MU-NLPC/Calc-aqua_rat huggingface dataset:
W and F represent two distinct digits. If the number 457W89F is divisible by 36, what is the value of (W+F)?
Choose the correct answer:
A) a) 9
B) b) 3
C) c) 12
D) d) 6
E) e) 10

Solution: A no. divisible by 36 means it is div by 49 .   to be div by 4 last 2 digits to be multiple of 4 So, F could be either 2 or 6 only   similarly for a number to be div by 9 its sum must be multiple of 9 first. filtering we find W could be either 1,4,7 only.   To be divisible by 9 only 1 works .(if we choose f=6 then W have to be 6 but as per condition WF are distinct) So   W=1   F=2   Ans:- 3.b) 3
Answer: B
A 7-in. pizza cost $8 and a 14-in . pizza cost $20. tommy says the smaller pizza is a better buy because the larger is twice as big and more than twice as expensive. do you agree with his reasoning?	Answers: A) Yes B) No C) yes , but pizza so expensive D) no i did like to purchase pizza in this shop E) neutral

Solution: No, pizza looks like a circle, and we know that area of a circle depends on the radius. Area of a circle = nr(squared), here pi (n) is constant.   so we can clearly say that area of a circle is proportional to the square of the diameter. similarly the cost a pizza depends on its area not its diameter. correct answer : (No)
Answer: B
A monkey ascends a greased pole 19 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ?	Choose the correct choice from the following choices:
A) 21st
B) 22nd
C) 23rd
D) 35th
E) None of these

Solution: In 2 minutes, he ascends = 1 metre   âˆ´ 17 metres, he ascends in 34 minutes.   âˆ´ He reaches the top in 35th minute.   Answer 35th
Answer: D
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 25 cm? Choices:	A) 827 cm2	B) 216 cm2	C) 285 cm2	D) 178 cm2	E) 475 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (25)   = 475 cm2   Answer:475 cm2
Answer: E
A boy rides his bicycle 20km at an average speed of 20km/hr and again travels 30km at an average speed of 10km/hr. His average speed for the entire trip is approximately? Choose the correct choice from the following answers: A) 10.6km/hr B) 8.9km/hr C) 15.5km/hr D) 12.5km/hr E) 15km/hr

Solution: Total distance traveled = 20+30= 
20+30 = 50
50km   Total time taken= 20/20 + 30/10= 
20/20 + 30/10 = 4
4 hrs   Average speed= 50/4= 
50/4 = 25/2 = around 12.5
12.5km/hr   Answer is 12.5km/hr
Answer: D
The average marks of a class of 12 students is 40 and that of another class of 28 students is 60. Find the average marks of all the students? Choose the correct choice from the following
A) 52.2 B) 59.5 C) 52.8 D) 52.5 E) 54.0

Solution: Sum of the marks for the class of 12 students = 12 * 40= 
12 * 40 = 480
480   Sum of the marks for the class of 28 students= 28 * 60= 
28 * 60 = 1_680
1680   Sum of the marks for the class of 40 students=   480 + 1680= 
480 + 1680 = 2_160
2160   Average marks of all the students= 2160/40= 
2160/40 = 54
54   Answer:54.0
Answer: E
In how many ways can the letters of the word APPLES be arranged in a row so that the vowels appear in alphabetic order?  Choose the correct answer:	A) 220	B) 320	C) 360	D) 420	E) 222

Solution: three letters can be arranged in 2! ways.   only one combination AEI is required.   6 letters can be arranged in 6! ways.   thus 6!/ 2! * 1 = 360.   360
Answer: C
Set R is composed of nine numbers, labeled R1 through R9. Set S is also composed of nine numbers, labeled S1 through S9. Set S is defined as follows: S1 = 1 + R1; S2 = 2 + R2; and so on, including S9 = 9 +R9. How much larger is the sum of set S's mean and range than the sum of set R's mean and range?
Choose the correct choice from the following options:	A) 8	B) cannot be determined	C) 4	D) 6	E) 9

Solution: Yes, the correct answer is cannot be determined
Answer: B
A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Select the correct option:
A) 28 B) 277 C) 12 D) 99 E) 32

Solution: Original price = 100   12P = 80   S = 80*(140/100)= 
80*(140/100) = 112
112   100 - 112= 12%   Answer: 12
Answer: C
3/8 of 168 * 15 / 5 + X = 549 / 9 + 275  Select the correct option:
A) 107 B) 147 C) 10 D) 296 E) None of these

Solution: Explanation:   Let 3/8 of 168 * 15 / 5 + X = 549 / 9 + 275   Then, 63 * 15 / 5 + X = 61 + 275   63 * 3 + X = 336   189 + X = 336   X = 147   ANSWER 147
Answer: B
The radius of a semi circle is 6.6 cm then its perimeter is?  Answers:  A) 32.7  B) 32.4  C) 22.4  D) 33.9  E) 32.1

Solution: 36/7 r = 6.6 = 33.9   Answer:33.9
Answer: D
Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 5, what is the probability that it is an odd number?  Choose the most appropriate option
A) 2/7
B) 3/7
C) 1/5
D) 2/5
E) 3/10

Solution: There are 5 numbers higher than 5 and 2 of them are odd.   The probability is 2/5.   The answer is 2/5.
Answer: D
A Train T1 starts from Ahmedabad to Mumbai at 7 am and reaches at 12 noon. A second train T2 starts at 7 am from Mumbai reaches Ahmedabad at 1 pm. When did the two train cross each other ?	Choose the most appropriate option.
A) 10.13 am  B) 10.00 am  C) 9.43 am  D) 9.35 am  E) none of these

Solution: Let the distance be x between the two stations.   Train T1 takes 5 hours to reach Mumbai.   Train T2 takes 6 hours to reach Ahemedabad.   Relative speed of both the train will be added = x/5 + x/ 6 = 11x/30   Time taken = (x/11)*(x/30) = 30/11   or, (30 X 60 )/11 =~ 2.43 hours   so 7 + 2.43= 
7 + 2.43 = 9.43
9.43 am   ANSWER:9.43 am
Answer: C
If r is a positive integer and 10^r – 74 in decimal notation has digits whose sum is 440, what is the value of r?	Choose the correct choice:
A) 40  B) 44  C) 45  D) 46  E) 50

Solution: Answer E = 50   We have (10^r)-74, where the sum of the digits is 440.   100-74= 
100-74 = 26
26, so we already have   2+6= 
  2+6 = 8
8 from the 440.   Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74= 9926.   So dividing the  432/9= 
 432/9 = 48
48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction.   So we have   48 + 2= 
  48 + 2 = 50
50
Answer: E
Find the odd man out
2, 4, 8, 16, 48, 64
Answers.
A) 48	B) 8	C) 16	D) 4	E) 2

Solution: 2*2= 
2*2 = 4
4   4*2= 
4*2 = 8
8   8*2= 
8*2 = 16
16   16*2= 
16*2 = 32
32   32*2= 
32*2 = 64
64   48NSWER:48
Answer: A
Pipes A and B can fill a tank in 4 and 8 hours respectively. Pipe C can empty it in 16 hours. If all the three pipes are opened together, then the tank will be filled in?	Options:
A) 3 9/97 hrs
B) 3 1/5 hrs
C) 3 9/17 hrs
D) 3 9/27 hrs
E) 3 9/19 hrs

Solution: Net part filled in 1 hour = 1/4 + 1/8 - 1/16   = 5/16   The tank will be full in 16/5 hrs, i.e., 3 1/5 hrs.   Answer:3 1/5 hrs
Answer: B
The fourth proportional to 8, 13, 56 is:
Choose the correct option: A) 91 B) 92 C) 93 D) 94 E) 95

Solution: Let the fourth proportional to 8, 13, 56 be x.   Then, 8 : 13 : 56 : x   8x = (13 x 56)   x =	(13 x 56)/8   x=728/8= 
728/8 = 91
91   91nswer: Option 91
Answer: A
Each of the three people individually can complete a certain job in 4, 5, and 8 hours, respectively. What is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates?  Choose the most appropriate option: A) 9/20 B) 11/20 C) 11/32 D) 13/40 E) 17/40

Solution: The two slowest people work at rates of 1/5 and 1/8 of the job per hour.   The sum of these rates is 1/5 + 1/8 = 13/40 of the job per hour.   The answer is 13/40.
Answer: D
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?	Choose the correct answer
A) 40 sec	B) 70 sec	C) 49 sec	D) 47 sec	E) 42 sec

Solution: Speed = 45 * 5/18   = 25/2 m/sec   Total distance covered   = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40 secnswer: 40 sec
Answer: A
Paul sells encyclopedias door-to-door. He earns $140 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:
Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->
He does not earn double commission.That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.
His largest paycheck of the year was $1,320. What were his sales for that pay period?
Choose the correct choice from the following answers.
A) 13,600 B) 14,800 C) 16,400 D) 15,800 E) 19,600

Solution: His pay check was $1320.   Out of this, $140 was his fixed salary so the total commission he earned was $1320 - $140 = $1180   He earns 10% on the sales of first $10,000 which gives a commission of $1000.   He earns 5% on every subsequent dollar. Since he earns another $180, he must have had sales of another 180*(100/5)  1320 -  140= 
 1320 -  140 = 1_180
$1180   He earns 10% on the sales of first $10,000 which gives a commission of $1000.   He earns 5% on every subsequent dollar. Since he earns another $180, he must have had sales of another   180*(100/5)= 
  180*(100/5) = 3_600
3600   So his total sales must have been $10,000 + $3600= $13,600   13,600
Answer: A
150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice? Select the correct option.
A) 968  B) 960  C) 911  D) 989  E) 922

Solution: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day   Let us say 70 men take x days to consume 150 kg.   Quantity consumed by each item in x days = (7x/30) kg   Quantity consumed by 70 men in x days = (7/30 x)(70) kg   = (7/30 x) * (70) = 960   x = 60 days.   Answer:960
Answer: B
How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?
Choose one
A) 40  B) 400  C) 5040  D) 2520  E) None

Solution: Solution   'LOGARITHM' contain 10 different letters.   Required number of words = Number of Arrangement of 10 letters, taking 4 at a time   = 10 P 4 = (10 × 9 × 7) = 5040 .   Answer 5040
Answer: C
In 15 year’s time the combined age of my four brothers will be 107. What will it be in six year’s time?
Pick one.
A) 56 B) 64 C) 71 D) 46 E) 77

Solution: C   Combined age in 15 years = 107.   4 × 15 = 60, therefore combined age now is 107 – 60 = 47.   In 6 years time, therefore, combined age will be   47 + 24 (4 × 6) = 71.
Answer: C
Naomi made a scarf for her brother using the yarn that cost $2.50 per skein. He offered to pay
Naomi for the yarn she used. If she used 1.5 skeins of yarn to make the scarf, what was the total
cost of the yarn?
Choices:
A) $2.25  B) $3.25  C) $4.25  D) $5.25  E) $6.25

Solution: $2.50 x 1.13 = 2.83 for one skein (rounded)   $2.83 x 1.5 = $4.25 (rounded)   You could have found the basic cost of 1.5 skeins first, and then figured tax and   shipping. Your answer may be slightly different because of rounding.   correct answer $4.25
Answer: C
Carol is Four times Alice’s age but only twice as old as Betty. Alice is eighteen years younger than Carol. How old is Betty?
Choose the correct choice
A) 6  B) 9  C) 12  D) 18  E) 24

Solution: ans B..9..   given that C=4A=29..AND A=C-18=4A-18   substituting the values A=6,C=18 AND 9=9..
Answer: B
George baked a total of 100 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday? Choose the correct answer:
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: 3/5 of the 100 pizzas cooked on Saturday = 60 pizzas   3/5 of the remaining pizzas on Sunday = 24 pizzas   We're left with   (100-60-24)= 
  (100-60-24) = 16
16 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.   M T W TH F   6 4 3 2 1=16   W =3   3
Answer: A
In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr? Choose the correct choice from the following answers:
A) 2.0 sec
B) 2.7 sec
C) 3.5 sec
D) 5.0 sec
E) 9.5 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 200/40= 
200/40 = 5
5.0 sec.   Answer: 5.0 sec
Answer: D
A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 300km less in time. Find his speed?  Choose the correct choice from the following answers
A) 20km/hr B) 30km/hr C) 60km/hr D) 50km/hr E) 60km/hr

Solution: Let the speed be x km/hr   50x-50* 9/10 *x = 300   50x - 45x = 300   5x = 300   x = 60km/hr   Answer is 60km/hr
Answer: C
How many integers between 324,700 and 375,600 have tens digit 1 and units digit 3? Choose the correct option.
A) 509 B) 624 C) 756 D) 832 E) 947

Solution: The integers are:   324,713   324,813   etc...   375,513   The number of integers is   3756 - 3247= 
  3756 - 3247 = 509
509   The answer is 509.
Answer: A
There were totally 100 men.82 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?	Choose one:
A) 11  B) 12  C) 13  D) 14  E) 15

Solution: 100-(100-82)-(100-75)-(100-85)-(100-70)= 100-18-25-15-30=100-88= 
100-88 = 12
12   ANSWER:12
Answer: B
In Net's hair salon 38% of the customers dye their hair blond, 36% dye their eyebrows blond and 35% straighten their hair. 20% of the customers have none of these three procedures, while 12% take all of these three procedures. What percent of the customers come for exactly 2 of these 3 procedures?	Pick one.
A) 5%
B) 9%
C) 12%
D) 15%
E) 21%

Solution: Let a total of 100 people visit the salon.   Total = 100   Dye hair blonde (5%) = 38 % = 38   Dye Eyebrows blonde (B) = 36% = 36   Straighten Hair (C) = 35% = 35   Neither = 20% = 20   5%ll Three = 12% =12   Total = 5%+B+C - (Sum of Exactly Two group overlaps) - 2*(5%ll three) + Neither   100 = 38+36+35 - (Sum of Exactly Two group overlaps) - 2*12 + 20   (Sum of Exactly Two group overlaps) = 9   %of customers coming for exactly 2 of the 3 procedures = 5%   5%
Answer: A
What is the area of a square field whose diagonal of length 26 m?
Options:
A) 287 B) 269 C) 338 D) 200 E) 230

Solution: d2/2 = (26 * 26)/2= 
(26 * 26)/2 = 338
338   Answer:338
Answer: C
A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1233. Find the number to be multiplied. Choose the correct choice from the following options.
A) 130  B) 132  C) 134  D) 137  E) 138

Solution: Let the required number be x. Then,   43x – 34x = 1233 or 9x = 1233 or x = 137.   Required number = 137.   ANSWER:137
Answer: D
Excluding stoppages, the speed of a train is 60 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?  Choose the correct choice:  A) A)12  B) B)18  C) C)24  D) D)30  E) E)36

Solution: Explanation:   T = 24/60 * 60= 
24/60 * 60 = 24
24   Answer: Option 24
Answer: C
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 6 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?	Choose the correct choice: A) 19:2 B) 18:3 C) 29:11 D) 29:5 E) 29:4

Solution: Quantity of alcohol in vessel P = 62.5/100 * 6 = 15/4 litres   Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres   Quantity of alcohol in the mixture formed = 15/4 + 7/2 = 29/4= 
29/4 = 29/4 = around 7.25
7.25 litres   As 10 litres of mixture is formed, ratio of alcohol and water in the mixture formed= 7.25 : 2.75 = 29 : 11.   Answer:29:11
Answer: C
A computer program generates a sequence of numbers a1, a2, a3,... such that a1=1, a2=2, and ak = a(k-1) + 3ak-2 for 2 < k < n for n=20. Find a5.	Choices
A) 10  B) 24  C) 28  D) 32  E) 38

Solution: a1=1   a2=2   a3=3*2-2= 
3*2-2 = 4
4   a4=3*4-2= 
3*4-2 = 10
10   a5=3*10-2= 
3*10-2 = 28
28   28
Answer: C
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio fo the speed of the train to that of the car is :
Choose one
A) 3:3 km	B) 3:5 km	C) 3:4 km	D) 2:3 km	E) None

Solution: Sol.   Let the speed of the train b x km/hr and that of the car be y km/hr.   Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/5   And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24   Soving (i) and (ii), we get x = 60 and y = 80. ∴ Ratio of speeds = 60 : 80 = 3:4.   Answer 3:4 km
Answer: C
A rectangular courtyard, the sides of which are in the ratio of 4:3, cost Rs.600 for paving at 50 p per m2; find the length of the diagonal of the courtyard?	Select.
A) 25 m	B) 11 m	C) 77 m	D) 86 m	E) 46 m

Solution: 1 m2 ---- 1/2   ? ----- 600 => 1200 m2   4x * 3x = 1200 => x = 10   25 mnswer:25 m
Answer: A
21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.  Choices:	A) 2/17	B) 3/37	C) P(E) 9 by 42	D) 8/97	E) 12/31

Solution: The probability that first toy shows the even number,   =1021= 1021   Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.   Hence, probability that second toy shows the even number,   =920=920   Required probability,   =(1021)×(920)= (1021)×(920)   =9/42   P(E) 9 by 42
Answer: C
What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12% p.a.?  Choose one:
A) Rs.10123.22
B) Rs.10823.20
C) Rs.10123.20
D) Rs.10123.29
E) Rs.10123.28

Solution: Explanation:   Amount = [25000 * (1 + 12/100)3]   = 25000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20   C.I. = (35123.20 - 25000) = Rs.10123.20   Answer:Rs.10123.20
Answer: C
When x is divided by y, the quotient is v with remainder r. What is x in terms of r, y, and v?
Choose the correct choice from the following choices
A) y + r +v B) yv + r C) x/y+r D) y/v+r E) rv + y

Solution: (x/y) = v + r   solve for x   x=(v*y)+r   Ans yv + r.
Answer: B
In a certain sequence of numbers, a1, a2, a3, ..., an, the average (arithmetic mean) of the first m consecutive terms starting with a1 is m, for any positive integer m. If a1=1, what is a11?	Choose the correct choice
A) 100
B) 55
C) 21
D) 19
E) 1

Solution:   As stated above, (a1+a2+a3......+a10+a11)/11=11   therefore a1+a2+a3.......a11=121 (1)   using the same logic, we got a1+a2+a3..........+a9+a10=100 (2)   (2)-(1) we got a11=21   21
Answer: C
A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?  Choose the correct choice from the following answers:  A) Rs. 1090  B) Rs. 1160  C) Rs. 1190  D) Rs. 1202  E) Rs. 1092

Solution: S.P. = 85% of Rs. 1400 = Rs.	85	x 1400/100 = Rs. 1190   Answer: Option Rs. 1190
Answer: C
The number of sailors on a ship is 85% more than the number of officers. The ratio of sailors to officers would be	Choose the correct choice from the following.
A) 37:20 B) 47:20 C) 47:25 D) 22:25 E) 97:50

Solution: Sailor = 1.85 * Officer   Sailor/Officer = 1.85/1 = 185/100 = 37/20   37:20nswer will be 37:20
Answer: A
which of the following options is the correct value of b, given the equation b^(-2) +b^3 = 64.1?	Choose the correct choice from the following options.
A) 2 B) 1 C) 3 D) 7 E) 4

Solution: Plugging in the various option into the equation to find out which is correct:   b^(-2)+b^3 = 64.1   4^(-2)+4^3 Ans. 4
Answer: E
A circular wheel 28 inches in diameter rotates the same number of inches per second as a circular wheel 35 inches in diameter. If the smaller wheel makes x revolutions per second, how many revolutions per minute does the larger wheelmakes in terms of x ?  Select
A) 48pi/x	B) 75x	C) 46x	D) 24x	E) 48x

Solution: C = (pi)d   C(small): (pi)*28   C(large): (pi)*35   Lets say the time horizon is 60 seconds, so during that time the smaller wheel covers a distance of (pi)*28*60 = (pi)*(1680) inches   (pi)*(1680) = (pi)*(35)(x)   pi*(48) = pi*(x)   48=x   Answer: E. 48x
Answer: E
Can you please walk me through how to best approach this problem? Thanks
If #p# = ap^3+ bp – 1 where a and b are constants, and #-5# = 10, what is the value of #5#?  Choose the correct choice from the following answers:  A) 5  B) -12  C) -2  D) -3  E) -5

Solution: #p# = ap^3 + bp - 1   #-5# = 10   putting p = -5 in above equation   -125a -(5b +1) = 10 or   #-5# = (125a+5b+1) = -10   therefore 125a+5b = -11 .....(1   now putting p = 5   #5# = 125 a+5b - 1   using equation 1(125a+5b = -11)   #5# = -11-1 = -12   hence -12
Answer: B
Jim is now twice as old as Fred, who is two years older than Sam. Seven years ago, Jim was three times as old as Sam. How old is Jim now?
Choose the correct choice from the following:
A) 18 B) 20 C) 24 D) 32 E) 40

Solution: J = 2F = 2(S+2) = 2S+4   J-7 = 3*(S-7)   (2S+4)-7 = 3S-21   S = 18 and so J = 40   The answer is 40.
Answer: E
A child has 12 crayons, then she finds 4 more crayons. Now how many crayons does she have.  Select
A) A) 8	B) B) 14	C) C) 22	D) D) 18	E) E) 16

Solution: 12 + 4= 
12 + 4 = 16
16. Answer is 16).
Answer: E
If 63 percent of a class answered the first question on a certain test correctly, 49 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
Choose the most appropriate option.
A) 22%
B) 24%
C) 26%
D) 28%
E) 32%

Solution: 63% answered the first question correctly and 20% answered neither correctly.   Then 17% missed the first question but answered the second question correctly.   Then the percent who answered both correctly is 49% - 17% = 32%.   The answer is 32%.49  - 17= 
49  - 17 = 32
32%.   The answer is 32%.
Answer: E
If m is the average (arithmetic mean) of the first 10 positive multiples of 4 and if M is the median of the first 10 positive multiples of 4, what is the value of M – m ?  Pick:
A) 0
B) -5
C) 5
D) 25
E) 27.5

Solution: The first 10 positive multiples of 4 is an evenly spaced set. One of the most important properties of evenly spaced set (aka arithmetic progression) is:in any evenly spaced set the arithmetic mean (average) is equal to the median.   Hence M=m --> M-m=0.   0nswer: 0.
Answer: A
The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?  Select the correct option: A) 180.27 cm B) 180.29 cm C) 978.29 cm D) 178.89 cm E) 176.29 cm

Solution: Calculated average height of 35 boys = 182 cm.   Wrong total height of 35 boys = 182 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182cm - (166 cm - 106 cm)/35   = 182 cm - 60 /35 cm   = 182 cm - 1.71 cm = 180.29 cm.   Answer: 180.29 cm
Answer: B
A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then what is B's share in the profit? Choices:	A) Rs. 2000	B) Rs. 3000	C) Rs. 4000	D) Rs. 5000	E) None of these

Solution: Explanation :   Ratio of the initial investment = 7/2 : 4/3 : 6/5   = 105 : 40 : 36   From this ratio, we can assume that actual initial investments of A, B and C   are 105x, 40x and 36x respectively   A increases his share 50% after 4 months. Hence the ratio of their investments =   (105x * 4) + (105x * 150/100 * 8) : 40x * 12 : 36x : 12   = 105 + (105 * 3/2 * 2) : 40*3 : 36 * 3   = 105 * 4 : 40 *3 : 36 * 3   = 35 * 4 : 40 : 36   = 35 : 10 : 9   B's share = total profit * (10/54) = 21,600 * 10/54 = 4000. Answer : Option Rs. 4000
Answer: C
Find the compound ratio of (1:2), (2:3) and (3:4) is Pick one
A) 1:2
B) 3:5
C) 5:7
D) 1:4
E) 2:1

Solution: Required ratio = 1/2 * 2/3 * 3/4 = 1/4 = 1:4   Answer is 1:4
Answer: D