MU-NLPC/Calc-aqua_rat huggingface dataset:
In a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose two flowers of the same color when randomly picking three flowers?	Choose the correct answer:
A) 11/10
B) 1/55
C) 31/10
D) 3/55
E) 2/11

Solution: P(all the same color) = P(1st flower is ANY colorAND2nd flower is same as first)   = P(1st flower is ANY color)xP(2nd flower is same as 1st)   = 1x2/11   =2/11   Answer: 2/11
Answer: E
In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of
students in the college is	Choose the correct choice from the following answers.
A) 420  B) 520  C) 780  D) 620  E) None of these

Solution: Explanation:   Let the boy are 8x and Girls are 5x   => 5x = 300   => x = 60   Total students = 8x+5x = 13x 8 +5= 
8 +5 = 13
13x= 13(60) = 780   Answer: 780
Answer: C
What is the least number of digits (including repetitions) needed to express 10^400 in decimal notation? Pick one.
A) a) 401	B) b) 100	C) c) 101	D) d) 1000	E) e) 1001

Solution: 10^n is a decimal number with a 1 followed by n zeros.   So 10^100 will include 400 0's + 1 digit for 1 = 401   So the answer is a) 401
Answer: A
The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 17 positive perfect squares?
Options:
A) 1,010
B) 1,164
C) 1,240
D) 1,316
E) 1,785

Solution: First we need to find the constant 'c'. The easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively.   Hence LHS = 1+4 and plug n=2 for RHS and simplify to get c = 1/2.   Plug values of n = 17 and c = 1/2 into the equation and simplify to get the answer 1785.   Option 1,785.
Answer: E
A can give B 50 meters start and C 100 meters start in a kilometer race. How much start can B give C in a kilometer race?
Select the correct option
A) 111.12  B) 111.67  C) 111.64  D) 52.63  E) 101.12

Solution: A runs 1000 m while B runs 950 m and C runs 900 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 900)/950 =947.37 m.   B can give C = 1000 - 947.37= 
1000 - 947.37 = 52.63
52.63m.   Answer:52.63
Answer: D
A powder tin has a square base with side 8 cm and height 14 cm. Another tin has a circular base with diameter 8 cm and height 14 cm. The difference in their capacities is :
Answers.
A) 168 cm³  B) 192 cm³  C) 228 cm³  D) 236 cm³  E) None

Solution: Sol.   Difference in capacities = [8 * 8 * 14 - 22/7 * 4 * 4 * 14= 
8 * 8 * 14 - 22/7 * 4 * 4 * 14 = 192
192cm³   Answer 192 cm³
Answer: B
The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?  Choose the correct choice from the following answers.
A) 8	B) 2	C) 9	D) 4	E) 6

Solution: Explanation:   [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96   15000[(1 + R/100)2 - 1 - 2R/100] = 96   15000[(100 + R)2 - 10000 - 200R]/10000 = 96   R2 = (96 * 2)/3= 
(96 * 2)/3 = 64
64=> R = 8   Rate = 8%   8nswer: Option 8
Answer: A
0, 1, 4, 15, 64, ____
Select.
A) 225	B) 325	C) 125	D) 145	E) none

Solution: 0,1,4,15,64.....   0*1+1= 
0*1+1 = 1
1   1*2+2= 
1*2+2 = 4
4   4*3+3= 
4*3+3 = 15
15   15*4+4= 
15*4+4 = 64
64   64*5+5= 
64*5+5 = 325
325   ANSWER:325
Answer: B
Mangala completes a piece of work in 14 days, Raju completes the same work in 30 days. If both of them work together, then the number of days required to complete the work is?	Choices:	A) 8 3/4 days	B) 10 1/2 days	C) 9 1/2 days	D) 12 1/4 days	E) 14 1/4 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 14 × 30/44 = 9 1/2 days   9 1/2 days)
Answer: C
A 4" cube is painted in all its faces and then it is cut down into 1" blocks. How many 1" blocks
are there even without a single face being painted?
Answers: A) 7 blocks B) 8 blocks C) 9 blocks D) 10 blocks E) 11 blocks

Solution: 4" cube is painted in all its faces and then it is cut down into 1" blocks.   Totally, 64 - 1" blocks   3 sides Painted are - 8 blocks   2 sides Painted are - 24 blocks   1 sides Painted are - 24 blocks   without a single face being Painted are - 8 blocks   ANSWER:8 blocks
Answer: B
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?	Answers:  A) 1000  B) 2090  C) 2882  D) 2770  E) 2882

Solution: 90%   104%   --------   14% ---- 140   100% ---- ? => Rs.1000   1000nswer: 1000
Answer: A
Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 570 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Select the correct option:
A) 8/3  B) 3/8  C) 38/15  D) 5/8  E) 5/3

Solution: Distance traveled by Eddy = 570 km   Time taken by Eddy = 3 hours   Average speed of Eddy = 570/3= 
570/3 = 190
190 km/hour   Distance traveled by Freddy= 300 km   Time taken by Freddy = 4 hours   Average speed of Freddy = 300/4= 
300/4 = 75
75 km/hour   Ratio of average speed of Eddy to Freddy= 190/75 = 38/15   Answer 38/15
Answer: C
?% of 360 = 180  Options
A) 277
B) 36
C) 50
D) 72
E) None of these

Solution: ?% of 360 = 180   or, ? = 180×100/360=50   Answer 50
Answer: C
Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 8/15, what is the probability that Taylor makes exactly one basket in three tries?
Select
A) 45/120  B) 45/113  C) 45/130  D) 35/130  E) 35/113

Solution: Probability of basket = 7/15   Probability of no basket = 8/15   Required probability= 3* 7/15*8/15*8/15=45/113   45/113 is the answer .
Answer: B
What least number should be added to 1536, so that the sum is completely divisible by 21?
Pick:
A) 16
B) 17
C) 18
D) 19
E) 20

Solution: 1536÷21=73 Reminder -3   3+18= 
3+18 = 21
21   Hence 18 should be added to 1536 so that the sum will be divisible by 21   answer :18
Answer: C
A factory produces 5505 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?  Choose one
A) 4436 toys	B) 5487 toys	C) 1101 toys	D) 2354 toys	E) 1375 toys

Solution: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.   5505 /5= 
5505 /5 = 1_101
1101 toys   correct answer 1101 toys
Answer: C
If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?	Select
A) 9:6:6 B) 9:6:8 C) 9:6:2 D) 9:6:4 E) 9:6:1

Solution: A:B = 1/2:1/3 = 3:2   B:C = 1/2:1/3 = 3:2   --------------------   A:B:C = 9:6:4   Answer:9:6:4:
Answer: D
Sandy walked 20 meters towards south. Then Sandy turned to her left and walked 20 meters. She then turned to her left and walked 20 meters. She then turned to her right and walked 25 meters. What distance is she from the starting point and in which direction? Answers:
A) 35 m East	B) 35 m North	C) 30 m West	D) 45 m West	E) 45 m East

Solution: The net distance is 20 + 25= 
20 + 25 = 45
45 meters to the east.   The answer is 45 m East.
Answer: E
How much time will it take for an amount of Rs. 600 to yield Rs. 12 as interest at 2% per annum of simple interest?	Choose the correct choice:
A) 8 years B) 4 years C) 7 years D) 1 years E) 2 years

Solution: Explanation:   Time = (100 x 12)/(600 x 2) years   = 1 years.   Answer: 1 years
Answer: D
If the average (arithmetic mean) of x, x + 2, and x + 4 is 53, what is the value of x?	Choices
A) 52	B) 53	C) 54	D) 55	E) 51

Solution: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2   Given that x + 2 = 53   x = 51   Answer : 51
Answer: E
In the following questions, the following letters indicate mathematical operations as indicated below:
A: Addition; V: Equal to; S: Subtraction; W:Greater than; M: Multiplication; X: Less than; D: Division
Find Out of the four alternatives given in these questions, only one is correct according to the above letter symbols. Identify the correct one.
Choices
A) 6 S 7 A 2 M 3 W 0 D 7 B) 6 A 7 S 2 M 3 W 0 A 7 C) 6 S 7 M 2 S 3 W 0 M 7 D) 6 M 7 S 2 A 3 X 0 D E) 6 M 7 S 2 A 4 X 0 D

Solution: Explanation:By BODM6 S 7 A 2 M 3 W 0 D 7S rule   6 – 7 + 3 × 2 > 0/7   6 S 7 A 2 M 3 W 0 D 7nswer: 6 S 7 A 2 M 3 W 0 D 7
Answer: A
If 2 cards are selected (with replacement) at random from the deck of 52 cards then what is the probability that one of the selected cards will be a red king and the other card will be a black jack? A deck of cards has a total of 52 cards, consisting of 4 suits: spades (black), hearts (red), diamonds (red), and clubs (black). In each suit, there are 13 cards including 1 king, 1 queen, and 1 jack.  Choose the correct choice from the following options.
A) 1/32  B) 1/64  C) 1/128  D) 1/169  E) 1/338

Solution: P(1 red king and 1 black jack) = 2(2/52*2/52) = 2(1/676) = 1/338   The answer is 1/338.
Answer: E
A furniture manufacturer has two machines, but only one can be used at a time. Machine S is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine S can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
Select the correct option
A) 14	B) 13	C) 11	D) 9	E) 7

Solution: 'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days.   To finish a work say Machine S you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=9
Answer: D
Lorna invests $5000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?	Choose one
A) $1,000	B) $1,600	C) $2,200	D) $4,400	E) $5,840

Solution: We have that 'x' invested at 6%   We also have that '6000-x' invested at 11%   Now then 580/5000 is approx 10%   Therefore, -4x+5000-x=0   5x=5000   x=1000 approximately. Probably higher   Only $1,000 matches
Answer: A
The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 300,000 bacteria  Answers.
A) 10	B) 12	C) 14	D) 16	E) 18

Solution: The question basically asks how many minutes it takes for a population to increase by factor 300 (300,000 / 1,000 = 300).   Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes:   2^x >= 300, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^8 = 256, i.e. the population has to double 8 times.   Since it takes the population 2 minutes to double once it takes 8*2= 
8*2 = 16
16 minutes to double 8 times.   Thus, solution 16= 16 is correct.
Answer: D
In what time will a train 90 meters long cross an electric pole, if its speed is 124 km/hr Choose the correct answer
A) 5 seconds B) 4.5 seconds C) 3 seconds D) 2.6 seconds E) None of these

Solution: Explanation:   First convert speed into m/sec   Speed = 124*(5/18) = 34 m/sec   Time = 2.6 secondsistance/speed   = 90/34 = 2.6 seconds   Option 2.6 seconds
Answer: D
Find the number which when multiplied by 15 is increased by 196	Pick one:	A) 10	B) 12	C) 14	D) 16	E) 18

Solution: Explanation:   Let the number be x.   Then, 15x = x + 196   =› 14 x= 196   =› x = 14.   Option 14
Answer: C
Company C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $9.00 each, what was Company C’s gross profit? Choose the most appropriate option:
A) $2,250
B) $2,900
C) $2,600
D) $3,250
E) $2,500

Solution: $2,600ost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400= 
500 + 1400 = 1_900
$ 1900   Revenue :  500 * 9= 
 500 * 9 = 4_500
$4500   Profit:   4500 - 1900= 
  4500 - 1900 = 2_600
$ 2600   Option $2,600 is correct
Answer: C
A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 7 Gallons of water and 14 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x? Choose the correct choice.
A) 37.5  B) 75  C) 105  D) 150  E) 175

Solution: Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.   Original mixture has 20% salt and 80% water.   Total = x   Out of which Salt = 0.2x and water = 0.8x   Now, 1/4 water evaporates and all salt remains.   So what remains is 0.2x salt and 0.6x water.   Now 14 gallons salt is added and 7 gallons of water is added.   So salt now becomes -> (0.2x + 14) and water --> (0.6x+7)   Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water.   So (0.2x+14) = (0.6x+7)/2 = > 0.2x = 21   Solving, x = 105   Answer : 105
Answer: C
A group of boy scouts and girls scouts is going on a rafting trip. 45% of the scouts arrived with signed permission slips. If 60% of the scouts were boy scouts and 25% of the boy scouts arrived with signed permission slips, then what percentage of the scouts were girl scouts who arrived with signed permission slips?
Answers.
A) 20  B) 21  C) 25  D) 28  E) 30

Solution: We don't know how many scouts went on the trip, so let's assume 100 scouts went on the trip   60% were boy scouts so 60% of 100 = 60 were boy scouts   25% of the boy scouts brought their permission slips signed, so  .25*60= 
 .25*60 = 15
15 boy scouts had signed slips    60-15= 
 60-15 = 45
45 boy scouts did not   45% of all the scouts had signed slips, so  .45*100= 
 .45*100 = 45
45 in total had signed slips   thus  45 - 15= 
 45 - 15 = 30
30 girl scouts had signed slips   thus the percentage of scouts who were girl scouts arriving with signed permission slips is  30/100= 
 30/100 = 3/10 = around 0.3
.30= 30%   30
Answer: E
Find the cost of fencing around a circular field of diameter 30m at the rate of Rs.1.50 a meter?  Choose the correct choice from the following answers.
A) A)Rs.150  B) B)Rs.141.37  C) C)Rs.100  D) D)Rs.125  E) E)Rs.225

Solution: 2 * 22/7 * 15 = 94.24   94.24 * 1 1/2 = Rs.141.37   ANSWER:Rs.141.37
Answer: B
The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8450. If his salary for the month of May is Rs.6500, find his salary for the month of January?  Choices:
A) 2177  B) 2876  C) 4700  D) 2981  E) 2711

Solution: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000= 
4 * 8000 = 32_000
32000 ----(1)   Sum of the salaries of the person for the months of February, March, April and May= 4 * 8450= 
4 * 8450 = 33_800
33800 ----(2)   (2)-(1) i.e. May - Jan= 1800   Salary of May is Rs.6500   Salary of January = Rs.4700.Answer: 4700
Answer: C
What is the next number in the sequence below?
1 4 9 16 25 36 49 __ ? Choose the correct choice from the following:
A) 64
B) 46
C) 47
D) 48
E) 49

Solution: as the series of numbers are squares of numbers   1^2=1   2^2=4   3^2=9   and so on   therefore 8^2=64   64NSWER:64
Answer: A
In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?
Pick one
A) 110  B) 120  C) 140  D) 195  E) 210

Solution: The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:   (i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1   x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1= 
80 + 90 + 24 + 1 = 195
195   195
Answer: D
What is the probability of getting at least one six in a single throw of three unbiased dice?	Choose the correct choice from the following answers:	A) 1/6	B) 125/216	C) 1/36	D) 81/216	E) 91/216

Solution: Find the number of cases in which none of the digits show a '6'.   i.e. all three dice show a number other than '6', 5 * 5 *5 = 125 cases.   Total possible outcomes when three dice are thrown = 216.   The number of outcomes in which at least one die shows a '6' = Total possible outcomes when three dice are thrown - Number of outcomes in which none of them show '6'.   = 216 - 125= 
216 - 125 = 91
91.   The required probability= 91/216.   ANSW91/216R:91/216
Answer: E
If a ring of diameter 4 inches moves at the rate of x inches/min and another ring of diameter 12 inches moves at the rate of y inches/min, and if they both cover a distance at the same time then find the value of x in terms of y?	Select the correct option
A) 6y/2	B) 3y/4	C) 5y/2	D) 2y/4	E) 1y/3

Solution: t=S1/V1=S2/V2   or 4/x=12/y   or x=4y/12=1y/3   Answer is 1y/3
Answer: E
Out of 19 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
Choose the correct choice from the following:  A) 12â„13  B) 11â„13  C) 10â„15  D) 23/31  E) None of these

Solution: Total possible ways of selecting 4 students out of 19 students = 19C4 = 3876   The no. of ways of selecting 4 students in which no student belongs to Karnataka = 14C4=1001   âˆ´ Hence no. of ways of selecting at least one student from Karnataka = 19C4 â€“ 14C4 = 2875   âˆ´ Probability = 2875â„3876 = 23/31   Answer 23/31
Answer: D
For the real value of x what is the maximum value of |x+2|+|x-1|-|2x-4|=? Pick:
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: value of expression will be maximum if mod(2x-4) will give minimum value   so 2x-4=0   x=2   maximum value=mod(2+2)+mod(2-1)-0=5   ANSWER:5
Answer: D
In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:  Select the correct option:
A) 3100	B) 6240	C) 6500	D) 9600	E) 9800

Solution: To obtain Rs. 10, investment = Rs. 96.   To obtain Rs. 650, investment = Rs. (96X650)/10 =6240 Answer: 6240
Answer: B
Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?	Choose the correct choice from the following answers:
A) 11 1/5%  B) 11 1/4%  C) 11 1/9%  D) 11 8/9%  E) 11 3/9%

Solution: 900 --- 100   100 --- ? => 11 1/9%   Answer: 11 1/9%
Answer: C
-45*29+108=?
Pick
A) 1197
B) 1897
C) -1197
D) -1900
E) None of these

Solution: => -45*(30-1)+108;   => -(45*30)+45+108;   => -1350+153=-1197.   -1197orrect Option: -1197
Answer: C
Farm Tax is levied on the 40% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : Choose the correct choice.
A) 31.25%	B) 25%	C) 12.5%	D) 0.2083%	E) none

Solution: Only trick n this question is to ignore 40% 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 (480/3840)x100 =12.5%in percentage terms.   But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/40) = 31.25% and the answer is not there in the options.   The correct answer is (31.25%).
Answer: A
You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.
What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?  Choose the most appropriate option.
A) 5	B) 8	C) 7	D) 6	E) 4

Solution: If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries.
Answer: C
What is the sum of all the composite numbers up to 20?	Options.
A) 130  B) 132  C) 124  D) 145  E) 166

Solution: 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 132   ANSWER 132
Answer: B
A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 120 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?  Choose the correct choice from the following answers:
A) 3/16,000 B) 1/8,000 C) 3/1,600 D) 1/90 E) 2/45

Solution: Solution provided by stanford2012 is correct: 120/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=120/800*1/600=1/8,000.   Answer: 1/8,000.
Answer: B
1,000^2 + 1,001^2 +1,002^2 =
Select:  A) 6,030,053  B) 6,030,054  C) 6,006,005  D) 6,030,056  E) 6,030,057

Solution: Interesting problem.   I think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total.   1000^2 -> 00   1001^1 -> 01   .   .   .   1002^2 -> 5   Total -> *5   Answer 6,006,005.
Answer: C
f two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?  Choose the correct choice from the following answers
A) 50%	B) 80%	C) 60%	D) 84%	E) 87%

Solution: Given ratio = 1/8 : 1/5 = 5 : 8   Let first number be 5x and the second number be 8x.   The second number is more than first number by 3x.   Required percentage = 3x/5x * 100 = 60%.   Answer:60%3 /5  * 100= 
3 /5  * 100 = 60
60%.   Answer:60%
Answer: C
How many 3-digit numbers are completely divisible 6 ? Pick one:
A) 149 B) 150 C) 151 D) 166 E) 182

Solution: 3-digit number divisible by 6 are: 102, 108, 114,... , 996   This is an A.P. in which a = 102, d = 6 and l = 996   Let the number of terms be n. Then tn = 996.   a + (n - 1)d = 996   102 + (n - 1) x 6 = 996   6 x (n - 1) = 894   (n - 1) = 149   n = 150   Number of terms = 150.   Answer: 150
Answer: B
The average age of 20 students of a class is 20 years. Out of these, the average age of 9 students is 11 years and that of the other 10 students is 24 years. The age of the 20th student is?
Choose the correct answer:
A) 65
B) 61
C) 59
D) 63
E) 64

Solution: Age of the 20th student = 20*20 - (9*11+10*24) = 400-339= 
400-339 = 61
61 years   Answer is 61
Answer: B
A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets? Choose the correct option.
A) 45
B) 500/11
C) 600/11
D) 55
E) 35

Solution: Explanation :   Number of runs made by running,   =>110−(3×4+8×6).   =>110−(60).   =>50.   Hence, the required percentage is:-   =>(50/100×100).   =>500/11.   Answer : 500/11
Answer: B