MU-NLPC/Calc-aqua_rat huggingface dataset:
Carol, Belle and Andrew are business partners. Carol's capital is Rs.12000. If his share of a profit of Rs.1000 is Rs.380 and Andrew's share is Rs.250, what is Belle's capital? Choose the correct choice from the following choices: A) 116847.21 B) 14684.21 C) 21684.21 D) 11684.21 E) 11685.21

Solution: 380 + 250= 
380 + 250 = 630
630   1000 - 630= 
1000 - 630 = 370
370   380 ---- 12000   370 ---- ?=> 11684.21   ANSWER:11684.21
Answer: D
12x − 12 = 12y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above? Choose the correct choice from the following choices:
A) More than three B) Exactly three C) Exactly two D) Exactly one E) None

Solution: => 12x - 12y = 12   => x- y =1 -- 1   5y + 5x = 15   =>x + y = 3 -- 2   From equation 1 and 2 , we get   2x = 2   => x=1   y=1   Therefore , the given system will have Exactly one solution   Answer : Exactly one
Answer: D
On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor	Choose the correct choice:  A) 12  B) 14  C) 16  D) 18  E) 19

Solution: d = (D-R)/Q   = (109 - 1)/9   = 108/9= 
108/9 = 12
12   12)
Answer: A
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?  Options
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 6   T = 6/2= 
6/2 = 3
3 3nswer:3
Answer: A
A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?	Choose the correct choice from the following answers
A) 2/91	B) 1/81	C) 1/8	D) 2/81	E) 3/40

Solution: Total number of balls = 4 + 5 + 6= 
4 + 5 + 6 = 15
15   Let S be the sample space.   n(S)= Total number of ways of drawing 3 balls out of 15 = 15C3   Let E = Event of drawing 3 balls, all of them are yellow.   n(E) = Number of ways of drawing 3 balls, all of them are yellow   = Number of ways of drawing 3 balls from the total 5 = 5C3   (∵ there are 5 yellow balls in the total balls)   P(E) = n(E)/n(S)   =5C3/15C3=5C2/15C3 [∵ nCr = nC(n - r). So 5C3 = 5C2. 2/91pplying this for the ease of calculation]   =(5×4/2×1)/(15×14×13/3×2×1)=5×4/(15×14×13/3)=5×4/5×14×13=4/14×13=2/7×13=2/91   2/91NSWER:2/91
Answer: A
Which of the following is equal to (n – 3)2*square* if
n = 11? Choose the correct choice:
A) (n + 6)(n – 6) B) (n + 5)(n – 7) C) (n + 4)(n – 8) D) (n + 3)(n – 9) E) (n + 2)(n – 10)

Solution: If n = 11, then:   (n – 3)2 = (11 – 3)2 = 82 = 64   Substitute 11 for n into each answer until you find one that equals 64:   (n + 6)(n – 6) = (17)(5) = 85   (n + 5)(n – 7) = (16)(4) = 64 You’ve found a match   correct answer (n + 5)(n – 7))(n + 5)(n – 7)
Answer: B
Rs. 5000 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/5:1/5:1/10?	Choose one.
A) 1000	B) 992	C) 772	D) 552	E) 312

Solution: 1/5:1/5:1/10 = 2:2:1   1/5*5000= 
1/5*5000 = 1_000
1000   2000-1000= 
2000-1000 = 1_000
1000   1000nswer: 1000
Answer: A
a, b are positive integers. The remainder of a to be divided by 7 is 6 and the remainder of b to be divided by 8 is 5.
Which is possible to be the remainder of a*b to be divided by 52
Select.
A) a) 2
B) b) 6
C) c) 8
D) d) 12
E) e) 30

Solution: Two ways to do it...   a=7x+6..   b=8y+5..   1) convenient way..   Take x and y as 0, and you will get a*b as   6*5= 
  6*5 = 30
30   Answer : e) 30
Answer: E
The ratio of the ages of Maala and Kala is 4 : 3. The total of their ages is 2.8 decades. The proportion of their ages after 0.8 decades will be [1 Decade = 10 years]  Pick
A) 4:3	B) 12:11	C) 7:4	D) 6:5	E) 6:7

Solution: Explanation:   Let, Maala’s age = 4A and Kala’s age = 3A   Then 4A + 3A = 28   A = 4   Maala’s age = 16 years   and Kala’s age = 12 years   Proportion of their ages after 8 is = (16 + 8) : (12 + 8)   = 24 : 20   = 6 : 5 .. Answer: 6:5
Answer: D
It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Choose the correct choice from the following answers
A) (2 16 + 1)
B) (2 16 - 1)
C) (7 x 2 23)
D) (2 96 + 1)
E) None of these

Solution: Explanation:   Let 232 = x. Then, (232 + 1) = (x + 1).   Let (x + 1) be completely divisible by the natural number N. Then,   (296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.   ANSWER IS (2 96 + 1)
Answer: D
A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 5? Choose the correct choice from the following.
A) 2 / 3  B) 1 / 6  C) 3 / 3  D) 4 / 5  E) 2 / 4

Solution: Only 6 so, 1 / 6   correct answer 1 / 6
Answer: B
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 12 seconds. Find the length of the faster train?
Choose the correct choice from the following options.
A) 270 B) 288 C) 266 D) 120 E) 126

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 12 sec= 27 * 10= 
27 * 10 = 270
270 m.   The length of the faster train= 120 m.   Answer: 120
Answer: D
The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is Choose the correct choice from the following
A) 16 cm  B) 25 cm  C) 30 cm  D) 35 cm  E) 40 cm

Solution: Explanation:   So by now, you must be knowing this is a question of HCF, right.   H.C.F. of (700 cm, 385 cm, 1295 cm) = 35 cm.   Option 35 cm
Answer: D
What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 7? Choose the correct choice: A) 70,592 B) 64,850 C) 64,749 D) 149,700 E) 156,720

Solution: Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 7   Seeing the Options 70,592fter Dividing an Finding the Reminder of 2   My 70,592nswer was 70,592
Answer: A
A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 4 km, if the person completes half of the distance by walking and the other half by running?
Choose the correct choice from the following answers
A) 0.25 B) 0.5 C) 0.75 D) 1 E) 1.25

Solution: time = 2/4 + 2/8 = 6/8= 
6/8 = 3/4 = around 0.75
0.75 hours   The answer is 0.75.
Answer: C
A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is  Choices.
A) 1/13 B) 2/13 C) 1/26 D) 1/52 E) 1/67

Solution: Explanation:   Total number of cases = 52   Favourable cases = 2   Probability = 2/56 = 1/26   Answer: Option 1/26
Answer: C
What is the remainder when the number Q=14^2 * 15^8 is divided by 5?	Choose the most appropriate option.
A) 0	B) 1	C) 2	D) 4	E) 5

Solution: 14^2 has units digit 6   15^8 has units digit 5   Thus Q=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero   0nswer: (0)
Answer: A
In an electric circuit, three resistors with resistances 2 ohms, 5 ohms and 6 ohms are connected in parallel. In this case, if R is the combined resistance of these three resistors, then the reciprocal of R is equal to the sum of the reciprocals resistors. What is R value?
Choose the correct answer.
A) 13/15 ohms	B) 15/13 ohms	C) 5/8 ohms	D) 3/7 ohms	E) 45/18 ohms

Solution: The wording is a bit confusing, though basically we are told that 1/R = 1/2 + 1/5 + 1/6, from which it follows that R=13/15ohms   Option: 13/15 ohms
Answer: A
An amount of Rs.3120 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of A? Choose one:
A) 1320 B) 1196 C) 1210 D) 1440 E) 1050

Solution: Let the shares of A, B and C be a, b and c respectively.   a : b : c = 1/2 : 1/3 : 1/4   Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.   a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.   Share of A = 6/13 * 3120 = Rs. 1440   Answer: 1440
Answer: D
Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio Q of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
Answers:
A) 8:3	B) 3:2	C) 4:3	D) 2:3	E) 3:8

Solution: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3= 
6/3 = 2
2 hours to do that.   Now, in this case the rate of Ann would be 3+3*1/3= 
3+3*1/3 = 4
4mph and the distance she covers would be   6*2= 
  6*2 = 12
12 miles, so she needs   12/4= 
  12/4 = 3
3 hours for that.   The ratio Q of Ann's time to Bob's time is 3:2.   Answer: 3:2.
Answer: B
The sum of four consecutive even numbers is 292. What would be the smallest number?
Choose the correct choice from the following choices: A) 33 B) 88 C) 70 D) 123 E) 12

Solution: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)   Their sum = 8x - 4 = 292 => x = 37   Smallest number is: 2(x - 2) = 70.   Answer: 70
Answer: C
The sum R of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Rn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted. Choose one.
A) 4345
B) 4302
C) 4258
D) 4214
E) 4170

Solution: a method to do it under one minutes is to take advantage of the choices given...   lets work on the last digit aswe have different units digit in each choice...   total sum of 1 to 100 inclusive will have 0 as the last digit..   this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...   now for single digit in sum R of even number from 25 to 63..   25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..   here too the units digit is 0, but 64 has to be excluded from the total..   two ways from here on..   1) we are subtracting 0 from 0   so units digit should be 0, but we have to add 64..   so last/units digit =4..   2)we subtract 64 from sum of even int..   so units digit=80-4=76..   or units digit =6...   so our answer should have units digit as 10-6=4..   only D has 4 as units digit..   ans 4214
Answer: D
A batsman scored 140 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Pick.
A) 45(4/11) % B) 45 % C) 45(5/11) % D) 57(1/7) % E) None of these

Solution: Explanation :   Total runs scored = 140   Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60   Total runs scored by running between the wickets = 140 - 60= 
140 - 60 = 80
80   Required %= (80/140) × 100 = 400/7 = 57(1/7)%   Answer : Option 57(1/7) %
Answer: D
How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	Choices:
A) 288	B) 266	C) 500	D) 277	E) 211

Solution: Let length of tunnel is x meter   Distance = 800+x meter   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s   Distance = Speed*Time   800+x = (65/3) * 60   800+x = 20 * 65= 
20 * 65 = 1_300
1300   x= 1300 - 800= 
1300 - 800 = 500
500 meters.Answer:500
Answer: C
During a clearance sale, a retailer discounted the original price of its TVs by 20% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?	Choose the correct choice from the following options:
A) 40%	B) 45%	C) 55%	D) 60%	E) 64%

Solution: VERITAS PREPOFFICIAL SOLUTION:   D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 80% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 80% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 80% sale price. Using fractions, that means they pay: 4/5*(4/5) of the original price, which nets to 0.64 of the original price, or 64%.   64%
Answer: E
The speed at which a man can row a boat in still water is 9 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
Choose the correct choice from the following answers:
A) 16 seconds  B) 34 seconds  C) 14 seconds  D) 18 seconds  E) 15 seconds

Solution: Speed of the boat downstream = 9 + 3= 
9 + 3 = 12
12 kmph= 12 * 5/18 = 10/3 m/s   Hence time taken to cover 60 m = 60*3/10= 
60*3/10 = 18
18 seconds.   Answer: 18 seconds
Answer: D
If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?	Options: A) $33.95 B) $47.47 C) $28.40 D) $60.60 E) $72.85

Solution: The tip is 20% of what he paid for lunch. Hence   tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10   Total spent     50.50 + 10.10= 
  50.50 + 10.10 = 60.6
$60.60   correct answer $60.60
Answer: D
A large no. N =1234567891011121314…99899100. What will be the remainder when 1st 100 digits of N is divided by 9?  Choose the correct choice from the following answers:	A) 2	B) 3	C) 5	D) 7	E) 8

Solution: Hence the first 100 digits of N goes like this 1234567891011121314.......5253545   We need to find the sum of the above number to check for divisibility by 9.   From 1 to 50, each of the digits 1 to 4 occurs 14 times, digit 5 occurs 6 times and each of 6 to 9 occurs 5 times   Sum of digits from 1 to 4 = 10   Sum of digits from 6 to 9 = 30   Therefore, sum of digits from 1 to 50 = 10 * 15 + 5 * 6 + 30 * 5= 
10 * 15 + 5 * 6 + 30 * 5 = 330
330   Sum of digits from 51 to 54 plus a 5= 5 * 4 + ( 1 + 2 + 3 + 4) + 5 = 20 + 15= 
20 + 15 = 35
35   Total sum= 330 + 35= 
330 + 35 = 365
365   When 365 is divided by 9, we get 5 as the remainder!   5orrect Answer: 5   5
Answer: C
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
Choices: A) 1/6 B) 1/2 C) 1/9 D) 1/1 E) 1/5

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then   = 18/36 = 1/2   P(E) = 1 - 1/2 =1/2.   Answer: 1/2
Answer: B
Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 10 machines produce in 6 minutes?  Choose the correct answer
A) 1344 B) 4200 C) 8400 D) 50400 E) 67200

Solution: 8 machines produce 560 in 1 min   8 machines produce 560* 6 in 6 min   10 machine produce 560*6*(10/8) in 6 minutes     560*6*10/8= 
  560*6*10/8 = 4_200
4200 answer is 4200.
Answer: B
Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.526. If Sanoop returned 3 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts?  Choose the most appropriate option.
A) 560	B) 561	C) 562	D) 563	E) 564

Solution: Total price of 8 t-shirts= 8*526= 
8*526 = 4_208
4208   Total price of 5 t-shirts=5*505= 
5*505 = 2_525
2525   Total price of 3 t-shirts=4208-2525= 
4208-2525 = 1_683
1683   Average price of 3 t-shirts=1683/3= 
1683/3 = 561
561   Correct option Answer:561
Answer: B
If a function f is defined by f(x)= 2x/(x-1) for all non zero numbers x. If f(a) = 4 and f(ab) = 6 then b= ? Pick one:
A) 3/2  B) 1/2  C) 7/2  D) 3/4  E) 1/4

Solution: Given that f(x) =2x/(x-1) and f(a) = 4, then f(a) =2a/(a-1)=4 ===> 2a = 4a -4 => a =2, then backsolve using the answer choices:   f(ab) = f(2b) = 6   A) 3/2 ===> f(2*3/2) = f(3) = 2*3/(3-1) = 6/ 2= 
6/ 2 = 3
3   B) 1/2===> f((2*1/2) = f(1) = 2*1/(1-1) = undefined   C) 7/2 ===> f(2*7/2) = f(7) = 2*7/(7-1) = 14/6 = 7/3   3/4) 3/4 ===> f(2*3/4) = f(3/2) (2*3/2)/(3/2-1) = 3/(1/2)= 
3/(1/2) = 6
6 WINS   E) 1/4===> f(2*-1/4) = f(1/2) = (2*1/2)/(1/2-1) = 1/-1/2 = -2   Answer: 3/4
Answer: D
Train X and train Y pass one another traveling in opposite directions. Twenty four minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?  Choose the correct choice from the following options.
A) 28  B) 40  C) 56  D) 72  E) 80

Solution: Let the rate of the Train Y be R   Then the rate of the Train X will be R+30 (given)   As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30   d=100 and t = 24 min i.e 24/60 hr   using RTD table, (2R+30) * 24/60 = 100 ==> R= 110 miles/hr   So the rate of train X is 140 miles/hr (since R+30)   The distance traveled by Train X in 24 min is R*T = 140 * 24/60= 
140 * 24/60 = 56
56 miles (56)
Answer: C
At a company, the average wage of male employees is $9.97 per hour, and the average wage of female employees is $10.37 per hour. If the average wage of all employees is $10.12 per hour, what is the ratio of the number of male employees to the number of female employees?	Choose the correct choice:  A) 1 to 2  B) 2 to 3  C) 3 to 2  D) 5 to 3  E) 2 to 1

Solution: Average hourly wage of male employees = 9.97 $   Average hourly wage of female employees = 10.37 $   Average hourly wage of all employees = 10.12 $   Let number of male employees = m   number of female employees = f   10.12 = (9.97m + 10.37f ) / m+f   =>10.12m + 10.12f = 9.97m + 10.37f   => .15m = .25f   => m/f = .25/.15 = 5/3   Answer 5 to 3
Answer: D
If the LCM of two integers X, Y (where Y> X and X>1) is X*Y, then which of the following can not be true?	Choose one
A) Both X and Y can be Prime Numbers.  B) All Prime factors of X must be Prime factors of Y.  C) Both X and Y can be consecutive integers.  D) X and Y do not share any Prime factors.  E) X and Y do not have a common factor

Solution: If LCM of two numbers X and Y is the product XY then both numbers are Co- prime.   (Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).   Numbers that can be Co-Prime are :   1) Two consecutive natural numbers.   2) Two consecutive odd numbers.   3) Two prime numbers.   4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.   With above four statements it can be concluded that Options A, C, D and E are all true.   Only Option B cannot be true.   Hence answer is All Prime factors of X must be Prime factors of Y.
Answer: B
(3x + 2) (2x - 3) = ax^2 + kx + n . What is the value of a - n + k ? Choose the correct choice
A) 5  B) 7  C) 9  D) 10  E) 11

Solution: Expanding we have 6x^2 - 9x + 4x -6   6x^2 - 5x - 6   Taking coefficients, a = 6, k= -5, n = -6   Therefore a - n + k = 6 - (-6) - 5 = 12 - 5= 
12 - 5 = 7
7   The answer is 7.
Answer: B
If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 3720 , R will receive  Choose the correct choice:
A) 720
B) 700
C) 800
D) 900
E) None of these

Solution: Explanation :   Let P's capital = p, Q's capital = q and R's capital = r   Then   4p = 6q = 10r   => 2p = 3q = 5r   =>q = 2p/3   r = 2p/5   P : Q : R = p : 2p/3 : 2p/5   = 15 : 10 : 6   R's share = 3720 * (6/31) = 120*6= 
120*6 = 720
720. 720nswer : Option 720
Answer: A
Two girls move in opposite directions, one from A to B and other from B to A. The girl from A reaches the destination in 16 hrs and girl from B reaches her destination in 25 hrs, after having met. If former's speed is 25 km/hr, what will be the speed of latter?  Choose the most appropriate option
A) 10 km/hr B) 12 km/hr C) 16 km/hr D) 20 km/hr E) 25 km/hr

Solution: Hint: If two bodies A and B move from each other's starting point in opposite directions, they reach their destinations after having met, then their speeds Sa & Sb are given by,   Sa	/ Sb = √tb / √ta   where t is the time taken by them to cover the distance.   Sb	(25 x 4)	/ 5 = 20 km/hr   ANSWER IS 20 km/hr
Answer: D
In expressing a length of 11.482 km as nearly as possible with the three significant digits, find the percentage error	Select: A) 0.157% B) 0.207% C) 0.016% D) 0.021% E) None of these

Solution: Explanation:   Error = (11.5 - 11.482)= 
(11.5 - 11.482) = 0.018
0.018   Required percentage=   0.018/ 11.482Ã—100=0.157   Option 0.157%
Answer: A
How can 0.1666 of 600 of 66.67 % can be written?	Select the correct option.
A) 66.67
B) 13.39
C) 16.67
D) 18.99
E) 12.5

Solution: 0.1666 = 1/6 of 600 = 100 of 66.67% = 100 of 2/3   100 * (2/3) = 66.67 ...... 66.67ns - 66.67
Answer: A
In a fruit bucket total number of fruits is 99. If ratio of apple guava and mango is 17:9:7. Find the number of mangoes?	Choose the correct choice from the following:  A) 24  B) 30  C) 16  D) 21  E) 33

Solution: Let the number of apple guava and mangoes are 17x, 9x, 7x   17x+9x+7x = 99   33x = 99   x = 3   Number of mangoes are = 3*7= 
3*7 = 21
21   Answer : 21
Answer: D
Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -5 then by what factors will the Mean,Variance and Standard Deviation respectively change ?  Choose the most appropriate option.
A) -5,-5,-5 B) -5,5,5 C) 1,1,1 D) -5,25,5 E) 5,5,25

Solution: Mean: If all values are multiplied by -5 then their sum will also be multiplied by -5 so Mean will also get -5   Variance:   Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values   When we multiply all the values by -5 then the difference between the mean and the individual values also gets multiplied by -5 and the square of that difference becomes 25. So, the variance gets multiplied by a factor of 25   SD:   Standard Deviation is the square root of variance so sqrt(25)=5. So SD gets multiplied by a factor of 5.   So, answer will be -5,25,5.
Answer: D
Which of the following equations has a solution in common with x^2 - 2x - 15 = 0? Choose the correct choice from the following options:  A) x^2 - 6x + 9 = 0  B) x^2 + 2x - 15 = 0  C) 2x^2 + 9x + 9 = 0  D) 2x^2 + x - 3 = 0  E) none of the above

Solution: Given : x^2 - 2x - 15 => (x+3) (x-5) = 0 => 5 and -3 are the roots..   A. x^2 - 6x + 9 = 0 => (x-3) (x-3)   B. x^2 + 2x - 15 = 0 => (x+5) ( x-3)   C. 2 x^2 + 9x + 9 = 0 => (x+3) ( 2x+3)   D. 2 x^2 + x - 3 = 0 => (x-1) (2x+3).... no eq has same roots as per the parent eq..   Answer: 2x^2 + 9x + 9 = 0 is correct answer
Answer: C
A man fell in a 30 meter deep well, in one day he climbs 4 meters up and slips 3 meters down. How many days would it take for him to come out of the well?  Choose the correct choice from the following options
A) 22
B) 46
C) 17
D) 27
E) 33

Solution: 27   I will take 27 days to come out of that well for that man,   He climbs 4 meter every day and slips 3 meter down that means he climbs 1 meter in total each day, so like this on 26th day he would have climbed 26 meter and on 27th day he will climb 4 meeter again so total 30 meter he will climb in 27 days.
Answer: D
If a set consists of all positive digits less than or equal to 3 and of the squares of those digits, what is the mode of the set?
Choices:
A) 1  B) 2  C) 3  D) 4  E) 9

Solution: let set X= {1, 1.5, 2, 2.5, 3}   Set in question consists of even the squares of the digits contained in set X.   Hence required set = { 1, 1, 1.5, 2, 2.25, 2.5, 3, 4, 6.25, 9}   Mode of set= 1   1NSWER:1
Answer: A
The ratio of the arithmetic mean of two numbers to one of the numbers is 5:8. What is the ratio of the smaller number to the larger number? Choose the correct choice from the following options:  A) 1:8  B) 1:6  C) 1:5  D) 1:4  E) 1:3

Solution: For two numbers, the arithmetic mean is the middle of the two numbers.   The ratio of the mean to the larger number is 5:8, thus the smaller number must have a ratio of 2.   The ratio of the smaller number to the larger number is 2:8 = 1:4.   The answer is 1:4.
Answer: D