MU-NLPC/Calc-aqua_rat huggingface dataset:
Two friends plan to walk along a 43-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 15% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other? Pick one:
A) 21  B) 21.5  C) 22  D) 22.5  E) 23

Solution: If Q complete x kilometers, then P completes 1.15x kilometers.   x + 1.15x = 43   2.15x=43   x = 43/2.15= 
43/2.15 = 20
20   Then P will have have walked   1.15*20= 
  1.15*20 = 23
23 km.   The answer is 23.
Answer: E
In the coordinate plane, points (x, 1) and (5, y) are on line k. If line k passes through the origin and has slope 1/5, then what are the values of x and y respectively?  Answers.
A) 4 and 1 B) 1 and 5 C) 5 and 1 D) 3 and 5 E) 5 and 3

Solution: Line k passes through the origin and has slope 1/5 means that its equation is y=1/5*x.   Thus: (x, 1)=(5, 1) and (5, y) = (5,1) -->x=5 and y=1   Answer: 5 and 1
Answer: C
For all numbers p and q, the operation @ is defined by p@q = p^2 - pq. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y) Choose the correct choice from the following options.
A) II B) I and II C) I and III D) II and III E) All of the above

Solution: p@q = p^2 - pq=p(p-q).... so p@q will be zero if p=q or p=0.. but a cannot be equal to 0.. as per Q, x and y can take any int value except 0...   now lets look at the choices..   when x=y, it will be 0... so ok...   when we put xy=y, it is possible when x=1 and y any integer... so ok again   when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible   only l and ll possible ans I and II....
Answer: B
Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 4%. What is the approximate interest he pays annually?  Pick.
A) $1600  B) $2000  C) $2150  D) $2500  E) $12000

Solution: Usually, you are given the annual rate of interest and it is mentioned that it is annual rate.   The bank charges him a quarterly compounded ANNUAL rate of 16%.   Here you find per quarter rate as  (16/4)= 
 (16/4) = 4
4%   I have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 4% annual rate of interest, it is apparent that the intent was a 4% quarterly rate. So the bank charges 4% every quarter and compounds it in the next quarter. Had it been a simple quarterly rate, we would have just found 4 * 4% of 10,000= $1600 as our answer.   But since, the interest is compounded, it will be a bit more than $1600. Option ($1600) looks correct.
Answer: A
The speed at which a man can row a boat in still water is 25 kmph. If he rows downstream, where the speed of current is 11 kmph, what time will he take to cover 80 metres?  Choose the correct choice from the following options
A) 18 seconds
B) 27 seconds
C) 26 seconds
D) 12 seconds
E) 8 seconds

Solution: Speed of the boat downstream = 25 +11= 
25 +11 = 36
36 kmph= 36 * 5/18= 
36 * 5/18 = 10
10 m/s   Hence time taken to cover 80 m= 80/10= 
80/10 = 8
8 seconds.   Answer:8 seconds
Answer: E
There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 6 possible combinations in which Jim and Ellen are not selected, what is the value of k?  Options
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: There are k-2 members in the band, and k-4 members without Jim and Ellen.   (k-4)C2 = 6   (k-4)(k-5)/2 = 6   (k-4)(k-5) = 12 = 4*3   k = 8   The answer is 8.
Answer: A
If (x^2 + 4x - 11)/5 ≤ x + 1, then x could be represented by which of the following?  Choose the most appropriate option:
A) − 3 ≤ x ≤ 4
B) − 4 ≤ x ≤ 3
C) − 3 ≤ x ≤ 3
D) − 4 ≤ x ≤ − 3
E) 3 ≤ x ≤ 4

Solution: IMO − 3 ≤ x ≤ 4 is correct answer   solving through eqautions   x^2 +4x-11<= 5x+5   (x+3)(x-4)<=0
Answer: A
Find the smallest number of five digits exactly divisible by 22,33,66 and 44. Pick one
A) 10101 B) 11000 C) 10110 D) 10111 E) 10100

Solution: Smallest number of five digits is 10000.   Required number must be divisible by L.C.M. of 22,33,66,44 i.e 132,   On dividing 10000 by 132,we get 32 as remainder.   Therefore, Required number = 10000 +( 132 â€“ 32 ) = 10100.   Answer is 10100.
Answer: E
The entrance fee for a fair is $5 for persons under the age of 18, and 20% more for persons older. Each ride at the fair costs $0.50. If Joe goes with her 6 years old twin brothers, and they each took 3 rides in total. How much money does Joe end up spending at the fair?
Choose the correct choice:
A) 16 B) 20.5 C) 17.5 D) 20 E) 4.5

Solution: Total entrance fee is (2*$5) + (1.20*5)= $16   Total rides fee is (0.50*3)*3(2* 5) + (1.20*5)= 
(2* 5) + (1.20*5) = 16
$16   Total rides fee is  (0.50*3)*3= 
 (0.50*3)*3 = 4.5
$4.50   Total money spent is $20.50   Answer is 20.5
Answer: B
If X and Y are digits and 8XY is a 3-digit number that is divisible by 2, which of the following is a possible product of X and Y? Choose the correct choice from the following answers
A) 15 B) 31 C) 12 D) 27 E) 91

Solution: Key to this question is to remember the fact that a number divisible by 2 must end with even OR 0 (i.e Y).   If Y had to be 0, product should also be 0 regardless of X.   Otherwise, product is a multiple of 2. Only one answer choice meets the requirement.   Ans 12.
Answer: C
If Tim had lunch at $50 and he gave 20% tip, how much did he spend?
Choose the correct option: A) A)$60.00 B) B)$35.42 C) C)$60.60 D) D)$21.56 E) E)$78.45

Solution: The tip is 20% of what he paid for lunch.   tip = 20% of 50.00 = (20/100)*50.00 = = $10.00   Total spent     50.00 + 10.00= 
  50.00 + 10.00 = 60
$60.00   correct answer is $60.00)$60.00
Answer: A
Rs. 825 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 825 become in 3 years ?  Choices:
A) Rs. 1020.80 B) Rs. 1025 C) Rs. 1055 D) Data inadequate E) None of these

Solution: Solution   S.I. = Rs.(956-825 )=Rs.131   Rate = (100x131/825x3) = 524/99%   New rate = (524/99 +4)% = 920/99%   New S.I. = Rs.(825 x 920/99 x 3/100) Rs. 230.   ∴ New amount = Rs.(825+230)= Rs. 1055.   Answer Rs. 1055
Answer: C
q is a positive integer and multiple of 2; p = 4^q, what is the remainder when p is divided by 10? Answers
A) 10
B) 6
C) 4
D) 0
E) It Cannot Be Determined

Solution: It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:   4/10 is 0 with a remainder of 4   14/10 is 1 with a remainder of 4   5/10 is 0 with a remainder of 5   105/10 is 10 with a remainder of 5   It is also essential to remember that the q is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, q must be a positive even integer.   With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?   The units digit of 4 raised to an integer follows a specific repeating pattern:   4^1 = 4   4^2 = 16   4^3 = 64   4^4 = 256   4^(odd number) --> units digit of 4   4^(even number) --> units digit of 6   There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.   Since q must be an even integer, the units digit of p=4^q will always be 6. Consequently, the remainder when p=4^q is divided by 10 will always be 6.   In case this is too theoretical, consider the following examples:   q=2 --> p=4^q=16 --> p/10 = 1 with a remainder of 6   q=4 --> p=4^q=256 --> p/10 = 25 with a remainder of 6   q=6 --> p=4^q=4096 --> p/10 = 409 with a remainder of 6   q=8 --> p=4^q=65536 --> p/10 = 6553 with a remainder of 6   Answer: 6.
Answer: B
If q is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
Choose the correct choice from the following answers:
A) √n + 1
B) n + 1
C) n^2 + 1
D) q + 2√q + 1
E) n^2 + 2n + 1

Solution: If q is the square of a positive integer, which of the following must be equal to the square of the next positive integer?   q = (x)^2 where x is a positive integer   To calculate -   (x+1)^2 = x^2 + 2x + 1   root(q) = x   Ans - q + 2 root(q) + 1   This should be q + 2√q + 1
Answer: D
Rs. 5600 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/7:1/7:1/14?  Choose the correct choice:
A) 300 B) 992 C) 1120 D) 552 E) 312

Solution: 1/7:1/7:1/14 = 2:2:1   1/5*5600= 
1/5*5600 = 1_120
1120   2240-1120= 
2240-1120 = 1_120
1120   Answer: 1120
Answer: C
If a/b=3/4 and 8a+5b=22,then find the value of a.  Select:	A) 1/2	B) 3/2	C) 5/2	D) 4/2	E) 7/2

Solution: (a/b)=3/4 b=(4/3) a.   Therefore, 8a+5b=22 = 8a+5*(4/3) a=22  8a+(20/3) a=22   =44a = 66 = a=(66/44)=3/2   Answer is 3/2.
Answer: B
Given that k/l < 1, and both k and l are positive integers, which one of the following must be greater than 1?
Choose the correct choice from the following:
A) k/l^2
B) k^2/l
C) k^2/l^2
D) l/k
E) √(k/l)

Solution: Since k/l is a fraction l must always be > 1   Given -   Which one of the following must be greater than 1   We can get the result one only when the denominator in k/l ( Which is less than 1 ) becomes numerator..   Among the given options only (D) has the required characteristic we are looking for...   Hence answer will be (l/k)
Answer: D
Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 10 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 716.67, what was the difference in the score of his last mock and his GMAT score?  Choices.
A) 20
B) 32
C) 40
D) 50
E) 60

Solution: One way to do this would be weighted average method..   1) let the average of 5 mocks be x...   so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 716.67...   By alligation/weighted average..   the difference in 760 and 716.67 is 5/6 of difference of 760 and x..   760-716.67 = 5/6 * (760-x)   760-x= 43.33*6/5=52...   so x = 708..   the last of mock test will be 708+10+10=728...   so ans = 760-728= 
760-728 = 32
32   32
Answer: B
John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
Choose the correct choice from the following.
A) 50  B) 45  C) 65  D) 78  E) 64

Solution: (x+x1+...x14)/15 = 40   50   Option 50
Answer: A
A person is traveling at 20 km/hr and reached his destiny in 2.5 hr then find the distance?  Choose the correct answer
A) 53 km	B) 55 km	C) 52 km	D) 60 km	E) 50 km

Solution: T = 2.5 hrs = 5/2 hrs   D= T*S = 20*5/2= 
20*5/2 = 50
50 km   Answer is 50 km
Answer: E
The first five numbers in a regular sequence are 4, 10, X, 46, and 94. What is x ?  Choose the correct choice from the following answers:
A) 28  B) 26  C) 30  D) 22  E) 24

Solution: it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals..   when we see the sequence 4, 10, x, 46, and 94, we see that each succeeding number is some value more than twice the previous number..   10=2*4+2..   x=2*10+2 = 22..   and so on..   so next number= 22   22
Answer: D
Tim has 350 pounds of cement in 100, 50, and 25 pound bags. He has an equal number of each size bag. How many bags of cement does Tim have?
Answers
A) 2	B) 4	C) 6	D) 8	E) 10

Solution: Let the number of each sized bag = c100c + 50c + 25c = 350175c = 350c = 2Therefore, Tim has 3c = 6 bags of cementAnswer: 6
Answer: C
What is the least value of x, So that 2x5475 is divisible by 9  Choose the correct choice:	A) 7	B) 8	C) 4	D) 3	E) 2

Solution: Explanation:   The sum of the digits of the number is divisible by 9.   Then the number is divisible by 9.   2 + x + 5 + 4 + 7 + 5 = 23 + x   Least value of x may be '4',   So that the total 23 + 4= 
23 + 4 = 27
27   is divisible by 9.   Answer: Option 4
Answer: C
Square P is inscribed in circle Q. If the perimeter of P is 40, what is the circumference of Q? Choose one.
A) 11√ 2π  B) 10√ 2π  C) 9√ 2π  D) 8√ 2π  E) 7√ 2π

Solution: square forms two right angled triangles.   Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter.   hypotenuse here = diagonal of the square = 10 sqrt(2) = diameter   => radius = 5 sqrt(2)   Circumference of the circle = 2pi r = 10 pi sqrt(2)   Answer is 10√ 2π.
Answer: B
A debtor reached an agreement with his creditor to repay a loan by making a monthly payment which is double of the amount she paid the previous month. If the debtors first payment was $200, and he is expected to pay back 51200, how many months will it take to fully repay the loan?	Select.
A) 9	B) 10	C) 9	D) 12	E) 10

Solution: First payment--$200   Total amount to be repaid--$25600   First month payment--$200   Second month payment( double the previous month payment)--$200*2=$400   Third month payment( double the previous month payment)--$400*2=$800   Fourth month payment( double the previous month payment)--$800*2=$1600   Fifth month payment( double the previous month payment)--$1600*2=$3200   Sixth month payment( double the previous month payment)--$3200*2=$6400   Seventh month payment( double the previous month payment)--$6400*2=$12800   Eight month payment( double the previous month payment)--$12800*2=$25600   Ninth month payment( double the previous month payment)--$25600*2=$51200   9nswer is 9
Answer: A
As a bicycle salesperson, James earns a fixed salary of $30 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true?
I. y<2x
II. y>x
III. y>3	Choose the correct choice from the following:
A) I,II only B) I only C) II,III only D) II only E) III only

Solution: II. y>x --> since this week, James earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);   III. y>3 --> if James sold 3 bicycles this week then this week he earned 30+3*6= 
30+3*6 = 48
$48, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $30. So y must be more than 3;   I. y<2x --> is not always true.   Answer: II,III only
Answer: C
A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio Q of students per class?
Pick one:
A) Q=3 B) Q=4 C) 6 D) 8 E) 12

Solution: Another way to look at the problem...   Since the total is 120, RATIO * CLASSES = R*C = 120.....(i)   we are looking where ratio increases by 1 and # of classes decreases by 10 = (R+1)(C-10) = RC+C-10R-10=120....(ii)   (ii)-(i)....   C=10R+10 = 10(R+1).......   so # of classes has to be multiple of 10   AS RC=120.... 10(R+1)*R = 120...................R(R+1) = 12..   so 12 is a multiple of consecutive numbers ONLY 3 *4 fits in..... and R=3   Q=3
Answer: A
A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $95,000, what is the average income of the other 40 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations?	Choose the correct option:	A) $32,500	B) $35,000	C) $37,500	D) $42,500	E) $50,000

Solution: let x be the average of 40 customers   40*x + 10* 95000 = 50*45000   solving this we have x= 32500   $32,500nswer is $32,500.
Answer: A
The slant height of a cone is 35 cm and radius of the base is 14cm, find the curved surface of the cone.
Options: A) 4150 B) 1780 C) 1540 D) 1500 E) 6100

Solution: π * 14 * 35= 1540   Answer:1540
Answer: C
A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of 8 cubic feet. If a small block has half the width, half the depth, and half the length of a normal block, what is the volume of cheese in a small block in cubic feet?  Choose the correct option:
A) 1
B) 5
C) 4
D) 6
E) 2

Solution: Volume of cube=lbh=8   New cube l ,b, h are decreases of .5l, .5b,.5h   New volume of cube =.5l*.5b*.5h=.125*lbh   .5 *.5 *.5= 
.5 *.5 *.5 = 0.125
.125*lbh=.125*8= 
.125*8 = 1
1   1nswer: 1
Answer: A
In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 20 feet between each tree. How many trees can be planted if the road is 148 feet long? Select:
A) 8	B) 9	C) 10	D) 11	E) 16

Solution: Let T be the number of trees. Then the length required for trees on the sidewalk will be 1*T= T   To maximize the number of trees, the number of 20 feet spaces between trees should be 1 less than total number of trees.   For example, If there are 3 trees, then there should be 2 spaces between them.   So the number of 20 feet spaces will be T-1. Then, the length of sidewalk required for 20 feet spaces will be 20*(T-1)   It is given that total length of sidewalk is 148 feet.   or 20(T-1)+T = 148   or 20T-20+T = 148   or 21T = 168   or T=8   8nswer:-8
Answer: A
What will be the difference in simple and compound interest on 2000 after three years at the rate of 10 percent per annum? Options:
A) 160
B) 42
C) 62
D) 20
E) None of these

Solution: For 3 years:   Diff.=Sum×(rate)2(300+rate)/(100)3   = 2000×10×10×310/100×100×100 = 62   Answer 62
Answer: C
A $500 investment and a $1,500 investment have a combined yearly return of 19 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have? Answers: A) 9% B) 10% C) 23% D) 21% E) 22%

Solution: The equation we can form the question :   Return on Total Investment = Sum of individual Investments   (500+1500)(19)=(500âˆ—7)+(1500x), where x is the return on investment of 1500.   Solving the equation, we get x = 23% ( Option 23% )	ANSWER:23%
Answer: C
Find the constant k so that : -x2 - (k + 11)x - 8 = -(x - 2)(x - 4)	Choose one.
A) 11  B) 12  C) 17  D) 14  E) 15

Solution: -x2 - (k + 11)x - 8 = -(x - 2)(x - 4) : given   -x2 - (k + 11)x - 8 = -x2 + 6x - 8   -(k + 11) = 6 : two polynomials are equal if their corresponding coefficients are equal.   k = -17 : solve the above for k   correct answer 17
Answer: C
A positive whole number has factors of 3 and 5. The number MUST be divisible by: I. 15 II. 30 III. 60	Select the correct option:
A) I & II
B) III
C) I & III
D) II & III
E) II

Solution: 15 , 30 is not divisible by 60.IIIut 60 is divisible by 3,5,15,30   So answer is III   Answer : III
Answer: B
Krishan and Nandan jointly started a business. Krishan invested six times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 6000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?	Choose the correct choice from the following choices:  A) Rs.78000  B) Rs.48000  C) Rs.6000  D) Rs.82000  E) Rs.32000

Solution: 6:1   2:1   ------   12:1   1 ----- 6000   13 ----- ? => Rs.78,000   Rs.78000nswer: Rs.78000
Answer: A
There are 8 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?	Choose the correct option:
A) 10	B) 30	C) 28	D) 60	E) 90

Solution: 10 players are there.   two players play one game with one another.   so 8282=8*7/2= 
8*7/2 = 28
28   SO OPTION 28 is correct
Answer: C
A pipe takes a hours to fill the tank. But because of a leakage it took 2 times of its original time. Find the time taken by the leakage to empty the tank	Choose the correct choice from the following choices.
A) 50 min  B) 60 min  C) 90 min  D) 80 min  E) 120 min

Solution: pipe a can do a work 60 min.   lets leakage time is x;   then   1/60 -1/x=1/120   x=120 min   ANSW120 minR:120 min
Answer: E
Today is 22 days before Mariah's graduation. If she graduates on a Friday, what day of the week is it today? Answers:
A) Monday B) Friday C) Tuesday D) Thursday E) Sunday

Solution: Each weekday is repeated every 7 days. 22 divided by 7 is 3, with a remainder of 1. Therefore, 22 days before the graduation occurs 1 day before the weekday of the graduation. Answer: Thursday
Answer: D
Suppose a, b, and c are positive integers with a < b < c such that
1/a
+
1/b
+
1/c
= 1. What is
a + b + c?  Answers.
A) 1 B) 4 C) 9 D) 11 E) no such integers exist

Solution: First note that we must have 1/a < 1, so a > 1. Since 1/a > 1/b > 1/c, we   must also have 1/a > 1/3; so a < 3. Thus, a/ 2. Now 1/b + 1/c = 1/2 where 2 < b < c.   Similar to before, 1/b > 1/4, so b < 4. Thus, b = 3. With a = 2 and b = 3 we have   1/2+1/3+1/c = 1, which is satisfied when c = 6. To conclude, a+b+c = 2+3+6= 
2+3+6 = 11
11.   correct answer 11
Answer: D
The age of man is three times the sum of the ages of his two sons.Four years hence,his age will be double of the sum of the ages of his sons.The fatherâ€™s present age is :  Choices.
A) 36 years B) 45 years C) 50 years D) 55 years E) 75 years

Solution: Solution   Let the sum of present ages of the two sons be x years.   Then,father's present age = 3x years.   âˆ´ (3x + 4)=2 (x +8) â‡” 3x + 4 = 2x + 16 â‡” x =12.   Hence,father's present age = 36 years. 36 yearsnswer 36 years
Answer: A
A bottle of coke contains 200gm in place of 1kg of fluid. Find the actual % difference, given a 10% gain on initial fluid? Choose the correct answer:
A) 32.5%
B) 112.5%
C) 35%
D) 40%
E) 50%

Solution: fluid price of 200gm = 100+10= 
100+10 = 110
110   Difference= 110-20= 
110-20 = 90
90   % of difference= 90*100/80= 
90*100/80 = 225/2 = around 112.5
112.5 %   Answer is 112.5%
Answer: B
A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 64 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?  Choose the correct choice from the following answers:	A) 20	B) 30	C) 48	D) 64	E) 72

Solution: Total distance = 64   64istance = Speed * Time   Walking speed = s1 = 8   Walking time = t1   Bike speed = s2 = 16   Time traveled in bike = t2   d1 + d2 = 64   s1t1 + s2t2 = 64   8*t1 + 16*t2 = 64   t1 + 2*t2 = 8 ----- (1)   Given: t1 + t2 = 8 ----- (2)   (1) - (2) --> t2 = 0 and t1 = 8 - 0= 
8 - 0 = 8
8   Walking distance= s1*t1 = 8*8= 
8*8 = 64
64   Answer: 64
Answer: D
5358 x 51 = ?	Answers
A) 273258  B) 273268  C) 273348  D) 273358  E) None of these

Solution: Explanation:   5358 x 51	= 5358 x (50 + 1)   = 5358 x 50 + 5358 x 1   = 267900 + 5358= 
267900 + 5358 = 273_258
273258.   273258NSWER IS 273258
Answer: A
3 persons (1 couple and 1 single) are seated at random in a row of 5 chairs. What is the probability that the couple does not sit together? Pick one
A) 5/7
B) 4/5
C) 2/5
D) 3/5
E) 11/8

Solution: Let's find the probability that a couple sits together (right next to each other) and subtract that value from 1.   Total # of ways 3 persons C1C1, C2C2 and SS to be seated in a row of 5 seats is 5!2!=605!2!=60. Consider this, we are interested in arrangement of C1, C2, S, E, EC1, C2, S, E, E, so in arrangement of 5 letters out of which 2 E's are identical (E denotes an empty seat);   # of ways for a couple to sit together is 4!2!∗2=244!2!∗2=24. Consider a couple as a single unit: {C1,C2}, S, E, E{C1,C2}, S, E, E, so we have total of 4 units out of which 2 E's are identical, # of arrangement of these units is 4!2!4!2!, but C1C1, C2C2 within their unit can be arranged in 2 ways ({C1,C2}{C1,C2} or {C2,C1}{C2,C1}), so total # of arrangement for this case is 4!2!∗2=244!2!∗2=24;   P=1−2460=35P=1−2460=35.   Answer: 3/5.
Answer: D