MU-NLPC/Calc-aqua_rat huggingface dataset:
The number of boys in a class is (3/2) times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?  Choose the most appropriate option:	A) A)48	B) B)44	C) C)42	D) D)40	E) E)38

Solution: Explanation:   Let number of girls = x and number of boys = 1.5x.   Then, 1.5x + x = 2.5x = total number of students.   Thus, to find exact value of x, the total number of students must be divisible by 2.5.   Answer:40
Answer: D
The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.460 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
Choose one:
A) 234 B) 254 C) 437 D) 450 E) 510

Solution: Let no. of non- officers be x   15 * 460 + x * 110 = (x + 15) 120   x = 510   510
Answer: E
Rs 80000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 9000 Find money given by 10%? Choose the correct option:  A) 30000  B) 40000  C) 50000  D) 60000  E) 70000

Solution: let first parrt is x and second part is y then x+y=80000----------eq1   total profit=profit on x +profit on y   9000=(x*10*1)/100 + (y*20*1)/100   90000=x+2y-----------------------------------eq2   90000=80000+y   so y=10000 then x =80000-10000= 
80000-10000 = 70_000
70000   first part=70000   ANSW70000R:70000
Answer: E
The amount of time that three people worked on a special project was in the ratio of 2 to 4 to 6. If the project took 144 hours, how many more hours did the hardest working person work than the person who worked the least?
Select the correct option.
A) 47 hours
B) 45 hours
C) 48 hours
D) 49 hours
E) 50 hours

Solution: Let the persons be A, B, C.   Hours worked:   A = 2*144/12= 
2*144/12 = 24
24 hours   B= 4*144/12= 
4*144/12 = 48
48 hours   C= 6*144/12= 
6*144/12 = 72
72 hours   C is the hardest worker and A worked for the least number of hours. So the difference is  72-24= 
 72-24 = 48
48 hours.   Answer : 48 hours
Answer: C
If a fair coin is flipped six times in a row, what is the probability that there will be at least one head and one tail? Choices.
A) 3/4 B) 11/12 C) 15/16 D) 31/32 E) 63/64

Solution: The number of possible outcomes is 2^6 = 64   There is one way to get no heads and one way to get no tails.   Thus there are 62 outcomes with at least one head and one tail.   P(at least one head and one tail) = 62/64 = 31/32   The answer is 31/32.
Answer: D
The 120 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT Pick one:
A) 4 B) 20 C) 30 D) 40 E) 90

Solution: Obviously the number of rows must be a factor of 120. The only option which is not a factor of 120 is E (90).   Answer: 90.
Answer: E
If 49x = 343^y, which of the following expresses x in terms of y?
Choose the correct option: A) (343/49)^y B) y^(343/49) C) y^(343-49) D) 7^(3y-2) E) 7^(2y-1)

Solution: By exponential simplification. 49 = 7^2 and 343=7^3 therefore (7^2)x=(7^3)^y gives x=(7^3y)/(7^2) further simplified to x=(7^3y)(7^-2) which gives x=7^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: 7^(3y-2)
Answer: D
Find the smallest number which when divided by 13 and 15 leaves respective remainders of 2 and 4
Choose the correct choice from the following options:
A) 187 B) 197 C) 184 D) 219 E) 227

Solution: Let 'N' is the smallest number which divided by 13 and 15 leaves respective remainders of 2 and 4.   Required number = (LCM of 13 and 15) - (common difference of divisors and remainders) = (195) - (11)= 
(195) - (11) = 184
184.   ANSWER:184
Answer: C
A train running at the speed of 54 km/hr crosses a pole in 7 seconds. Find the length of the train. Choose the correct choice from the following choices.
A) 150 meter	B) 105 meter	C) 140 meter	D) 135 meter	E) None of these

Solution: Explanation:   Speed = 54*(5/18) m/sec = 15 m/sec   Length of Train(Distance) = Speed * Time   =15*7= 
15*7 = 105
105 meter   Option 105 meter
Answer: B
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Answers:
A) 12 B) 11 C) 10 D) 9 E) 5

Solution: A   12   In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.   Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.   This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.   Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Answer: A
There were two candidates in an election. Winner candidate received 70% of votes and won the election by 280 votes. Find the number of votes casted to the winning candidate?  Choose the correct choice from the following answers
A) 228  B) 744  C) 490  D) 199  E) 231

Solution: W = 70% L = 30%   70% - 30% = 40%   40% -------- 280   70% -------- ?  70  - 30= 
 70  - 30 = 40
40%   40% -------- 280   70% -------- ?=> 280/40*70= 
280/40*70 = 490
490   Answer: 490
Answer: C
If the area of a circle decreases by 42%, then the radius of a circle decreases by
Choose the correct option:
A) 20%
B) 18%
C) 24%
D) 64%
E) None of these

Solution: If area of a circle decreased by x % then the radius of a circle decreases by   (100−10√100−x)%=(100−10√100−42)%   = (100−10√58)%   = 100 - 76= 
100 - 76 = 24
24%   Answer 24%
Answer: C
Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
Choose the correct choice from the following options:
A) 20 1/2 hours
B) 20 1/7 hours
C) 22 1/2 hours
D) 20 1/3 hours
E) 20 3/2 hours

Solution: 1/18 + 1/24 = 7/72   72/7 = 10 2/7   7/72 * 10 = 35/36 ----- 20 hours   WR = 1 – 35/36 = 1/36   1 h ----- 1/18   ? ----- 1/36 = 1/2 hours   => 20 1/2 hours   20 1/2 hoursnswer: 20 1/2 hours
Answer: A
How many arrangements of the letters of the word ‘BENGALI’ can be made if the vowels are to occupy only odd places.	Choose the correct choice from the following answers:
A) 334
B) 576
C) 776
D) 297
E) 271

Solution: Explanation:   There are 7 letters in the word Bengali of these 3 are vowels and 4 consonants.   There are 4 odd places and 3 even places. 3 vowels can occupy 4 odd places in \inline {\color{Black}4P_3{}} ways and 4 constants can be arranged in \inline {\color{Black}4P_4{}} ways.   Number of words = \inline {\color{576lack}4P_3{}} x \inline {\color{576lack}4P_4{}}= 24 x 24 = 576   Answer: 576
Answer: B
The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 10 homes?
Choose the most appropriate option
A) $200,000  B) $212,000  C) $215,000  D) $220,000  E) $230,000

Solution: IMO the answer has to be D.   5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 10 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 10x=120,000.   x=12,000.   The 10 houses are sold at $12,000 profit or at $212,000. (ANSWER $212,000)
Answer: B
Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin? Select the correct option:
A) 23 B) 23.5 C) 24 D) 24.5 E) 25

Solution: Let the present ages of sachin and rahul be 7x and 9x   sachin is younger than rahul in 7 years   So 9x-7x=7   2x=7   x=3.5   Sachin;s age= 7x= 7*3.5= 
7*3.5 = 24.5
24.5   answer :24.5
Answer: D
A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 86. How many points altogether did the team score? Pick one
A) 662 B) 678 C) 652 D) 642 E) 721

Solution: 8 * 86= 
8 * 86 = 688
688 – 10= 678   ANSWER:678
Answer: B
The mean of (54,824)^2 and (54,826)^2 =  Options
A) (54,821)^2
B) (54,821.5)^2
C) (54,820.5)^2
D) (54,825)^2 + 1
E) (54,821)^2 – 1

Solution: 54824^2 = (54825-1)^2 = 54825^2 + 1^2 - 2*54825*1   54826^2 = (54825+1)^2 = 54825^2 +1^2 + 2*54825*1   Taking the average of above 2 , we get (54825)^2 +1   hence the answer is (54,825)^2 + 1
Answer: D
Rahul went to a shop and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?	Choose the correct choice from the following options
A) 15	B) 12	C) 19.7	D) 16	E) 18

Solution: Total cost of the items he purchased = Rs.25   Total tax = 30 paise = 30/100   cost of tax = x   given that tax rate = 6%   (25-30/100-x)6/100=3/100   6(25-0.3-x)=30   x=19.7   ANSWER 19.7
Answer: C
The charge for a single room at Hotel P is 55 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G? Choose the correct choice from the following options: A) 50% B) 60% C) 75% D) 80% E) 100%

Solution: P = 0.45R = 0.9G   R = 0.9G/0.45 = 2G   Thus R is 100% greater than G.   The answer is 100%.0.9 /0.45= 
0.9 /0.45 = 2
2G   Thus R is 100% greater than G.   The answer is 100%.
Answer: E
There are 16 bees in the hive , then 10 more fly. How many bees are there in all?	Select the correct option
A) 7  B) 33  C) 12  D) 17  E) 26

Solution: 16+10= 
16+10 = 26
26 . Answer is 26.
Answer: E
Walking at the rate of 3 kmph a man cover certain distance in 3hr 20 min. Running at a speed of 9 kmph the man will cover the same distance in.	Choose the correct choice:
A) 45 min  B) 50 min  C) 40 min  D) 48 min  E) 54 min

Solution: Distance = Speed * time     3*10/3= 
  3*10/3 = 10
10km   New Speed= 9 kmph   Therefore time = D/S = 10/9 = 54min   Answer : 54 min.
Answer: E
What is the average (arithmetic mean) of all the multiples of ten from 10 to 110 inclusive?  Pick one
A) 60	B) 95	C) 100	D) 105	E) 110

Solution: The multiples of ten from 10 to 110 inclusive would be an evenly spaced set with 11 terms - 10, 20, 30,.......110   So average = (First term + Last Term)/2 = (10 + 110)/2 = 120/2= 
120/2 = 60
60   Hence, the correct answer is 60.
Answer: A
A certain fruit stand sold apples for $0.80 each and bananas for $0.70 each. If a customer purchased both apples and bananas from the stand for a total of $6.50, what total number of apples and bananas did the customer purchase? Choose the correct choice from the following answers.
A) 8	B) 9	C) 10	D) 11	E) 12

Solution: Let's start with 1 apple for $0.80.   Let's subtract $0.80 from $6.50 until we get a multiple of $0.70.   $6.50, $5.70, $4.90 = 7*$0.70   The customer purchased 7 bananas and 2 apples.   The answer is 9.
Answer: B
A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 9 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price
Select:
A) 70
B) 68
C) 66
D) 64
E) 62

Solution: Responding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:   Assuming x motorcycles were sold every month initially.   (568000/x + 1000)(x-9) = 594000   (568/x + 1)(x-9) = 594   Now 568 = 8*71   Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.   We get  9*66= 
 9*66 = 594
594 (matches)   So he will sell  71 - 9= 
 71 - 9 = 62
62 bikes this month   Answer (62)
Answer: E
If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 6 years would be  Select:	A) (1.5)^4	B) 4(1.5)	C) (1.05)^6	D) 1 + (0.05)^4	E) 1 + 4(0.05)

Solution: f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 6 years would be   1(1.05)^6   1.05^6   C. (1.05)^6
Answer: C
A bag contains equal number of Rs.5, Rs.2 and Re.1 coins. If the total amount in the bag is Rs.1152, find the number of coins of each kind? Select
A) 432  B) 288  C) 144  D) 72  E) 152

Solution: Let the number of coins of each kind be x.   => 5x + 2x + 1x = 1152   => 8x = 1152 => x = 144   ANSWER:144
Answer: C
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 54/r years. If Pat's parents invested $6,000 in a long-term bond that pays 6 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
Choose the correct choice from the following answers:	A) $20000	B) $15000	C) $12000	D) $10000	E) $9000

Solution: Since investment doubles in 54/r years, then for r=6 it'll double in   54/6= 
  54/6 = 9
~9 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $6,000*2=$12,000 .   Answer: $12000.
Answer: C
In a bag of small balls 1/4 are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?	Select the correct option:
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: Let us first find the fraction of green, blue and yellow balls   1/4 + 1/8 + 1/12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator   = 11 / 24 , add numerators   The fraction of white balls is given by   24 / 24 - 11 / 24 = 13 / 24   So the fraction 13 / 24 corresponds to 26 balls. If x is the total number of balls then   (13 / 24) of x = 26 balls   or (13 / 24) × x = 26   x = 26 × (24 / 13) = 48 , total number of balls   The fraction of blue balls is 1 / 8 of x. The number of blue balls is given by   (1 / 8) of 48 = 6 balls.   correct answer is 6)6
Answer: C
Set M contains numbers that satisfy the condition that, if integer x is in the set then x+3 will also be in the set M. If -4 is one of the value in the set, which of the following numbers must also be present in the set M.
I. 5
II. 2
III. -7 Pick:
A) I only	B) II only	C) I and II only	D) II and III only	E) I, II and III

Solution: Notice that we are askedwhich of the following numbers MUST also be present in the set MnotCOULD be in the set.   Now, if -4 is in the set, then -4+3=-1mustbe in the set. Since -1 is in the set then   -1+3= 
  -1+3 = 2
2mustbe in the set.so do 5. Could -7 be in the set? Certainly, but we don't know that for sure.   Answer: I and II only.
Answer: C
An inspector rejects 0.05% of the meters as defective. How many will he examine to reject 4? Select the correct option
A) 4000 B) 8000 C) 5000 D) 4500 E) 6000

Solution: Let the number of meters to be examined be x   Then, 0.05% of x = 4   (5/100)*((1/100)*x = 4   x = 8000   Answer is 8000
Answer: B
What least whole no. should be added to 532869 to make it divisible by 9?
Pick
A) 6	B) 7	C) 9	D) 10	E) 12

Solution: If a number is divisible by 9, the sum of its digits must be a multiple of 9.   Here, 5+3+2+8+6+9=33, the next multiple of 9 is 36.   3 must be added to 532869 to make it divisible by 9   9
Answer: C
If D is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT
Choose the correct answer.
A) z - w = 3(y - x)	B) D is divisible by 8	C) The average of w, x, y, and z is odd	D) D is divisible by 4	E) w + x + 8 = y + z

Solution: Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.   D = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12   Focus on the easiest options first. You see that D is not divisible by 8. Answer (D is divisible by 8)
Answer: B
For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6 , -8?
Choose the most appropriate option:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Given sequence: {1, -3, 2, 5, -4, -6, -8}   The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative.   1*(-3)=-3=negative;   -3*2=-6=negative;   2*5= 
2*5 = 10
10=positive;   5*(-4)=-20=negative;   (-4)*(-6)= 
(-4)*(-6) = 24
24=positive.   So there are 3 pairs of consecutive terms of the sequence for which the product is negative.   Answer: 3.
Answer: C
Line W has the equation 3x + y = 7. Which of the following lines is perpendicular to Line W? Choose the most appropriate option.
A) y = 3x + 4  B) y = –3x – 6  C) y = (1/3)x – 1  D) y = (–1/3)x + 2  E) y = (–7/3)x – 5

Solution: I first rewrote the equation in the standard y=mx+b form. Therefore, Line W as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.   Thought process next is what line would be perpendicular to Line W? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice y = (1/3)x – 1 as the only one.
Answer: C
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was.	Pick:
A) 15000	B) 2655	C) 16888	D) 6677	E) 1871

Solution: Principal = Rs. (100 x 5400)/(12*3) = Rs. 15000.   15000nswer:15000
Answer: A
A can do a work in 30 days, B can do it in 20 days. They together under took to do a piece of work for Rs.1000, what is the share of B?
Select.
A) Rs.500	B) Rs.400	C) Rs.800	D) Rs.600	E) Rs.200

Solution: Explanation:   Share of their work days = 30:20   Share of their work =20:30   Share of B’s money = 3/5*1000= 
3/5*1000 = 600
600   Answer: Option Rs.600
Answer: D
What least number should be added to 1056, so that the sum is completely divisible by 23	Choose the correct choice from the following: A) 4 B) 1 C) 2 D) 3 E) 5

Solution: Explanation:   (1056 / 23) gives remainder 21   21 + 2= 
21 + 2 = 23
23, So we need to add 2   Answer: Option 2
Answer: C
Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 6% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Choose the correct choice from the following
A) 2:9
B) 2:7
C) 1:6
D) 1:1
E) 1:3

Solution: (10/100)A+(2/100)B = (6/100)(A+B)   4A =4B   => A/B = 1/1   Answer is 1:1.
Answer: D
In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 56 as quotient. What is the correct quotient ?
Options:
A) 0 B) 12 C) 32 D) 20 E) 25

Solution: 12*56= 
12*56 = 672
672   672%21=32   ANSWER:32
Answer: C
How many odd numbers between 10 and 1600 are the squares of integers?	Answers:
A) 9 B) 12 C) 15 D) 18 E) 21

Solution: The numbers are the squares of 5, 7, 9,...,39 which includes 18 numbers.   The answer is 18.
Answer: D
How many minutes is it before 12 noon if 16 minutes ago it was three times as many minutes after 9 am?	Pick one.
A) 41 minutes
B) 49 minutes
C) 40 minutes
D) 42 minutes
E) 44 minutes

Solution: 41 minutes   41 minutes
Answer: A
A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?	Choose the correct choice from the following answers.
A) 30  B) 31 5/7  C) 32  D) 33  E) 35

Solution: Required average   = 67 x 2 + 35 x 2 + 6 x 3   2 + 2 + 3   = 134 + 70 + 18   7   =	222   7   = 31 5	years.   7   31 5/7)
Answer: B
Which of the following is true about 0<|x|-x<5?	Answers:	A) -1<x<0	B) 0<x<1	C) 1<x<2	D) 2<x<3	E) 3<x<4

Solution: when can be |x|-x be greater than 0..   NEVER when x is positive..   ONLY A is left..   you can also substitute any value within the given range to check for answer   Example - put x as -0.5 for A. -1<x<0..   so |x|-x = |-0.5|- (-0.5) = 1 and it satisfies 0<|x|-4x<5   -1<x<0
Answer: A
If logx y = 10 and log2 x = 1000, what is the value of y?
Answers
A) 210002	B) 277889	C) 210000	D) 27788	E) 788291

Solution: Explanation:   log2 x = 1000   => x = 21000   logx y = 10   => y = x10   = (21000)10   = 2(1000 × 10)   = 210000   Answer: Option 210000
Answer: C
A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
Choose the correct choice from the following choices
A) 1.5
B) 1.8
C) 1.6
D) 1.3
E) 1.1

Solution: 72 --- 9 DS = 8   ? ---- 1   45 ---- 9 US = 5   ? ---- 1 S = ?   S = (8 - 5)/2= 
(8 - 5)/2 = 3/2 = around 1.5
1.5   Answer:1.8
Answer: B
Factory X's bulbs work for over 5000 hours in 37% of cases, whereas factory Y's bulbs work for over 5000 hours in 75% of cases. It is known that factory X supplies 40% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours?	Select the correct option:
A) 56.4%  B) 58%  C) 57.4%  D) 55%  E) 59.8%

Solution: For X, 40% of 37% will work.   For Y, 60% of 75% will work. *60% is the rest of the bulb supply in the market.   So, the probability that a purchased bulb will work is:   0.40(0.37) = .148   0.60(0.75) = 0.45   The combined probability then is 14.8 + 45= 
14.8 + 45 = 59.8
59.8%   ANS 59.8%
Answer: E
A shop owner sells 30mtr of cloth and gains SP of 10 metres. Find the gain %?
Choices:
A) 40%	B) 45%	C) 50%	D) 65%	E) 70%

Solution: Here, selling price of 10 m cloth is obtained as profit.   Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)   Selling price of 20 m cloth = Selling Price of 30 m of cloth   Let cost of each metre be Rs. 100.   Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000   Profit% = 10 × 100 = 50%   20   Profit of 50% was made by the merchant.   50%
Answer: C
What least number must be added to 1145, so that the sum is completely divisible by 23 ?	Choose one
A) 2
B) 3
C) 4
D) 5
E) 8

Solution: 50*23= 
50*23 = 1_150
1150   1150 - 1145= 
1150 - 1145 = 5
5   Answer : 5
Answer: D
A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is	Pick one
A) 145	B) 185	C) 253	D) 370	E) None

Solution: Solution   Let the number be x.   Then 2x = 10 or x = 5. So, the number is either 253 or 352. Since the number increases on reversing the digits, so the hundred's digit is smaller than the units digit.   Hence, required number = 253.   Answer 253
Answer: C
A certain manufacturer of cake, muffin, and bread mixes has 70 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
Choose the correct option
A) a. 1/10 B) b. 3/10 C) c. 1/2 D) d. 3/7 E) e. 9/10

Solution: C+M+B-CM-MB-CB-2CMB = 70   C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.   the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.   50 + 40 + B-CB-MB-20-2CMB = 70   B-CB-MB-2CMB = 30   hence the probability = 30/70 = 3/7.   d. 3/7
Answer: D
Find the least number which when divided by 33 and 8 leaves a remainder of 2 in each case. Options:
A) 266
B) 268
C) 270
D) 272
E) 274

Solution: The least number which when divided by different divisors leaving the same remainder in each case   = LCM(different divisors) + remainder left in each case.   Hence the required least number   = LCM(33, 8) + 2 = 266.   266NSWER:266
Answer: A