MU-NLPC/Calc-aqua_rat huggingface dataset:
If w = 20! + 17, then w is divisible by which of the following?
I. 15
II. 17
III. 19	Choose the correct choice from the following answers:  A) None  B) I only  C) II only  D) I and II  E) II and II

Solution: Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included.   So w!+17 = xxxx00 +17= 
00 +17 = 17
xxxx17 which is only possibly divisible by 17. Hence Option II only is the answer.
Answer: C
A batsman makes a score of 83 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?	Choose the correct choice from the following choices.
A) 19
B) 29
C) 35
D) 49
E) 59

Solution: let the average after 17th inning =x   Then average after 16th inning=(x-3)   Therefore 16(x-3)+83=17x   Therefore x=35   ANSWER:35
Answer: C
The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
Choose the correct answer.
A) 377	B) 800	C) 278	D) 277	E) 281

Solution: Area of the square = s * s = 5(125 * 64)   => s = 25 * 8= 
25 * 8 = 200
200 cm   Perimeter of the square= 4 * 200= 
4 * 200 = 800
800 cm.   Answer: 800
Answer: B
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?  Choose one
A) 2 hours	B) 9 hours	C) 3 hours	D) 7 hours	E) 2 hours

Solution: Part filled by A + B + C in 1 hour   = 1/5 + 1/10 + 1/30   = 1/3   All the three pipes together will fill the tank in 3 hours.   Answer:3 hours
Answer: C
Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?
Choose the correct choice from the following answers.
A) 6 B) 8 C) 10 D) 14 E) 16

Solution: In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT.   So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/3!2!=10.   Answer: 10.
Answer: C
The price of a book is increased from $300 to $420. What is the % of increase in its price? Choose the correct answer:
A) 10%	B) 20%	C) 40%	D) 50%	E) 60%

Solution: Explanation: Change in the price = Rs 420 â€“ Rs 300   = Rs 120   Percentage of increase = Change in the price Initial Price   * 100.   Percentage increase in price =( 120 300   ) *100 = 40%   40%
Answer: C
The greatest number which on dividing 1442 and 1816 leaves remainders 12 and 6 respectively, is:  Choose the correct choice from the following options
A) 123 B) 127 C) 235 D) 305 E) 10

Solution: Explanation:   Required number = H.C.F. of (1442 - 12) and (1816 - 6)   = H.C.F. of 1430 and 1810 = 10. Answer: 10
Answer: E
A can do a work in 20 days and B in 30 days. If they work on it together for 4 days, then the fraction of the work that is left is :  Choose the correct choice from the following answers:	A) 1/3	B) 2/3	C) 4/3	D) 5/3	E) 7/3

Solution: Ans is:2/3   A's 1 day's work =1/20   2/3's 1 day's work =1/30   (A + 2/3)'s 1 day's work =(1/20+1/30)=1/12   (A + 2/3)'s 4 day's work =(1/12*4)=1/3   Therefore, Remaining work =(1-1/3)=2/3
Answer: B
There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. Wbat was the original expenditure of the mess? Pick one.
A) 147 B) 258 C) 451 D) 361 E) 420

Solution: Let the original average expenditure be Rs. x. Then,   42 (x - 1) - 35x=42;	7x= 84;	x =12.   Original expenditure = Rs. (35 x 12) =Rs. 420. .   Ans: 420
Answer: E
Along a yard 273 metres long, 14 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees	Choose the correct choice.
A) 18  B) 19  C) 10  D) 21  E) 12

Solution: Explanation:   14 trees have 13 gaps between them,   Required distance (273/13)= 
(273/13) = 21
21   Option 21
Answer: D
A train 132 m long passes a telegraph pole in 6 seconds. Find the speed of the train	Choose the most appropriate option:  A) 70 km/hr  B) 72 km/hr  C) 79.2 km/hr  D) 80 km/hr  E) None

Solution: Solution   Speed	= (132 / 6) m/sec   = (22 x 18 /5)km/hr   = 79.2 km/hr   Answer 79.2 km/hr
Answer: C
If an integer n is to be selected at random from 1 to 105, inclusive, what is probability n(n+1) will be divisible by 7?	Choose the most appropriate option.
A) 1/7	B) 3/14	C) 1/2	D) 2/7	E) 3/4

Solution: For n(n+1) to be a multiple of 7, either n or n+1 has to be a multiple of 7.   Thus n must be of the form 7k or 7k-1.   The probability is 2/7.   The answer is 2/7.
Answer: D
If both the product and sum of four integers are even, which of the following could be the number of even integers in the group?
I. 0
II. 2
III. 4	Pick one:
A) I only
B) II only
C) III only
D) II and III only
E) I, II, and III

Solution: for four int to have their product and sum as even..   2 and 4 are ok..   but 0 even number will result in an odd integer as product..   ANSWER:II and III only
Answer: D
A person bought 135 glass bowls at a rate of Rs. 15 per bowl. He sold 115 of them at Rs. 18 and the remaining broke. What is the percentage gain for A?  Choices:  A) 40  B) 30/11  C) 20/9  D) 27/11  E) 29/8

Solution: 20/9P=135*15= 
135*15 = 2_025
2025 and SP=115*18= 
115*18 = 2_070
2070   Gain %= 100*(2070-2025)/2025= 20/9   ANSWER:20/9
Answer: C
In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
Choose the correct choice:
A) 8 1/3
B) 8 1/6
C) 8 1/9
D) 8 1/1
E) 8 1/5

Solution: (4000*3*R)/100 = (5000*5*4)/100   R = 8 1/3   8 1/3nswer: 8 1/3
Answer: A
On a Monday in a certain restaurant, 20 percent of the 180 customers ordered the daily special. On Tuesday, only 10 percent of the 120 customers ordered the special. For the two days combined, what percent of the customers ordered the daily special? Choose the correct answer:
A) 15%  B) 16%  C) 18%  D) 23%  E) 30%

Solution: 20% of 180= 36   10% of 120=12   Total =48   percent for 2 days combined =48/300 ≈ 50/300=1/6 =0.1666. so it should be less than 0.1666 so it is 16%   Another approach 48/300= 48/(3*100)= 16/100= 
16/100 = 4/25 = around 0.16
0.16   Answer:16%
Answer: B
emblem is coded as 216;
crude is coded as 125
bump will be ?
Choose the correct answer:
A) 86  B) 72  C) 64  D) 32  E) 44

Solution: coding follows (no. of letters)^3   emblem = 216 = 6^3   crude = 125 = 5^3   bump = 4^3 =64   ANSWER:64
Answer: C
If 9210 - 9124 = 210-square, the value represented by the square is Select the correct option
A) 296 B) 210 C) 186 D) 124 E) 24

Solution: Evaluating the left side of the equation, we get   9210 -9124= 
  9210 -9124 = 86
86.   Therefore the right side of the equation, 210 - , must also equal 86.   Since 210 -124= 
210 -124 = 86
86, then the value represented by the is 124.   correct answer 124
Answer: D
A baker charges W dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week?
Choose the correct answer:
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: We're told that by selling cakes at W dollars/cake, a baker will make $320.   Reducing the price by 20% and selling 2 MORE cakes will also make her $320.   We're asked for the original number of cakes that the baker intends to sell.   $320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....   Let's TEST ANSWER D: 8 cakes   IF....   Original cakes = 8   8(W) = $320, so W = $40/cake   20% off = $8 off = 40-8= 
40-8 = 32
$32/cake   +2 more cakes= 8+2= 
8+2 = 10
10 cakes   10(32)= $320   This is an exact MATCH for what we were told, so this MUST be the answer.   Final Answer:   8
Answer: D
Bond (007) wants to move from a point A to point D, but here 2 watchtowers (B & C ) are present in the way of A to D. soldier on watchtowers has rifles with range of 1 kilometer. A,B,C,D are in straight line and distance between All points is 1 kilometer respectively. Find the minimum distance covered by 007 in journey between point A to D while his distance from watchtowers is always >=1 .	Choices:  A) 2.14  B) 3.4  C) 1.4  D) 6.21  E) 4.14

Solution: bond has to travel on quarter circumference of circle centered B then wakl streight 1 km then again walk on circumference of circle centered C.   = 2*pi*1/4 + 2*pi*1/4 + 1   = 1.57 +1.57 + 1= 
1.57 +1.57 + 1 = 4.14
4.14   ANSW4.14R:4.14
Answer: E
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?  Pick one
A) 388	B) 267	C) 245	D) 288	E) 261

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.   Answer: 245
Answer: C
What is the sum of the digits of integer k, if k = (10^50- 50) Select:
A) 337  B) 437  C) 457  D) 537  E) 412

Solution: There are 51 digits in 10^50   When we subtract 50 from it, there will be 50 digits left.   10^50 can be written as 9999999....(50 times) + 1   So,   10^50 - 50 = 9999999....(50 times) + 1 - 50 = 9999999....(50 times) - 49   Consider the last 2 digits,   99-49= 
99-49 = 50
50   The last 2 digits will be 50.   And our number would be 99999......99950 with 2 less 9s after subtraction.   Number of 9s left are 48 and the last two digits are 50   The sum of the digits will be     (48*9) + 5 + 0= 
  (48*9) + 5 + 0 = 437
437   Answer:- 437
Answer: B
E, B, C are three consecutive positive integers (E>B>C). What is the value of the expression 2E +B +3C?
Choose the correct choice from the following choices
A) 6A+7.  B) 5A+1.  C) 5A-1.  D) 6A-5.  E) 6E-7.

Solution: => E+E+(E-1)+3(E-2)   Ans E. 66E-7.-7.
Answer: E
What is the greatest prime factor of 8!7! + 7!6! ?  Select the correct option:	A) 7	B) 11	C) 13	D) 17	E) 19

Solution: 8!7! + 7!6! = 7!6!(8*7+1) = 7!*6!*57 = 7!*6!*3*19   The answer is 19.
Answer: E
In Karthik's opinion, his weight is greater than 55 Kg but less than 62 Kg. His brother does not agree with Karthik and he thinks that Karthik's weight is greater than 50 Kg but less than 60 Kg. His father's view is that his weight cannot be greater than 58 Kg. If all of them are correct in their estimation, what is the average of different probable weights of Karthik?	Answers:  A) 54.5  B) 56.5  C) 59.2  D) 61  E) 62

Solution: Explanation :   Solution: Assume Karthik's weight be x Kg.   According to Karthik, 55 < x < 62   According to Karthik;s brother, 50 < x < 60.   According to karthik's mother, x <58.   The values satisfying all the above conditions are 56 and 57.   .'. Required average = (56+57)/2 = 56.5.   Answer : 56.5
Answer: B
The banker's discount on Rs.1800 at 24% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time? Choose one
A) 2 months	B) 4 months	C) 5 months	D) 6 months	E) 7 months

Solution: Solution   S.I on Rs.1800 = T.D on Rs.1872.   P.W on Rs.1872 is Rs.1800.   Rs.72 is S.I on Rs. 1800 at 24%.   Time	=(100x72 / 24x1800)   = 1/6 year   = 2 months.   2 monthsnswer 2 months
Answer: A
An investment compounds annually at an interest rate of 30% What is the smallest investment period by which time the investment will more than double in value? Choose the correct choice from the following answers
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: 1 year: 100/3 = 33.33 approx $34: Total: 134   2nd year: 134/3 = 45: Total: 134+45= 
134+45 = 179
179   3rd year: 179/3= 60: Total: 179+60= 
179+60 = 239
239 > 2 (100)   ;3 years;   3NSWER:3
Answer: A
A hiker walking at a constant rate of 5 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 25 kilometers per hour. The cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up? Choose the correct choice from the following.
A) 10  B) 15  C) 20  D) 25  E) 30

Solution: In 5 minutes, the cyclist travels a distance of (5/60)*25 = 25/12 km.   The time it takes the hiker to complete this distance is (25/12) / 5 = 5/12 hours = 25 minutes   The cyclist needs to wait  25 - 5= 
 25 - 5 = 20
20 minutes   The answer is 20.
Answer: C
The diagonal of a square is 40 m. The area of the square is:
Select:
A) 600
B) 900
C) 800
D) 500
E) 400

Solution: Arear = 1/2 × ( diagonal )(power)2   = ( 1/2 × 40 × 40 )m(power)2   = 1600/2= 
1600/2 = 800
800 m(power)2   Answer is 800.
Answer: C
The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students? Pick one.
A) 23
B) 25
C) 30
D) 36
E) 39

Solution: Let the boys are X, then girls are 7X, total = X+7X = 8X   So it should be multiple of 8, 30 is not a multiple of 8.   30
Answer: C
A chemist mixes one liter of pure water with x liters of a 50% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x? Pick one:
A) 1/4	B) 1/3	C) 1/2	D) 1	E) 3/7

Solution: Concentration of salt in pure solution = 0   Concentration of salt in salt solution = 50%   Concentration of salt in the mixed solution = 15%   The pure solution and the salt solution is mixed in the ratio of --> (50 - 15)/(15 - 0) = 7/3   1/x = 7/3   x = 3/7   Answer: 3/7
Answer: E
In 2010, Arman’s birthday was on a Thursday. What day of the week was it 67 days after his birthday?	Choose the correct choice from the following
A) Thursday  B) Friday  C) Saturday  D) Sunday  E) Monday

Solution: Day of week after 67 days after Arman's birthday = 7*9 + 4   Saturday as the period will have 9 weeks and 4 days .   The 4 days in the end will be Friday - Saturday - Sunday and Monday .   Answer Monday
Answer: E
The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?  Choose the most appropriate option
A) 240
B) 273
C) 328
D) 428
E) 248

Solution: A   240   Let the five consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) and 2(x + 2)   Their sum = 10x = 440   x = 44 => 2(x - 2) = 84   Second least number of the other set = 2(84) - 121 = 47   This set has its least number as 46.   Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50   = 48 - 2 + 48 - 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240
Answer: A
Dana borrows 5500 pounds annually for her college education. If Dana gives her parents 3% of that amount back each month, how much will she still owe her parents after four years of college?
. Select the correct option:  A) 12,430.  B) 13,640.  C) 14,000.  D) 14,080.  E) 15,020

Solution: dana borrows 5500 and returns 3% per month.   so returns 165 per month. and 1980 per year.   so dana owes  5500-1980= 
 5500-1980 = 3_520
3520 per year.   after 4 years she will owe 14080.   Answer: (14,080.)
Answer: D
The cost of 3 pens and 5 pencils is Rs.100. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens? Choose the correct choice from the following options:
A) Rs.200
B) Rs.250
C) Rs.300
D) Rs.150
E) None of these

Solution: Explanation:   Let the cost of one pen is ‘5x’ and pencil is ‘x’   3 X 5x + 5x = Rs.100   15x + 5x = Rs.100   X = 100/20= 
100/20 = 5
5   :. Cost of 1 pen= 5x = 5 x 5 = 25   :. Cost of 12 pens, i.e. (one dozen) = 25 x 12 = Rs.300   Answer: Option Rs.300
Answer: C
How many times the keys of a writer have to be pressed in order to write first 400 counting no.'s? Answers:
A) 998	B) 1000	C) 1092 times	D) 1100	E) 1200

Solution: 1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 400= 301 * 3= 
301 * 3 = 903
903   -----------   1092   1092 times
Answer: C
Six participants are participating in a competition. In how many ways can the first three prizes be won?	Choose the correct answer:
A) 920 B) 120 C) 820 D) 720 E) 620

Solution: Out of 6 participants, the first three prizes can be won in,   6P3 = 6! / (6 - 3)!   = 6 x 5 x 4   = 120 ways   ANSWER:120
Answer: B
Average expenditure of a person for the first 3 days of a week is Rs. 320 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is: Choose one.
A) 350 B) 370 C) 390 D) 360 E) None

Solution: Explanation:   Assumed mean = Rs. 320   Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280   Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40   Therefore, Average expenditure for 7 days = Rs. 320 + Rs. 40 = Rs. 360   Correct Option: 360
Answer: D
he length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is: Select the correct option.
A) 288  B) 266  C) 245  D) 277  E) 211

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.Answer: 245
Answer: C
A car salesman earns a base salary of $1,000 per month plus a commission of $200 for each car he sells. If the car salesman earned $1800 in January, how many cars does he need to sell in February in order to double his January earnings? Choose one.
A) 13	B) 14	C) 15	D) 16	E) 17

Solution: 1000+200x=3600   x=13 cars.   The answer is 13.
Answer: A
A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?  Choose the correct choice: A) 1/12 B) 1/6 C) 1/5 D) 1/3 E) ½

Solution: We are asked to find the probability of one particular pattern: WRRW.   Total # of ways a gardener can plant these four bushes is the # of permutations of 4 letters WWRR, out of which 2 W's and 2 R's are identical, so 4!/2!2!=6;   So p=1/6   Answer: 1/6.
Answer: B
The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?	Answers.
A) 36  B) 32  C) 19  D) 10  E) 16

Solution: A/8 = 8 * 8 => A = 8 * 8 * 8   x * 2x = 8 * 8 * 8   x = 16 => 2x = 32   Answer: 32
Answer: B
Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?	Choose the correct choice from the following choices:	A) 30	B) 36	C) 70	D) 80	E) 150

Solution: Method I: the rates solution   “Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Rane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Rane + Zane is   R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12   That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time:   T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12= 
3*12 = 36
36   BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Rane and Zane need 36 weeks to make 15 drums.   Answer= 36.
Answer: B
There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?	Choose the correct choice from the following options.
A) 2/21  B) 1/21  C) 3/25  D) 3/29  E) 8/21

Solution: Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(8/21) = 8/21.
Answer: E
30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years? Choose the correct option:
A) 60%	B) 80%	C) 50%	D) 90%	E) 70%

Solution: Explanation:   Let total number of men = 100   Then   80 men are less than or equal to 50 years old   (Since 80% of the men are less than or equal to 50 years old)   => 20 men are above 50 years old (Since we assumed total number of men as 100)20% of the men above the age of 50 play football⇒Number of men above the age of 50 who play football = 20 × 20/100 = 4   Number of men who play football = 20 (Since 20% of all men play football)   Percentage of men who play football above the age of 50 = 420 × 100 = 20%   =>Percentage of men who play football less than or equal to the age 50 = 100% − 20% = 80%   Answer: Option 80%
Answer: B
Set A: 3, e, 8, 10
Set B: 4, y, 9, 11
The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – e?  Choose the correct choice from the following answers:
A) -2
B) -1
C) 0
D) 1
E) 2

Solution: So we have even no. of elements in the Set   So median is the average of Middle two numbers   (e+8)/2= (y+9)/2   y - e= -1   Answer -1
Answer: B
A woman and a girl complete a work together in 24 days. If for the last 6 days woman alone does the work then it is completed in 26 days. How long the girl will take to complete the work alone?  Select the correct option
A) days
B) days
C) days
D) days
E) days

Solution: Explanation:   (woman + girl )’s 1 day’s work = 1/24   Their 20 day’s work = 1/24 × 20 = 5/6   The remaining 1/6 work is done by the woman in 6days   Therefore, the woman alone will finish the work in 6 × 6 days = 36 days   woMan’s 1 day’s work = 1/36   Therefore, girl 1 day’s work = 1/24 – 1/36 = 3 – 2 /72 = 1/72   Therefore, the girl alone will finish the work in 72 days.   daysnswer: Option days
Answer: A
The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 48 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons?	Select the correct option
A) 55	B) 56	C) 57	D) 58	E) 59

Solution: 20x + 48 = 21(x – 5)   X=57   ANSWER:57
Answer: C
There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of mess were increased by 42 per day while the average expenditure per head diminished by 1. What was the original expenditure of the mess?
Answers:
A) 400 B) 420 C) 445 D) 465 E) None of the above

Solution: Let the original average expenditure be `x.   Then,   42(x – 1) – 35x = 42 ⇔ 7x = 84 ⇒ x = 12.   ∴ Original expenditure = (35 × 12)= 420.   Answer 420
Answer: B
Mike needs 30% to pass. If he scored 212 marks and falls short by 16 marks, what was the maximum marks he could have got?
Choose the correct choice from the following answers.
A) 643 B) 677 C) 760 D) 767 E) 832

Solution: If Mike had scored 16 marks more, he could have scored 30%   Therefore, Mike required 212 + 16= 
212 + 16 = 228
228 marks   Let the maximum marks be m.   Then 30 % of m= 228   (30/100) × m = 228   m = (228 × 100)/30   m = 22800/30= 
22800/30 = 760
760   Answer:760
Answer: C
If A is thrice as fast as B and together can do a work in 24 days. In how many days A alone can do the work?	Choose the correct answer
A) 36	B) 42	C) 28	D) 32	E) 45

Solution: A’s one day’s work= 1/X   B’s one day’s work= 1/3x   A + B’s one day’s work= 1/x + 1/3x = 1/24   = 3+1/3x = 4/3x = 1/24   x = 24*4/3= 
24*4/3 = 32
32   ANSWER:32
Answer: D