MU-NLPC/Calc-aqua_rat huggingface dataset:
A train 125 m long passes a man, running at 5 kmph in the same direction in which the train is going, in 10 seconds. The speed of the train is: Select:	A) 38 km/hr	B) 40 km/hr	C) 44 km/hr	D) 50 km/hr	E) None

Solution: Sol.   Speed of the train relative to man = [125/10] m/sec = [25/2] m/sec.   = [25/2 * 18/5] km/hr = 45 km/hr.   Let the speed of the train be x kmph. Then, relative speed = (x - 5) kmph.   ∴ x - 5 = 45 or x = 50 kmph.   Answer 50 km/hr
Answer: D
In a meeting of 3 representatives from each of 6 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?	Choose the most appropriate option
A) 45  B) 135  C) 144  D) 270  E) 288

Solution: There are total 18 people from 6 companies,3 from each.Now each of them starts shaking hands one by one with other companies representative. If the companies are A,B,C,D,E,F.   Each member from company A gets to shake hands with 15 people(Total 18 minus member from his company and himself).   Then each member from company B shakes hands with 12 people because they already shook hands with company A members. Similarly company C member shakes hand with 9 members and so on.   so we have   (15*3)+(12*3)+(9*3)+(6*3)+(3*3)= 
  (15*3)+(12*3)+(9*3)+(6*3)+(3*3) = 135
135   ANS:135
Answer: B
If X and Y are digits and 3XY is a 3-digit number that is divisible by 20, which of the following is a possible product of X and Y? Choose the correct answer
A) 45 B) 40 C) 35 D) 23 E) 47

Solution: Key to this question is to remember the fact that a number divisible by 20 must X is a even, Y is a zero.   Only one answer choice meets the requirement.   Ans 40.
Answer: B
Tough and Tricky questions: Word Problems.
If Bill's salary increased by 16 percent, he would earn $812 per month. If instead, his salary were to increase by only 10 percent, how much money Y would he earn per month?  Select the correct option:
A) $700	B) $754	C) $770	D) $782	E) $893

Solution: OFFICIAL SOLUTION:   (C) If Bill’s salary increased by 16% he would earn $812. Algebraically, this can be written as:   $812 = 1.16S, where S is his current salary.   Then S = $812/1.16= 
812/1.16 = 700
$700.   Now that we know his current salary is $700, we can calculate what his salary would be if it were increased by 10%. We know that 10% of $700 is $70, so his salary would be:   Y=$700 + $70 = $770.   The correct answer is choice ($770).700 +  70= 
700 +  70 = 770
$770.   The correct answer is choice ($770).
Answer: C
A committee of 6 is chosen from 8 men and 4 women so as to contain at least 2 men and 3 women. How many different committees could be formed? Pick one:	A) 252	B) 700	C) 1404	D) 2620	E) 3510

Solution: The only cases possible are :   1. 2 men and 4 women : 8C2 * 4C4 = 28   2. 3 men and 3 women: 8C3*4C3 = 224   Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)   Total possible combinations = 28+224= 
28+224 = 252
252. Thus 252 is the correct answer.
Answer: A
In the faculty of Reverse-Engineering, 226 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 75% of the total?  Pick: A) 515. B) 545. C) 618. D) 687. E) 666.

Solution: Answer is D :687   Solution : Total number of students studying both are 423 + 226 - 134= 
423 + 226 - 134 = 515
515 (Subtracting the 134 since they were included in the both the other numbers already).   So 75% of total is 515, so 100% is approx. 687.
Answer: D
A reservoir is provided by two pipes A and B. A can fill the reservoir 5 hours faster than B. If both together fill the reservoir in 6 hours, the reservoir will be filled by A alone in	Choices:
A) 12 hours  B) 8 hours  C) 10 hours  D) 11 hours  E) None of these

Solution: If x is the speed then speed of A= x + 5 and B = x   Time taken by A and B will be x and x + 5 resp.   1/x + 1/x + 5 = 1/6 ; x2 – 7x - 30 = 0 x = -3 or x = 10.   Since time can’t be negative, x =10.   Answer: 10 hours
Answer: C
If x = y+3+4.5x and y = x+18, what is the value of x/y ?  Select the correct option.
A) -6/5 B) -7/20. C) 1/4. D) 5/6. E) 1.5

Solution: Given x = y+3+4.5x --> Eq 1   and y = x+18 --> Eq 2   Here we are asked to find the value of X/Y ?   If you observe eq 1 , then we can understand that if we take Y as X then we get X value very quickly   Let's take X/Y = 1/4 => 4X = Y - eq 3.   Sub this value in eq 1 => we get X = 4X + 3 + 4.5 X   => - 7.5X = 3   => X = -2/5 --> Sub X in eq 3 to get Y, we get Y as -8/5.   X/Y = -2/5 / -8/5 => 1/4. we get the same value again.   Answer:option 1/4. is correct answer
Answer: C
When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 83.2 , what is the value of n?	Choose the most appropriate option:
A) 9
B) 20
C) 55
D) 70
E) 81

Solution: Here's an approach that's based on Number Properties and a bit ofbrute forcemath:   We're told that K and N are both INTEGERS.   Since K/N = 81.2, we can say that K = 81.2(N)   N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.   With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)   Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH   Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.   Final Answer:   81
Answer: E
Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets R did Irwin score? Choose the correct choice from the following choices
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: First thing I noticed was that all these numbers are prime...   Prime factorization gives the following   Step 1:2*1210   Step 2:2*11*110   Step 4:2*11*11*10   Step 5:2*11*11*2*5   So he scored R=2 11-point baskets in my opinion.   Answer 2
Answer: C
The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?	Choose the correct answer.
A) 5	B) 4	C) 7	D) 9	E) 1

Solution: P(1 + 20/100)n > 2P or (6/5)n > 2   Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So,   n = 4 years.   Answer: 4
Answer: B
A die is thrown. If G is the event 'the number appearing is a multiple of 3' and H be the event
'the number appearing is even' then find whether G and H are independent ?
Choose one.
A) G and H are not independent events.  B) G and H are independent events.  C) Only G independent event  D) Only H independent event  E) None

Solution: We know that the sample space is S = {1, 2, 3, 4, 5, 6}   Now G = { 3, 6}, F = { 2, 4, 6} and E n F = {6}   Then P(G) = 2/6 = 1/3   P(H) = 3/6 = 1/2 and P(G ∩ H) = 1/6   P(G n H) = P(G). P (H)   G and H are independent events.   G and H are independent events.
Answer: B
A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 4 hours longer than the first half, how many hours did it take the runner to run the second half?  Choose one.
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2.   The time T2 to run the second half must be twice the time T1 to run the first half.   T2 = 2*T1 = T1+4   T1 = 4 and so T2 = 8.   The answer is 8.
Answer: C
Divide Rs. 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is?  Options
A) 227  B) 299  C) 266  D) 828  E) 291

Solution: Let the parts be x, y and [2379 - (x + y)]   x + (x * 2 * 5/100) = y + (y * 3 * 5/100) = z + (z * 4 * 5/100)   11x/10 = 23y/20 = 6z/5 = k   x = 10k/11, y = 20k/23, z = 5k/6   But x + y + z = 2379   10k/11 + 20k/23 + 5k/6 = 2379   k = (2379 * 11 * 23 * 6)/3965 = (3 * 11 * 23 * 6)/5   x = [10/11 * (3 * 11 * 23 * 6)/5= 
10/11 * (3 * 11 * 23 * 6)/5 = 828
828   Hence, the first part is Rs. 828.   Answer: 828
Answer: D
A person covered one-fourth of the total distance at 18 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?  Choose the correct choice from the following options
A) 21 (1/18)
B) 21 (1/13)
C) 21 (8/13)
D) 22 (2/13)
E) 21 (4/13)

Solution: Let the total distance be x km   total time taken = (x/4)/18 + (3x/4)/24 = 13x/288   Average speed = x/(13x/288) = 22 (2/13)kmph.   Answer: 22 (2/13)
Answer: D
Which of the following equations represents a line that is perpendicular to the line described by the equation 3x + 4y = 12?	Choose the correct choice from the following options:
A) 5x + 4y = 7	B) 3x – 4y = 25	C) 4y – 3x = 2	D) 1.5y + 2x = 11	E) 8x – 6y = 12

Solution: Perpendicular lines have slopes which are negative reciprocals of each other.   The line 3x + 4y = 12 in slope-intercept form is y = -(3/4)x + 3   The slope of this line is - 3/4.   The slope of a perpendicular line is 4/3.   8x - 6y = 12 in slope-intercept form is y = (4/3)x - 2   The answer is 8x – 6y = 12.
Answer: E
The average of 10 consecutive odd numbers is 22. What is the sum of the first 3 numbers?
Choose the correct choice from the following:
A) 13  B) 45  C) 17  D) 220  E) 90

Solution: 22 = (n + n+2 + n + 4 + ... + (n + 18))/10   22 = (10n + (2 + 4 + ... + 18))/10   220 = 10n + 2(1 + 2 + ... + 9)   220 = 10n + 2(9)(10)/2   220 = 10n + 90   220 - 90 = 10n   130 = 10n   n = 13   So the first three numbers are 13, 15, 17   13 + 15 + 17= 
13 + 15 + 17 = 45
45   Option 45
Answer: B
How many three digit numbers Q are divisible by 78 or 91?
Choices:  A) 17  B) 19  C) 20  D) 21  E) 22

Solution: The answer will be 19.   Explanation:   78= 2*3*13 now multiples of 78, 156 ....780, now   1000-780= 
  1000-780 = 220
220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are   9+2= 
  9+2 = 11
11   91= 13*7--Total number of three digit multiples --9   No remember we have a common multiples as well-- 13*7*6=91*6= 
91*6 = 546
546   So total number of multiples Q  --11+9 -1= 
 --11+9 -1 = 19
19.   Hence Answer is 19.19
Answer: B
How many positive integers less than 5,000 are evenly divisible by neither 17 nor 21?
Choose the correct choice from the following answers.
A) 4,514
B) 4,480
C) 4,521
D) 4,428
E) 4,349

Solution: integers less than 5000 divisible by 17 5000/17 =333.something , so 333   integers less than 5000 divisible by 21 5000/21 = 238.## , so 238   we have double counted some, so take LCM of 17 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 17 and 21 = 333 +238 -47= 
333 +238 -47 = 524
524   now subtract that from 4999. 4999- 524= 4480 answer 4,480.
Answer: B
A trade analyst announced 8% reduction in the unit price of bike. As a result, the sales volume went up by 20%. What was the net effect on the sales revenue?	Choose the correct option:
A) no change	B) decreases by 10.4%	C) increases by 10.4%	D) increases by 10%	E) None of these

Solution: Explanation :   Reduction of price = (100 -8)= 
(100 -8) = 92
92%= 0.92   Increase of sale = (100+20)= 
(100+20) = 120
120%= 1.20   Total effect = 0.92 X 1.20 = 110.4%, Increases by 10.4%   Answer : increases by 10.4%
Answer: C
What least number should be added to 1057, so that the sum is completely divisible by 23 Choose the correct choice from the following answers.
A) A)4	B) B)1	C) C)2	D) D)3	E) E)5

Solution: Explanation:   (1057 / 23) gives remainder 22   22 + 1= 
22 + 1 = 23
23, So we need to add 1   Answer: Option 1
Answer: B
If 3 taps are opened together a tank is filled in 3 hrs. One of the taps alone can fill it in 10 hrs. and another in 15 hrs. In how many hours will the third tap fill it ?
Select the correct option:
A) 7 hrs. B) 4 hrs. C) 5 hrs. D) 6 hrs. E) 8 hrs.

Solution: Part filled by three taps together in 1 hr =1/3 Part filled by one of the tap in 1 hr =1/10 Part filled by another tap in 1 hr =1/15 Part filled by third tap in 1 hr =1/3-(1/0+1/15) =5/30 Therefore the third tap can fill the whole tank in : 30/5 hrs. =6 hrs. Answer : 6 hrs.
Answer: D
In the middle of a round pool lies a beautiful water lily. The water lily doubles in size every day. After exactly 20 days, the lily will cover the complete pool. After how many days will the water lily cover half of the pool?
Choose the correct choice from the following:
A) 16 B) 18 C) 19 D) 10 E) 20

Solution: C   Because the water lily doubles its size every day and the complete pool is covered after 20 days, half of the pool will be covered one day before that, after 19 days.   19onclusion: after 19 days, the water lily will cover half of the pool.
Answer: C
There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of sections A is 40 kg and that of section b is 35 kg. Find the average weight of the whole class?
Choose the most appropriate option.
A) 36.25	B) 37.25	C) 38.25	D) 17.25	E) 27.25

Solution: 36*40= 
36*40 = 1_440
1440   44*35= 
44*35 = 1_540
1540   1440+1540= 
1440+1540 = 2_980
2980   2980/(36+44)= 
2980/(36+44) = 149/4 = around 37.25
37.25   ANSWER:37.25
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train?	Choose the correct choice from the following choices.
A) 150 meter
B) 876 meter
C) 200 meter
D) 719 meter
E) 169 meter

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 12= 
  (50/3) * 12 = 200
200 meter   Answer: 200 meter
Answer: C
If both m and n are negative integers, which of the following must be positive?
Select
A) m/n-1  B) m(n+1)  C) mn-5  D) m^2+n^2-1  E) mn+3n

Solution: Given m and n are negative integers.   Now take m = -1 and n = -1. sub these values in options..   A) m/n-1 = -1/-1 - 1= 
-1/-1 - 1 = 0
0.   B. m(n+1)= 0   C. mn-5 = -4   D. m^2+n^2-1 = 1   E. mn+3n = -4   If we take any negative value , say m = -1 or n = -2 etc..only D satisfies...   ANSWER:m^2+n^2-1
Answer: D
If a/x = 1/5 and a/y =1/ 4, then (x + y) =
Choose the most appropriate option.
A) A)2a  B) B)a/2  C) C)6a  D) D)7a  E) E)9a

Solution: Ratio 1:   5a = x   Ratio 2:   4a = y   x+y = 9a   Answer is 9a
Answer: E
Which fraction should be added to:
1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ....... + 1/(27 Ã— 28)
so that the result is equal to 1?  Choices:
A) 11/28
B) 13/28
C) 15/28
D) 17/28
E) 19/28

Solution: The given expression   = 1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ...... + 1/(27 Ã— 28)   = (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + .......... + (1/27 - 1/28)   = 1/2 - 1/28 = 13/28   Thus, the fraction we should add = 1 - 13/28 = 15/28   The answer is 15/28.
Answer: C
A part of certain sum of money is invested at 10% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? Choose the most appropriate option.
A) 4:2 B) 4:8 C) 4:3 D) 4:0 E) 6:5

Solution: 12:10   = 6:5   Answer: 6:5
Answer: E
A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
Choose the correct answer:  A) 3.75 days  B) 3.99 days  C) 2.99 days  D) 2.98 days  E) 2.44 days

Solution: 1/6 + 1/10 = 8/30 = 4/15   15/4= 
15/4 = 15/4 = around 3.75
3.75 days   3.75 daysnswer: 3.75 days
Answer: A
A college has classes from 10:00 AM until 1:50 PM. In this duration, there are five periods. If 5 minutes are provided between each period to leave one class and enter the next class, how many minutes long is each period?
Choose one:  A) 38 min  B) 41 min  C) 40 min  D) 42 min  E) 52 min

Solution: The total time is 230 minutes.   There are four breaks of five minutes between the classes for a total of 20 minutes.   The total class time is 210 minutes.   210 / 5= 
210 / 5 = 42
42 minutes per class   The answer is 42 min.
Answer: D
The current birth rate per thousand is 42, whereas corresponding death rate is 15 per thousand. The net growth rate in terms of population increase in percent is given by Pick
A) .027%
B) 27%
C) 2.7%
D) .0027%
E) none

Solution: Sol.   Net growth on 1000 = (42 - 15)= 
(42 - 15) = 27
27.   Net growth on 100= (27/1000 Ã— 100)% = 2.7%.   Answer 2.7%
Answer: C
The sum of two numbers is 77. Five times one number is equal to 6 times the other. The bigger of the two numbers is	Choose the correct choice from the following choices:
A) 10
B) 42
C) 14
D) 15
E) 60

Solution: a:b 5:6   a+b=77   5x+6x=77   x=7   then two numbers are 35,42. The bigger number is 42   ANSWER:42
Answer: B
In a ratio, which is equal to 3 : 4, if the antecedent is 12, then the consequent is
Pick.
A) 6 B) 9 C) 16 D) 10 E) 12

Solution: Sol.   We have 3/4 = 12/x ⇔ 3x = 48 ⇔ x = 16.   ∴ Consequent = 16.   Answer 16
Answer: C
On dividing 127 by a number, the quotient is 5 and the remainder is 2. Find the divisor.	Choices:
A) 25 B) 30 C) 35 D) 40 E) 45

Solution: d = (D-R)/Q   = (127 - 2)/5   = 125/5= 
125/5 = 25
25   25
Answer: A
Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Select the correct option
A) 4556  B) 2354  C) 4576  D) 6768  E) 5184

Solution: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184   432 12 x 62   5184
Answer: E
Consider a Number 3.1n7
n represent the hundredths digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?	Choose the correct choice: A) 1 B) 5 C) 4 D) 3 E) 2

Solution: In this ques we are given the thousandth digit as 6, so the hundreth digit can take any value from 0-9. For the hundreth digit i considered 2 set of values (i) 0, 1, 2, 3 and (ii) 4, 5, 6, 7, 8, 9. Given that the thousandth digit is 6, the hundreth digit has to go up by 1, and correspondingly, the tenth digit should increase by one.i.e 0-9.say 2.   2
Answer: E
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?	Choose the correct option
A) 190	B) 399	C) 372	D) 389	E) 281

Solution: Time taken by B run 1000 meters = (1000 * 10)/50= 
(1000 * 10)/50 = 200
200 sec.   Time taken by A= 200 - 10= 
200 - 10 = 190
190 sec.   Answer: 399
Answer: B
If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can do the same work?	Choose the correct option:
A) 42 days  B) 22 days  C) 32 days  D) 82 days  E) 72 days

Solution: C   32 days   Given that 5 women is equal to 8 girls to complete a work.   So, 10 women = 16 girls.   Therefore 10 women + 5 girls = 16 girls + 5 girls = 21 girls.   8 girls can do a work in 84 days then 21 girls can do a work in (8*84/21)= 
(8*84/21) = 32
32 days.   Therefore 10 women and 5 girls can a work in 32 days
Answer: C
Which of the following values is the greatest
Select the correct option.
A) a) 30% of 89	B) b) 22% of 78	C) c) 33% of 67	D) d) 44% of 56	E) e) 55% of 45

Solution: a) 30% of 89re you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says a) 30% of 89
Answer: A
How long will a boy take to run round a square field of side 55 meters, if he runs at the rate of 9km/hr?	Choose the correct option:
A) 88sec  B) 45sec  C) 1min  D) 32sec  E) 25sec

Solution: Speed = 9 km/hr = 9*5/18 = 5/2 m/sec   Distance = 55*4= 
55*4 = 220
220m   Time taken= 220*2/5= 
220*2/5 = 88
88sec   88secnswer is 88sec
Answer: A
What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years ? Choose the correct choice from the following answers.
A) 1 : 3	B) 1 : 4	C) 2 : 3	D) Data inadequate	E) None of these

Solution: Solution   22.20   Let the principal be P and rate of interest be R%.   ∴ Required ratio =[(pxRx6/100) / (pxRx9/100)]=6PR/9PR   =6/9=2 : 3 .   Answer 2 : 3
Answer: C
The proportion of copper and zinc in the brass is 13:7. How much zinc will there be in 100 kg of brass?  Select:
A) 65 kg	B) 35 kg	C) 88 kg	D) 66 kg	E) 44 kg

Solution: 7/20 * 100= 
7/20 * 100 = 35
35   Answer:35 kg
Answer: B
If a: b = 3:4, b:c = 7:9, c:d = 5:7, find a:d? Choose the correct choice from the following choices
A) 5:12	B) 7:12	C) 3:11	D) 5:11	E) 7:11

Solution: Explanation:   a/d = (3/4)*(7/9)*(5/7) => 5/12   5:12NSWER IS 5:12
Answer: A
A cistern 7 m long and 5 m wide contains water up to a breadth of 1 m 40 cm. Find the total area of the wet surface.
Choose the correct choice from the following options:
A) 69 m sqaure  B) 49 m sqaure  C) 52 m sqaure  D) 64 m sqaure  E) None of these

Solution: Explanation:   69 m sqaurerea of the wet surface =   2[lb+bh+hl] - lb = 2 [bh+hl] + lb   = 2[(5*1.40+7*1.40)]+7*5 = 69 m square   Option 69 m sqaure
Answer: A
Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 40kmph and Prasanna moves southward at a speed of 38 kmph. How far will be Prasanna from Laxmi after 60 minutes ?
Choose the most appropriate option: A) 11 B) 50 C) 78 D) 27 E) 18

Solution: Explanation:   We know 60 min = 1 hr   Total northward Laxmi's distance = 40kmph x 1hr = 40 km   Total southward Prasanna's distance = 38kmph x 1hr = 38 km   Total distance between Prasanna and Laxmi is = 40 + 38= 
40 + 38 = 78
78 km.   Answer: 78
Answer: C
A rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is:
Answers
A) 5m	B) 12m	C) 13m	D) 14.5m	E) 15.5m

Solution: Let, length= x meters and breadth= y meters   Then xy=60 and (x2+y2) + x= 5   Therefore, x=60 and (x2+y2)= (5y-x)2   Or xy=60 and 24y2-10xy=0.   Therefore, 24y2-10*60=0 or y2= 25 or =5.   Therefore, x= (60/5)= 
(60/5) = 12
12m. So, length of the carpet= 12m   ANSWER:12m
Answer: B
In a survey of 335 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured? Choices.
A) 38/67
B) 8/41
C) 9/348
D) 1/8
E) 41/91

Solution: ---------UI----------------NUI-------Total   PT ----(12.5/100)*104= 
 ----(12.5/100)*104 = 13
13----------- --54   NPT---104-13-------------- x--------281   Total--104----------------------------335   we have to find not part time and not uninsured . in other words not part time and insured= x/335 = (281-104+13)/335   = 38/67   38/67nswer is 38/67.
Answer: A
What is the next number in the sequence : 12,15,21,24,30,33,39,51 __?	Pick:
A) 59	B) 53	C) 57	D) 52	E) 51

Solution: next no. = previous + (sum of digits)   12 + (1+2)= 
12 + (1+2) = 15
15   15 + (1+5)= 
15 + (1+5) = 21
21   21 + (2+1)= 
21 + (2+1) = 24
24   24 + (2+4)= 
24 + (2+4) = 30
30   30 + (3+0)= 
30 + (3+0) = 33
33   33 + (3+3)= 
33 + (3+3) = 39
39   39 +(3+9)= 
39 +(3+9) = 51
51   51 + (5+1)= 
51 + (5+1) = 57
57   ANSWER:57
Answer: C
To get the more profit, which is the best transaction?  Choose the correct choice from the following answers
A) C.P. = Rs. 18, profit = Rs. 9  B) C.P. = Rs. 25, profit = Rs. 12  C) C.P.= Rs. 20, profit = Rs. 8  D) C.P.= Rs. 30, profit = Rs. 18  E) None of these

Solution: Explanation :   Solution: (A) Profit% = (9*100/18)= 
(9*100/18) = 50
50%.   (B) profit%= (12*100/25)= 
(12*100/25) = 48
48%.   (C)profit%= (8*100/20)= 
(8*100/20) = 40
40%.   (D) profit%= (18*100/30)= 
(18*100/30) = 60
60%.   From the above results clearly, (D) is the best transaction.   Answer : C.P.= Rs. 30, profit = Rs. 18
Answer: D
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:	Select
A) 2700	B) 2900	C) 3000	D) 3100	E) 3500

Solution: Number of valid votes = 80% of 7500 = 6000.   Valid votes polled by other candidate = 45% of 6000   = 45 divided by 100x6000 =2700   2700nswer: Option 2700
Answer: A