MU-NLPC/Calc-aqua_rat huggingface dataset:
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 55?
Choose the most appropriate option:
A) s.3944  B) s.3948  C) s.3942  D) s.3965  E) s.3740

Solution: Let the side of the square plot be a ft.   a2 = 289 => a = 17   Length of the fence = Perimeter of the plot = 4a = 68 ft.   Cost of building the fence = 68 * 55   = Rs.3740.   Answer: s.3740
Answer: E
Four cups of milk are to be poured into a 3-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 4-cup bottle? Options
A) 2/3 B) 7/3 C) 5/7 D) 16/7 E) 3

Solution: Let x be the # of cups going into the 4 cup bottle.   so.... x/4 = ((4-x)/3)   16 - 4x = 3x   16 = 7x   x = 16/7.   Answer : 16/7.
Answer: D
The average of first four prime numbers greater than 10 is?
Select the correct option
A) 10
B) 20
C) 15
D) 40
E) 50

Solution: 11 + 13 + 17 + 19= 
11 + 13 + 17 + 19 = 60
60/4= 
60/4 = 15
15   ANSWER:15
Answer: C
At what rate percent on simple interest will a sum of money double itself in 30 years?
Choose the correct choice from the following.
A) 3 1/3%	B) 3 1/8%	C) 3 6/3%	D) 9 1/3%	E) 3 3/3%

Solution: P = (P*30*R)/100   R = 3 1/3%   3 1/3%nswer: 3 1/3%
Answer: A
The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? Choose the correct choice.
A) 18/35
B) 18/38
C) 18/34
D) 18/31
E) 18/30

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 3/5 * 4/7 + 2/5 * 3/7   = 12/35 + 6/35 = 18/35.   18/35nswer:18/35
Answer: A
John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house? Choose the correct answer.
A) 3 1/5 Km	B) 3 Km	C) 4 1/5 Km	D) 3 2/5 Km	E) 5 1/5 Km

Solution: Formula = S1*S2/S2-S1 * T1+T2/60   = 4*6/2 * 16/6   = 24/2 * 16/60   = 8 * 2/5   = 16/5 = 3 1/5 Km   3 1/5 Km
Answer: A
How many words with or without meaning, can be formed by using all the letters of the word, DELHI using each letter exactly once?  Select the correct option: A) 100 B) 110 C) 120 D) 130 E) 140

Solution: DELHI=5 letters   5! ways =5p5=5*4*3*2*1= 
5*4*3*2*1 = 120
120 ways   ANSWER:120
Answer: C
An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?	Choose the correct choice from the following options:
A) Rs.4082.21  B) Rs.4082.98  C) Rs.4032.40  D) Rs.4282.40  E) Rs.4082.40

Solution: Length of the first carpet   = (1.44)(6) = 8.64 cm   Area of the second carpet   = 8.64(1 + 40/100) 6 (1 + 25/100)   = 51.84(1.4)(5/4) sq m   = (12.96)(7) sq m   Cost of the second carpet = (45)(12.96 * 7)   = 315 (13 - 0.04) = 4095 - 12.6   = Rs.4082.40   Answer:Rs.4082.40
Answer: E
The length of the bridge, which a train 180 metres long and travelling at 45 km/hr can cross in 30 seconds, is?	Choose the correct choice from the following options
A) 245	B) 777	C) 282	D) 195	E) 288

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (180 + x)/30 = 25/2 => 2(180 + x) = 750 => x = 195 m.   Answer: 195
Answer: D
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 17 cm  Pick one.
A) 178 cm2  B) 323 cm2  C) 285 cm2  D) 167 cm2  E) 197 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (17)   = 323 cm2   Answer: 323 cm2
Answer: B
Some part of the 50% solution of acid was replaced with the equal amount of 30% solution of acid. As a result, 40% solution f acid was obtained. what part of the original solution was replaced? Choose the correct choice
A) 1/5
B) 1/4
C) 1/2
D) 3/4
E) 4/5

Solution: Let X = Part of acid solution replaced, then 1-X will be the parts not replaced.   (1-X)*0.5 + 0.3*x = 0.4   0.5 - 0.5X +0.3X = 0.4   -0.2X = -0.1   X=1/2   So the answer is 1/2
Answer: C
What will come in place of the x in the following Number series? 25, 100, x, 1600, 6400  Answers.
A) 6400
B) 4346
C) 5674
D) 7674
E) 6576

Solution: (6400)   25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.
Answer: A
In a car wheel, two spokes cover 15 degree. Then for the entire car,how many spokes are there?	Select the correct option:
A) 92  B) 128  C) 192  D) 208  E) 252

Solution: given, 2 spokes cover 15degrees,   so for 360 degrees.---->360*2/15=48..   so, for entire car, 4*48=192   ANSWER:192
Answer: C
What is the perimeter of a triangle with sides 5 and 4 that has the maximum possible area?	Choose the correct choice: A) 9 + 3√2 B) 9 + √41 C) 16 D) 9 + √37 E) 9 + 3√6

Solution: We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(25+16)= 
(25+16) = 41
√41   The perimeter is 9 + √41   The answer is 9 + √41.
Answer: B
A palindrome is a number that reads the same forward and backward, such as 343. How many odd, 8-digit numbers are palindromes?	Pick one
A) 4000  B) 4500  C) 5055  D) 5000  E) 2500

Solution: First recognize you only need to consider the first four digits (because the second four are just the first four flipped)   There are 9000 possibilities for the first four digits of a 8 digit number, 1000-9999 inclusive. Everything starting with a 1,3,5,7,9 will be odd, which is 5/9ths of the combinations.   5/9*9000= 
5/9*9000 = 5_000
5000   ANSWER:5000
Answer: D
In a museum, the entrance ticket costs Rs. 250. In vacation, the cost of the ticket is reduced, there by increasing the sale by 50%. but it was found that the collection is decreased by 17.5%. What is the deduction in the ticket price?
Choose the correct option.
A) Rs.100
B) Rs. 112.5
C) Rs. 110
D) Rs. 115.5
E) Rs. 115

Solution: Let there is sell of 100 tickets.   So total Collection = 250 *100 = Rs. 25,000 [Price of one ticket = Rs. 100]   Now, Total ticket sale = 100 + 50 % of 100 = 150.   This effected 17.5% decrease in collection.   So, Collection after increased sale,   = 25000 - 17.5% of 25000 = Rs. 20, 625.   In vacation time per ticket price,   = 20625/150 = Rs. 137.5.   Decreased in each ticket price,   = 250 - 137.5 = Rs. 112.5.   ANSWER : OPTION Rs. 112.5
Answer: B
If, 3 years ago, Jamie was half as old as he is now, how old will he be in x years?	Choose the correct choice from the following answers
A) x + 10
B) x + 5
C) x + 2
D) x + 6
E) 2x

Solution: let his age be a. a-3=a/2 hence a=6. 6 years hence, a =x+6   Answer x + 6
Answer: D
Before a salary increase, the weekly salary of a worker for 42 hours in a week was as much as the worker is paid now for 35 hours of work in a week. What is the percent increase in the worker's salary per hour?
Choose the correct option: A) 20 B) 22 C) 24 D) 26 E) 28

Solution: Let x be the original salary per hour.   Let y be the salary per hour after the increase.   35y=42x   y=(42/35)= 
(42/35) = 6/5 = around 1.2
1.2x   The salary increased 20%.   The answer is 20.
Answer: A
Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 39 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:06, at what time will they be reading the same page?	Choose the correct choice from the following options: A) 6:06 B) 6:36 C) 7:06 D) 7:36 E) 8:06

Solution: Since Tom reads an average of 1 page every 2 minutes, Tom will read 18 pages in the first 36 minutes. Jan can catch Tom at a rate of 9 pages per hour, so it will take 2 hours to catch Tom.   The answer is 7:06.
Answer: C
m is a positive integer. m! is ending with k zeros, (m+2)! is ending with k+2 zeros. Find the number of possible values of m, if 90 ≤ m ≤ 190.  Choose the correct choice from the following choices
A) 2
B) 3
C) 4
D) 6
E) 8

Solution: Possible values of m where (m+2)! has two zeroes more than the no. of zeroes in m! are   m=98,99--No of zeroes 22 (m+2)! i.e, 100 and 101 have 24 zeroes each.   m=148,149   m=174,175   no. of possible values of m=6.   Answer has to be 6.
Answer: D
In how many ways can the letters of the word "MARS" be arranged? Answers.
A) 16	B) 20	C) 24	D) 28	E) 32

Solution: The total ways of arranging the letters = 4! = 24   The answer is 24.
Answer: C
A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?  Pick:
A) 60
B) 90
C) 220
D) 170
E) 120

Solution: Let x be the number he chose, then   2*x−138=102   2x=240   x=120   Anser is 120.
Answer: E
A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?
Select the correct option.
A) Rs.256.27  B) Rs.256.29  C) Rs.256.20  D) Rs.256.22  E) Rs.256.25

Solution: Let the principal be Rs.P   S.I at 5% p.a in 8 years on Rs.P = Rs.500   (P)(8)(5)/100 = 500   P = 1250   C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years   =2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}   = 2500/400(441 - 400)   = 25/4(41) = 1025/4 =Rs.256.25   Answer:Rs.256.25
Answer: E
A firm has 2 senior partners and 5 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)	Choose the correct choice from the following options:
A) 17  B) 21  C) 25  D) 29  E) 33

Solution: The number of ways to form a group of 3 is 7253 = 35   The number of groups with no senior partner is 5253 = 10   The number of groups with at least one senior partner is 35-10= 
35-10 = 25
25   The answer is 25.
Answer: C
The average of 10 consecutive integers is 11. Then, 9 is deducted from the first consecutive number, 8 is deducted from the second, 7 is deducted form the third, and so on until the last number which remains unchanged. What is the new average?  Choose one:
A) 5 B) 5.5 C) 6 D) 6.5 E) 7

Solution: The total subtracted is (9+8+...+1) = (9*10) / 2= 
(9*10) / 2 = 45
45   On average, each number will be reduced by   45/10= 
  45/10 = 9/2 = around 4.5
4.5   Therefore, the overall average will be reduced by 4.5   The answer is 6.5.
Answer: D
Calculate f(3), given that f(x) = x3 + f0(-1)x2 + f00(1)x + f0(-1)f(-1). Options.
A) 198 B) 197 C) 196 D) 195 E) 194

Solution: Differentiating, we compute   f0(x) = 3x2 + 2f0(-1)x + f00(1)   f00(x) = 6x + 2f0(-1):   Plugging in x = -1 into the first equation and x = 1 into the second, we obtain a system of   equations in f0(-1) and f00(1):   f0(-1) = 3 - 2f0(-1) + f00(1);   f00(1) = 6 + 2f0(-1):   Denoting f0(-1) and f00(1) by a and b respectively, we have   a = 3 - 2a + b   b = 6 + 2a:   Plugging the second equation into the first, we get   a = 3 - 2a + (6 + 2a) = 9:   Thus, b 3 - 2  + (6 + 2 )= 
3 - 2  + (6 + 2 ) = 9
9:   Thus, b= 6 + 2a = 24, so   f(x) = x3 + ax2 + bx + af(-1) = x3 + 9x2 + 24x + 9f(-1):   Finally, plugging x = -􀀀1 into this equation, we get   f(-1) =-1 + 9-24 + 9f(-1)   -8f(-1) = -16   f(-1) = -2   We conclude that   f(x) = x3 + 9x2 + 24x + 18   f(3) = 33 + 9* 32 + 24 *3 + 18   = 27 + 81 + 72 + 18= 
27 + 81 + 72 + 18 = 198
198   correct answer 198
Answer: A
A man can row upstream at 4kmph and downstream at 10 kmph. The speed of the stream is Select:	A) 2.5 km/hr	B) 4.2 km/hr	C) 3 km/hr	D) 10.5 km/hr	E) None

Solution: Sol.   Speed of stream = 1/2(10 -4) kmph = 3 kmph.   Answer 3 km/hr
Answer: C
A motorist covers a distance of 39km in 45min by moving at a speed of x kmph for the first 15min, then moving at double the speed for the next 20 min, and then again moving at his original speed for the rest of the journey. Find x.  Choose the correct choice.
A) 60 km/h	B) 48 km/h	C) 36 km/h	D) 58 km/h	E) 68 km/h

Solution: Total distance = 39 km   Total time = 45 min   D = S*T   x * 15/60 + 2x * 20/60 + x * 10/60 = 39 km   x = 36 kmph   Answer : 36 km/h.
Answer: C
Abhishek started a business investing 50,000. After one year he invested another 30,000 and Sudin also joined him with a capital of 70,000. If the profit earned in three years from the starting of business was 87,500, then find the share of Sudin in the profit Choose the correct choice from the following choices
A) 37,500  B) 32,500  C) 38,281  D) 52,500  E) None of these

Solution: Ratio of Abhishek and Sudin for one month   = (50,000 × 36) + (30,000 × 24) : (70,000 × 24)   = (18,00,000 + 7,20,000) : 16,80,000 = 3 : 2   Hence share of Sudin in the profit earned from the business.   = 87,500/(3+2)×2= 35,000   Answer None of these
Answer: E
A sells to B goods at five-thirds the rate of profit at which B has decided to sell it to C. C, on other hand sells it to D at one-third the rate of profit at which B sold it to C. If D gives Rs. 2145 to C at 10%, how much did A buy it for ?	Pick one.
A) 1000 B) 1100 C) 1200 D) 1300 E) 1400

Solution: let profit rate of b = x   acc to question profit rate of a becomes 5/3 x   and that of c= 1/3 x which is given as 10%   1/3 x= 10   therefore x=30   now b=30% , a=50%   now we will find out c's price-   11/10 * price = 2145   price = 1950   in similar way we will find out b's price as we know that profit is 30%   therefore 130/100 * price = 1950   so b 's price =1500   similarly for a ('profit is 50%)   150/100 * price = 1500   on solving it we get   a's price = 1000   1000NSWER:1000
Answer: A
Sagar was riding bike towards north,turned left road 1 km turnes towrds left &road 2km found himself 1km west of starting how far did he road north?	Select the correct option.
A) 2km in north.  B) 2km in south.  C) 2km in east.  D) 2km in west.  E) 4km in north.

Solution: He travelled total distance of 3km.   From which he travelled 1km in west.   Hence in all he travelled total 2km in north.   2km in north.NSWER:2km in north.
Answer: A
Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?  Choose the correct choice from the following answers:
A) 20  B) 21  C) 23  D) 25  E) 27

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131   a + b + c = √400 = 20   20
Answer: A
Which of the following ranges of numbers includes the greatest number of prime numbers? Choose the correct choice from the following answers: A) 10-19, inclusive B) 20-29, inclusive C) 40-49, inclusive D) 60-69, inclusive E) 70-79, inclusive

Solution: Prime numbers between -   A. 10-19, inclusive is 4 (11 , 13 , 17 , 19)   B. 20-29, inclusive is 2 ( 23, 29)   C. 40-49, inclusive is 3 ( 41 , 43 , 47)   D. 60-69, inclusive is 2 ( 61, 67)   E. 70-79, inclusive is 3 ( 71, 73, 79)   Thus A. 10-19, inclusive contains greatest number of prime numbers.   10-19, inclusiveNSWER:10-19, inclusive
Answer: A
A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2hours30minutes to cover a distance of 5km upstream. find the speed of the river current in km/hr.  Options.
A) 2km/hr	B) 1km/hr	C) 5km/hr	D) 2m/hr	E) 4km/hr

Solution: rate downstream=(15/3 ¾)km/hr=(15*4/15)km/hr=4km/hr.   Rate upstream=(5/2 ½)km/hr=(5*2/5)km/hr=2km/hr.   Speed of current=1/2(4-2)km/hr=1km/hr   Answer is 1km/hr.
Answer: B
If the terms of a series are either2or24and the sum of all the terms D of the series is 124, then which of the following could be the number of2sin the series?  Choose the correct choice from the following answers:
A) 26  B) 29  C) 35  D) 40  E) 48

Solution: Ans: A   Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms is 124 means  24*5= 
 24*5 = 120
120 so number of 24 can't be more than 5   so D=24x +2y = 124   24*5 + 2y =124 then y=2   24*4 + 2y = 124 then y=14   24*3 +2y = 124 then y= 26   24*2 +2y =124 then y = 38   24 +2y = 124 then y= 50   26 is the ans.26
Answer: A
The distance between X&Y is 400km. A person is traveling from X to Y at 60km/hr started at 11AM and another person is traveling from Y to X at 40km/hr and started at same time. Then at what time they meet together.?	Choose the correct choice:
A) A)2PM B) B)4PM C) C)1PM D) D)3PM E) E)5PM

Solution: Let x hours be they will meet together   distance covered by 1st person+distance covered by 2nd person = 400km   60x+40x = 400   x= 4 hr   They will meet = 11AM +4hr = 3PM   Answer is 3PM
Answer: D
If a quarter kg of potato costs 60 yen, how many paise will 200 gm cost? Pick one:	A) yen 48	B) yen 54	C) yen 56	D) yen 72	E) None

Solution: Explanation: Let the required weight be x kg.   Less weight, Less cost (Direct Proportion)   250 : 200 :: 60 : x 250 x x = (200 x 60)   x= (200 x 60)/250   x = 48   yen 48nswer: Option yen 48
Answer: A
The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is:  Options:
A) 12
B) 16
C) 24
D) 48
E) 98

Solution: Let the numbers be 3x and 4x.   Then their H.C.F = x. So, x = 4.   So, the numbers are 12 and 16.   L.C.M of 12 and 16 = 48.   ANSWER:48
Answer: D
Find the mean proportional between 7921 & 9409?	Pick one.
A) 8163  B) 8633  C) 8663  D) 8636  E) None of these

Solution: Explanation:   Formula = √a×b   A = 7921 and 8633 = 9409   √7921×9409 = 89 × 97 = 8633   Answer: Option 8633
Answer: B
0---:-|---:--|-:--:-|--:---|-:----1
On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance Z between any two of the tick marks?  Select.
A) 1/70 B) 1/35 C) 2/35 D) 1/12 E) 1/7

Solution: divisions are 0 1/7 2/7 3/7 4/7 5/7 6/7 1   1/5 2/5 3/5 4/5 5/5   expressing the same in terms of the lcm of 5,7 ,i.e 35   0 7/35 14/35 21/35 28/35 35/35   5/35 10/35 15/35 20/35 25/35 30/35   by comparing the divisions with each other we can see 1/35 is the shortest possible distance between any two selected divisions.   Z=1/35   Answer is 1/35.
Answer: B
Find the product of the local value and absolute value of 8 in 564823 Choose the most appropriate option.
A) 1600  B) 6400  C) 16000  D) 12000  E) 18000

Solution: Explanation:   Place value = Local value   Face value = Absolute value   The place value of 8 in 564823 is 8 x 100 = 800   The face value of 8 in 564823 is nothing but 8.   => 800*8= 
800*8 = 6_400
6400   Answer: Option 6400
Answer: B
In a certain city, 80 percent of the households have cable television, and 50 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:  Select the correct option.
A) 45,000 to 90,000 inclusive	B) 30,000 to 120,000 inclusive	C) 45,000 to 75,000 inclusive	D) 75,000 to 120,000 inclusive	E) 90,000 to 120,000 inclusive

Solution: The maximum percentage with both is 50% which is 75,000 households.   This means that every household with a recorder also has cable television.   The minimum percentage with both is 30% which is 45,000 households.   This means that 20% of households have only recorders but not cable television.   The other 30% of households with recorders have cable television.   The answer is 45,000 to 75,000 inclusive.
Answer: C
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 24 seconds. The ratio of their speeds is?  Select the correct option
A) 3/7  B) 3/2  C) 3/5  D) 3/1  E) 7/3

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 24   ==> 27 x + 17 y = 24 x + 24 y ==> 3 x = 7 y ==> x/y   = 7/3.   Answer: 7/3
Answer: E
A thief goes away with a SANTRO car at a speed of 25 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start? Choose the most appropriate option
A) 5/3 hours B) 2/7 hours C) 1 hours D) 3 hours E) 2 hours

Solution: -----------25--------------------|   50 25   D = 25   RS = 50 â€“ 25 = 25   T = 25/25= 
25/25 = 1
1 hours   ANSWER:1 hours
Answer: C
how many 1x1x1 cubes can you fit in a 15x16x13 box?	Choose the correct choice from the following answers
A) 3,200
B) 3,150
C) 3,448
D) 3,120
E) 2,980

Solution: The answer is D) 3,120. A 1x1x1 cube has an area of 1. The 15x16x13 box has an area of 3,120. If you divide 3,120 by 1, you get 3,120. Therefore the answer is 3,120.
Answer: D
At a certain rate of simple interest per annum the amount due in 3 & 1/2 yrs and 5 & 1/2 yrs are respectively Rs4560 & Rs4840. Find the rate of Simple Interest ?
Choose the correct choice from the following answers:
A) 1.43  B) 4.43  C) 2.43  D) 3.43  E) 5.34

Solution: let the amount p & rate r   now 4560-p=(p*r*7/2)/100 .....(1)   4840-p=(p*r*11/2)/100 .....(2)   by solving the eq. we get the p=4070 and r=3.43   so the ans is 3.43   ANSWER:3.43
Answer: D
A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?  Choose the correct choice from the following choices:  A) 130 m  B) 360 m  C) 500 m  D) 540 m  E) 580 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (800 + x)/60 = 65/3   x = 500 m.   ANSWER:500 m
Answer: C
A trained covered x km at 65 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km. Choose one:  A) 22  B) 99  C) 26  D) 66  E) 887

Solution: Total time taken = x/65 + 2x/20 hours   = 3x/26 hours   Average speed = 3x/(3x/26) = 26 kmph   Answer: 263 /(3 /26)= 
3 /(3 /26) = 26
26 kmph   Answer: 26
Answer: C
A set of 11 positive integers has an average of 35. Which of the following is the greatest possible value for the median of this set?  Choose the most appropriate option:
A) 64  B) 30  C) 36  D) 45  E) 46

Solution: for the median to be max , we should take all the values below meadian to be the lowest and the remaining values to be the same..   here 1 is the lowest value(positive int) so the lowest 5 int will equal 5..   remaining 6= 35*11-5=380..   therefore each valueof these 6 int =380/6=64   ans 64
Answer: A
The sum of the non-prime numbers between 60 and 70, non-inclusive, is	Select:
A) 387	B) 429	C) 457	D) 499	E) 536

Solution: sum of consecutive integers from 61 to 69, inclusive ====> (A1 + An)/2 * # of terms = (61 + 69)/2 * 9 = 65 *9= 
65 *9 = 585
585   sum of non-prime numbers b/w 60 and 70, non inclusive===> 585 - 128 (i.e., 61 + 67, being the prime #s in the range) =457   Answer: 457
Answer: C
Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 70 white marbles. How many red marbles could be in bag A? Choose the correct option.
A) 1	B) 3	C) 4	D) 6	E) 14

Solution: 6 is the answer.   Bag A-   R:W:B = 2:6:9   Let W in bag A be 6K   Bab B -   R:W = 1:4   Let W in bag B be 4k   W = 70 = 6K+4k   =>k=7   Total Red's in bag A will be 2K = 14   14
Answer: E
If S is the sum of the reciprocals of the consecutive integers from 81 to 90, inclusive, which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
IV. 1/5
V. 1/8>S >1/9
Pick one
A) V B) I C) II D) III E) IV

Solution: Since we summarize the reciprocals from 90 to 81, we can say also that we add ten numbers who are all (with one exception 1/90) greater than 1/90, so that the sum must be greater than 1/9.   On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.   sum has to be greater than 1/9 and less than 1/8   V
Answer: A