MU-NLPC/Calc-aqua_rat huggingface dataset:
An outlet pipe can empty 2/3 rd of a cistern in 20 minutes. In 8 minutes, what part of the cistern will be emptied?	Choose one.
A) 4/9  B) 4/3  C) 4/2  D) 4/8  E) 4/15

Solution: 2/3 ---- 20   ? ----- 8 ==> 4/15   Answer: 4/15
Answer: E
On Children’s Day, sweets were to be equally distributed among 175 children in a school. Actually on the Children’s Day 35 children were absent and therefore, each child got 4 sweets extra. How many sweets were available in all for distribution?  Choose the correct answer:
A) 2480 B) 2680 C) 2750 D) 2400 E) None of these

Solution: Let the original number of sweets be x.   According to the question,   x⁄140 - x⁄175 = 4   or, 175x – 140x = 4 × 140 × 175   or, x = 4×140×175/35=2800   Answer None of these
Answer: E
A fellow borrowed a certain sum of money at 5% per annum at simple interest and in 5 years the interest amounted to Rs.2250 less than the sum lent. What was the sum lent?	Choose the correct option
A) 1050 B) 1220 C) 1250 D) 1060 E) 3000

Solution: P - 2250 = (P*5*5)/100   P = 3000   Answer: 3000
Answer: E
A man can row downstream at 18 kmph and upstream at 6 kmph. Find the speed of the man in still water and the speed of stream respectively? Choices
A) 3	B) 5	C) 6	D) 4	E) 9

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 18 --- (1)   and x - y = 6 --- (2)   From (1) & (2) 2x = 24 => x = 12, y = 6. Answer: 6
Answer: C
Factor | Percent of Respondents |
User-friendly | 56% |
Fast response time | 48% |
Bargain prices | 42% |
The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,500 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?” Choose the correct choice from the following options
A) 312  B) 336  C) 360  D) 390  E) 420

Solution: The way I looked at is is as follows:   UserFriendly(UF) + FastResponse (FR) = 30%   UF leftover = 56 - 30= 
56 - 30 = 26
26%   FR leftover= 48 - 30= 
48 - 30 = 18
18%   Sum these= 74% (ie. 74% were either UF+FR, UF, FR)   26% leftover is the maximum number for Bargain Price   26/100 * 1500 = 26 * 15= 
26 * 15 = 390
390 (390).
Answer: D
Can you find the missing number in the sequence given below?
11 18 25 12 19 ? 13 20 27 14 21 28
Choices:
A) 20 B) 21 C) 22 D) 23 E) 26

Solution: Solution:   26   Explanation :   The sequence is given in the puzzle is :   11 18 25 12 19 ? 13 20 27 14 21 28   Let's break the given series as below:   11 18 25   12 19 ?   13 20 27   14 21 28   Now read the number from left hand side from top to bottom as :   So the number that will replace '?' is 26.   Answer 26
Answer: E
The average price of an decoration piece increases over the years. If from 1990 to 1996, the price of the decoration piece increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the decoration piece in 2001 if the price in 1990 was $11,500? Choose one:
A) $15,594.	B) $15,322.	C) $14,786.	D) $14,543.	E) $12,988.

Solution: Whenever you have a question in which a value is increased by x% and then increased by y% then the overall effective increase = (x + y + xy/100 ) %   The effective increase = 13 + 20 + (13×20/100) = 35.6%   This is a little more 33% or 1/3 the original value.   THE QUICKEST WAY TO SOLVE THIS QUESTION IS TO USE APPROXIMATION.   11500 + 1/ 3 (12000) = 15500   Therefore option A is the answer.   I selected 12000 because it's value is a little more 11500 and it's easier to divide by 3 ( ie to calculate 1/3 or 33%).
Answer: A
In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 14 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
Answers:
A) 80%
B) 112%
C) 120%
D) 124.2%
E) 138%

Solution: x = profits   r= revenue   x/r = 0,1   x= 10   r=100   2009:   r=80   x/80 = 0,14 = 14/100   x= 80*14/100= 
80*14/100 = 56/5 = around 11.2
11.2   11.2/10= 1,12 = 112%, Answer 112%
Answer: B
3 man had collected 65 apples by visiting different tress. At tree 1 the collected some apples. At tree 2 they had 3 times the apple that they collected in tree 1. At tree 3 they had 5 times the no of apples when they reach there. At tree 4 they could collect only 5 apples. What was the no of apples they had in tree 1
Options:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: At tree 1: x   At tree 2: 3x   At tree 3: 5(3x+x)   At tree 4: 20x + 5   20x+5=65   x=3   ANSWER:3
Answer: C
What is the dividend from Tony's stock, if he invested Rs. 3200 at 85 to obtain an income of Rs. 250.
Choose the correct choice:	A) 4	B) 7.6	C) 6.6	D) 7.6	E) 9.6

Solution: By investing Rs.3200, income = Rs.250   By investing Rs.85, income = 250Ã—85/3200=6.6   ie, dividend = 6.6%   Answer is 6.6.
Answer: C
There is a road beside a river.two friends started from a place A,moved to a temple situated at another place B and then returned to A again.one of them moves on a cycle at a speed of 12 km/hr,while the other sails on a boat at a speed of 10 km/hr.if the river flows at the speed of 4 km/hr,which of the two friends will return to placeA first?	Choose the correct choice from the following:
A) cyclist and boat sailor
B) boat sailor
C) none
D) cyclist
E) cyclist and boat sailor both are reached at the same time

Solution: Clearly the cyclist moves both ways at a speed of 12 km/hr.   The boat sailor moves downstream @ (10+4)i.e.,14 km/hr and upstream @ (10-4)i.e., 6km/hr.   So,average speed of the boat sailor=(2*14*6/14+6)km/hr   =42/5 km/hr=8.4 km/hr.   since the average speed of the cyclist is greater ,he will return ta A first.   Answer is cyclist.
Answer: D
What is the difference between the largest number and the least number written with the digits 7, 3, 1, 4?  Choose the correct choice from the following choices
A) 6084
B) 3788
C) 2077
D) 2721
E) 1812

Solution: Explanation:   1347   7431   ------------   6084   6084nswer:6084
Answer: A
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? Answers:
A) 5040
B) 40
C) 400
D) 5000
E) 6000

Solution: LOG5040RITHM => 10 diff letters   req no of words = No of arrangements of 10 letters taking 4 at a time   => 10P4 = (10*9*8*7)   ==> 5040   5040NSWER 5040
Answer: A
Bexy walks 5 miles from point A to point B in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Bexy’s average speed. How many minutes does Ben spend on his round trip?	Choose the correct choice from the following answers.
A) 40	B) 80	C) 120	D) 160	E) 180

Solution: Bexy walks 5 miles from point A to point B in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Bexy’s average speed. How many minutes does Ben spend on his round trip?   Average speed = total distance/total time   We know the total distance is 5+5 (going from A to B then from B to A)   Time = distance/speed   Time = 5/15   Time = 1/3 hour   Average speed = (10)/(1hr + 1/3hr)   Average speed (Bexi) = 10 / 1.33   Therefore, if Ben's average speed is 1/2 of Bexi's then his speed = 10/2.66.   This means it took him 2.66 hours to cover the same 10 miles Bexi did. 2.66 hours = roughly 160 minutes.   Answer: D). 160
Answer: D
Selling an kite for Rs. 30, a shop keeper gains 35%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is? Choose the correct option
A) 8%
B) 10%
C) 11%
D) 15%
E) 21.5%

Solution: Explanation:   Marked price = Rs. 30   C.P. = 100/135 * 30 = Rs. 22.22   Sale price = 90% of Rs. 30 = Rs. 27   Required gain % = 4.77/22.22 * 100 =21.5%.   Answer: 21.5%
Answer: E
The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y? Options: A) 2010 B) 2001 C) 2012 D) 2011 E) 2009

Solution: Suppose commodity X will cost 40 paise more than Y after z years.   Then, (4.20 + 0.40z) - (6.30 + 0.15z) = 0.40   0.25z = 0.40 + 2.10= 
0.40 + 2.10 = 2.5
2.50/0.25= 250/25= 
250/25 = 10
10.   Therefore, X will cost 40 paise more than Y 10 years after 2001 i.e., 2011.   Answer is 2011.
Answer: D
A certain school implemented a reading program for its students, with the goal of getting each student to read 4 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year?
Choose the correct choice from the following
A) 20cs
B) cs/2
C) 48cs
D) (2cs)/12
E) (24c)/s

Solution: Ans: 48cs   Solution: simple multiplication s students , c classes , 4 books/ month= 48 books a year   total number of books = 48cs
Answer: C
Solve the equation: -3(-x + 5) + 20 = -10(x - 3) + 4
x=? Choose the most appropriate option:
A) 28/12  B) 12/28  C) 13/29  D) 29/13  E) 10/22

Solution: Expand the expressions with brackets in the given equation   3x - 15 + 20 = -10x + 30 + 4   Group like terms   3x + 5 = -10x + 34   Solve   13 x = 29 , x = 29 / 13   correct answer 29/13)29/13
Answer: D
Avinash covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time? Pick one:	A) 15 Kmph	B) 17 Kmph	C) 18 Kmph	D) 19 Kmph	E) 20 Kmph

Solution: Total distance = 8 Km   Total time = 50 Km   Time taken to cover the distence of 3 Km = 50*2/5= 
50*2/5 = 20
20 min= 1/3 hours   Remaining distance = 8 - 3= 
8 - 3 = 5
5 Km   Required speed= 5/1/3 = 15 Kmph   15 Kmph)
Answer: A
What is the perimeter, in meters, of a rectangular garden 4 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide?	Choose the correct choice:  A) 48  B) 56  C) 60  D) 76  E) 104

Solution: Say Length of garden is L meters.   Then (L*4) = 16 * 12 [Given area is same. Area= L * B]   Therefore L works out to 48 meters.   Perimeter of Garden = 2* (48+4)= 
2* (48+4) = 104
104 meter.   Answer is 104
Answer: E
if set a ={2,3,5,7} and two numbers are selected at random from A(duplicates allowed), then what is the probability that the sum of the numbers is even?  Choose the correct option:  A) 1/8  B) 13/16  C) 5/12  D) 5/8  E) 2/3

Solution: Sum of the two numbers would be even if   (1) Both digits are even.   (2) Both digit are odd.   (1) only one case is there: 22   (2) Following cases are there: 33, 35, 37 - 3 nos. Similarly 3 nos, with 5 (53, 55, 57) and 3 nos. with 7 (73, 75, 77)   Total 10 nos.   Total nos. that can be formed (repetition is allowed)   {1st no. can be chosen in 4 ways. Similarly 2nd no. can be chosen in 4 ways. Total  4*4= 
 4*4 = 16
16 ways}   Prob : 10/16= 5/8   5/8 is the answer.
Answer: D
3 Years ago, the average age of a family of 5 members was 21 years. A baby having been born, the average age of the family is the same today. The present age of the baby is  Choose the correct choice from the following choices:
A) 1 year.
B) 1.5 Years.
C) 2 Years.
D) 3 Years.
E) 6 Years.

Solution: We're told that 3 YEARS AGO, the average age of a family of 5 members was 21 years.   This means that the SUM of their ages was (5)(21) = 105 years.   A baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME.   This means that the sum of the ages is (6)(17) = 102 years.   We're asked for the PRESENT age of the baby.   Since each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is...   105 + (5)(3) = 120.   126-120= 
126-120 = 6
6   6 Years.
Answer: E
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? Pick:
A) 1000	B) 2876	C) 1977	D) 2778	E) 2711

Solution: 90%   104%   --------   14% ---- 140   100% ---- ? => Rs.1000   1000nswer: 1000
Answer: A
C & D started one company. They invest Rs. 100,000/- each. They deposit the money to Bank. Bank give 1% interest per month. After 2 years D left from company and asked C to return the money with interest. C says it will take time to release the FD and he assure D to give the money withinterest @0.5%. D Agreed this. What is the profit of C ? Choose the correct choice from the following options:  A) A)48000  B) B)12000  C) C)3600  D) D)24000  E) E)30000

Solution: Total Investment : 10000/-*2=20000/-   Interest rate @ 1%= 20000*1%*12*2= 4800/-   Total : 248000/-   Interest to B : 10000/-*0.5%*12*2 = 1200/-   Paid to B : 10000/- + 1200/- = 11200/-   profit of A : 3600/-   Answer is 3600
Answer: C
Henry answered 4/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework?  Choose the correct option:	A) x	B) (85/12)*x	C) (85/24)*x	D) (85/36)*x	E) (85/48)*x

Solution: Let Q be the number of homework questions.   Q = 4Q/5 + (5/17)(Q/5) + x   Q = 68Q/85 + 5Q/85 + x   12Q/85 = x   Q = (85/12)*x   The answer is (85/12)*x.
Answer: B
All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?	Pick one.
A) 1884 liters  B) 1180 liters  C) 1984 liters  D) 1184 liters  E) 1194 liters

Solution: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.   Quantity of water in B = 8k - 5k = 3k.   Quantity of water in container C 8  - 5= 
8  - 5 = 3
3k.   Quantity of water in container C= 8k - 3k = 5k   Container: A B C   Quantity of water: 8k 3k 5k   It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.   5k - 148 8  - 3= 
8  - 3 = 5
5k   Container: A B C   Quantity of water: 8k 3k 5k   It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.   5k - 148= 3k + 148 => 2k = 296 => k = 148   The initial quantity of water in A = 8k = 8 * 148= 
8 * 148 = 1_184
1184 liters.   Answer:1184 liters
Answer: D
Students of three different classes appeared in common examination. Pass average of 10 students of first class was 70%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes? Select the correct option
A) 74% B) 75% C) 69% D) 72% E) None

Solution: Solution:   Sum of pass students of first, second and third class,   = (70% of 10) + (60% of 15)+ (80% of 25)   = 7+9+20= 
7+9+20 = 36
36   Total students appeared,= 10+15+25= 
10+15+25 = 50
50   Pass average,= 36*100/50= 
36*100/50 = 72
72%.   Answer: Option 72%
Answer: D
In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 10 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?	Select the correct option
A) 30  B) 45  C) 62  D) 90  E) 120

Solution: I believe there is a better way to do it.   Basically one of the options should satisfy the given criteria.   60 did    1/5 *60= 
 1/5 *60 = 12
12   2/3*60= 
2/3*60 = 40
40   so total distance   52 + remaining 10=62   Answer 62
Answer: C
In Set T, the average (arithmetic mean) equals the median Q. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above. Options
A) I only
B) I and II
C) II and III
D) I, II, and III
E) IV only

Solution: This is a very good 'trap question'.   Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR   Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3   If you think that only in 'consecutive integers' the average is equal to the median Q you might fall for 'D'.   Ans: IV only
Answer: E
The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ?
Choose the correct choice.
A) 6 years
B) 7 years
C) 8 years
D) 9 years
E) None

Solution: Answer   Let the age of youngest child be y.   so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12   ⇒ 4y + 24= 48   ∴ y = 6 years   Correct Option: 6 years
Answer: A
Sum of the squares of three numbers is 267 and the sum of their products taken two at a time is 131. Find the sum?  Pick one.
A) 20	B) 25	C) 26	D) 23	E) 29

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 267 + 2* 131   a + b + c = √529 = 23   23
Answer: D
A man can row his boat with the stream at 16 km/h and against the stream in 6 km/h. The man's rate is?
Choose the correct option.
A) 5 kmph  B) 6 kmph  C) 7 kmph  D) 4 kmph  E) 9 kmph

Solution: Explanation:   DS = 16   US = 6   S = ?   S = (16 - 6)/2= 
(16 - 6)/2 = 5
5 kmph   5 kmphnswer: 5 kmph
Answer: A
In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 70 as quotient. What is the correct quotient ? Answers.
A) 0	B) 12	C) 13	D) 40	E) 25

Solution: 12*70= 
12*70 = 840
840   840%21=40   ANSWER:40
Answer: D
The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with (m + 2)?	Select the correct option.
A) m + 4
B) n + 6
C) n + 3
D) m + 5
E) n + 4

Solution: Explanatory Answer   Approach: Work with a numerical example   The fastest way to solve problems of this kind is to take numerical examples.   Let the 5 consecutive integers be 1, 2, 3, 4, and 5.   The average of 5 consecutive integers from 1 to 5 is 3.   Therefore, the value of m is 1 and the value of n is 3.   9 consecutive integers starting from m + 2 will be 3, 4, ... , 11   The average of positive integers from 3 to 11 is 7.   We know n = 3. So, 7 has to be (n + 4)   Choice n + 4 is the correct answer.
Answer: E
Two buses each 3125 m long are running in opposite directions on parallel roads. Their speeds are 40 km/hr and 35 km/hr respectively. Find the time taken by the slower bus to pass the driver of the faster one?  Select.
A) 50 sec  B) 66 sec  C) 48 sec  D) 55 sec  E) 45 sec

Solution: Relative speed = 40 + 35= 
40 + 35 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 3125+3125= 
3125+3125 = 6_250
6250 m.   Required time= 6250 * 6/125 = 50 sec.   50 secnswer: 50 sec
Answer: A
From the integer n, if n*n*n is odd, then what is true from below options?	Choose the correct answer:
A) n is odd
B) n is odd and n*n is even
C) n is even
D) n*n is even
E) n*n odd

Solution: n is odd and n*n is even   Option n is odd and n*n is even
Answer: B
Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?	Select:	A) 5/16	B) 5/12	C) 5/19	D) 5/17	E) 5/15

Solution: Using question number 11 and 12, we get the probability as   1 - (1/36 + 5/9) = 5/12   Answer: 5/12
Answer: B
Find the HCF of 2.1, 1.05 and 0.63
Choose one:  A) 0.44  B) 0.64  C) 0.21  D) 0.24  E) None of above

Solution: Explanation:   To solve this question quickly, first remove decimal by multiplying each term with 100,   Then terms become 210, 105, 63   Then H0.21F of above terms is 21,   So Answer is 0.21   Answer: Option 0.21
Answer: C
There are 4 red shoes & 6 green shoes . If two of red shoes are drawn what is the probability of getting red shoes	Select the correct option.
A) 1/13  B) 1/14  C) 1/2  D) 2/15  E) 2/16

Solution: taking 4 red shoe the probablity is 4C2   from 10 shoes probablity of taking 2 red shoe is 4C2/10C2=2/15   ANSWER:2/15
Answer: D
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 41 kg, then the weight of B is:
Choose the correct choice from the following options
A) 27 kg B) 20 kg C) 26 kg D) 31 kg E) 35 kg

Solution: let d sum of a, b, c is 3*45= 
3*45 = 135
135   and sum of a and b s 2*40= 
2*40 = 80
80   sum of b and c is 2*41= 
2*41 = 82
82   hence 80+82-135= 
80+82-135 = 27
27   ans=27   27 kgNSWER:27 kg
Answer: A
In the junior basketball league there are 18 teams, 2/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad  Pick.
A) 4. B) 6. C) 7. D) 10. E) 8.

Solution: total teams =18   bad teams=(2/3)*18= 
(2/3)*18 = 12
12   rich teams=9   so maximum value that the both rich and bad can take will be 9. so E= 10 can not be that value.   ans 10..
Answer: D
In a public show 75 % of the seats were filled. If there were 700 seats in the hall, how many seats were vacant? Choose the correct answer:  A) 100  B) 110  C) 120  D) 175  E) 150

Solution: 75 % of 600   = 75/100 × 700   = 450   Therefore, the number of vacant seats = 700 - 450 = 175.   Answer:175
Answer: D
The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
Choose the correct choice
A) 9  B) 11  C) 13  D) 15  E) 16

Solution: 1 to 9 = 9 * 9= 
9 * 9 = 81
81   1 to 5= 5 * 10= 
5 * 10 = 50
50   5 to 9= 5 * 8= 
5 * 8 = 40
40   5th= 50 + 40= 
50 + 40 = 90
90 – 81= 9   9)
Answer: A
Replace the ? by the correct Mathematics symbol to make the expression true
16 ? 10 ? 4 ? 5 = 45 Choose the correct option
A) 16 ÷ 10 x 4 - 5 = 45  B) 16 + 10 ÷ 4 - 5 = 45  C) 16 x 10 + 4 - 5 = 45  D) 16 x 10 ÷ 4 + 5 = 45  E) 16 x 10 ÷ 4 - 5 = 45

Solution: Answer : 16 x 10 ÷ 4 + 5 = 45
Answer: D
A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? Choose the correct option
A) 230	B) 228	C) 268	D) 279	E) 270

Solution: Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 * 5/18 = 500/9 m/sec.   Let the length of the other train be x m.   Then, (x + 270)/9 = 500/9 => x   = 230.   230nswer: 230
Answer: A
There are 5 identical pens and 8 identical books. In how many different ways can a person select at least one object from this set?	Choices:
A) 27 B) 35 C) 41 D) 47 E) 53

Solution: We can select from 0 to 5 pens and from 0 to 8 books.   Thus the total possible ways to select objects is   6*9= 
  6*9 = 54
54   We must subtract 1 for the case with 0 pens and 0 books.   The answer is 53.
Answer: E
How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board? Choose the correct choice from the following:
A) 99
B) 18
C) 26
D) 17
E) 12

Solution: 30 * 33/2 = 5/2 * 2 * x => x   = 99   99nswer: 99
Answer: A
A 11 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point?	Choose the correct choice from the following answers.
A) 5/8
B) 1/5
C) 6/11
D) 3/11
E) 2/5

Solution: A square with an area of 4 has a perimeter of 8.   For the area to be >4, the longer piece must be >8.   The wire must be cut within 3 meters from either end.   The probability of this is 6/11.   The answer is 6/11.
Answer: C
If (x + 2)^2 = 144, which of the following could be the value of 2x?	Choose the correct choice from the following:	A) –26	B) –22	C) –11	D) 12	E) 14

Solution: You can also get to the answer by backsolving using answer choices   Starting with choice C = -14   (x + 2)^2 = 144   (-14 + 2)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -14 will result in 144 in the equation so x must be -14,   Then 2x = 2 * -18 = -22   Answer: 14
Answer: E