A) 9
B) 12
C) 15
D) 16
E) 18

Solution: in 24 liters, Red = 6/9 * 24= 
6/9 * 24 = 16
16 and 12lue= 8   so, 16/(8+x) = 4/5   or, x = 12 (Answer 12)
Answer: B
A = {2, 3, 5, 7, 11}
B = {2, 4, 6, 19}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?  Answers:
A) 15	B) 16	C) 19	D) 24	E) 36

Solution: Step 1: Find out the number of products you get.   5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4= 
5*4 = 20
20   Step 2: Remove the products that appear more than once.   Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.   2, 3   2, 4, 6   The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.   Answer= 20 - 1 = 24   Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.   24
Answer: D
Three printing presses, L, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take L, working alone at its constant rate, to do the same job?	Choose the correct option
A) 8 B) 10 C) 12 D) 15 E) 20

Solution: =1/4-1/5=1/20   L can do 1/20 job in 1 hour   L can do the whole job in 20 hours=20
Answer: E
Some of the people in Town V are left-handed, some are tall, some are both, and some are neither. In Town Y, three times as many people are left-handed > as are left-handed in Town V, three times as many people are tall as are tall in Town V, three times as many people are both as are both in Town V, but no one is neither. If the total number of people in Town V is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town V who are neither left-handed nor tall?
Options:
A) 23 B) 39 C) 72 D) 143 E) 199

Solution: Yes, correct answer is indeed D.   {V}={Left} + {Tall} - {Both} + {Neither};   {Y} = 3*{Left} + 3*{Tall} - 3*{Both};   Since the total number of people in Town V is four times greater than the total number of people in Town Y, then:   {Left} + {Tall} - {Both} + {Neither}=4*(3*{Left} + 3*{Tall} - 3*{Both});   {Neither}=11*({Left} + {Tall} - {Both}), which means that # of people in Town V who are neither left-handed nor tall must be a multiple of 11.   Only answer choice D, is a multiple of 11: 143=11*13.   Answer: 143.
Answer: D
There are 1000 buildings in a street. A sign-maker is contracted to number the houses from 1 to 1000. How many zeroes will he need?
Choose the correct choice from the following choices.
A) 190 B) 191 C) 192 D) 193 E) 194

Solution: divide as (1-100)(100-200)....(900-1000)   total 192   ANSWER:192
Answer: C