MU-NLPC/Calc-aqua_rat huggingface dataset:
If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?  Choices
A) 21 days	B) 15 days	C) 12 days	D) 9 days	E) 6 days

Solution: Explanation:   C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days   Answer: 9 days
Answer: D
S is a set of 100 consecutive multiples of 8. If the smallest number in S is 108, then the greatest number in S is Pick.
A) 998
B) 297
C) 999
D) 902
E) 900

Solution: last term =first term +(total no. of terms-1)consecutive difference   S is a set of 100 consecutive multiples of 8. If the smallest number in S is 108, then the greatest number in S is   first term = 102 ; total terms =100 ; difference = 3   108+(99)8 = 900   Ans 900
Answer: E
What percent is 3% of 5% ?  Options:
A) 15%
B) 1.5%
C) 0.15%
D) None of these
E) Cannot be determined

Solution: Answer   Required percent = [(3/100) / (5/100)] x 100]%   = [(3/100) x (100/5) x 100] %   = 60%   Correct Option: None of these
Answer: D
If N = 2^0.3 and N^b = 16, b must equal
Select
A) 3/80 B) 3/5 C) 4 D) 5/3 E) 40/3

Solution: 30/100 = 3/10   N = 2 ^ 3/10   N^b = 2^4   (2^3/10)^b = 2^4   b = 40/3   Answer: 40/3
Answer: E
If sushi rows 27 km upstream and 81 km down steam taking 9 hours each, then the speed of the stream	Choose the most appropriate option
A) 12 kmph  B) 13 kmph  C) 22 kmph  D) 20 kmph  E) 15 kmph

Solution: Speed upstream = 27/9= 
27/9 = 3
3 kmph   Speed down stream= 81/3= 
81/3 = 27
27 kmph   Speed of stream= ½ (27-3) = 12 kmph   12 kmphNSWER:12 kmph
Answer: A
What is the number of integers from 1 to 500 (inclusive) that are divisible by neither 10 nor by 15?	Choose the correct answer
A) 170
B) 250
C) 300
D) 560
E) 420

Solution: In 500 consecutive numbers, number of multiples of 10 = 500/10= 
500/10 = 50
50 (Ignore decimals)   In 500 consecutive numbers, number of multiples of 15= 500/15 = 33   Number of multiples of 10*15 i.e. 150 = 500/150 = 3   Number of integers from 1 to 500 that are divisible by neither 10 nor by 15 = 500 - (50 + 33 - 3) {Using the concept of sets here) = 420   Answer is 420
Answer: E
In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that at least 1 women is included in the committee  Choose the correct choice from the following answers.
A) 40 B) 46 C) 52 D) 54 E) 56

Solution: 1W 2M 2W 1M 3W   = 3C1 × 5C2 + 3C2 × 5C1 + 3C3s   = 3 × (5 × 4)/2 + 3 × 5 + 1   = 30 + 15 + 1= 
30 + 15 + 1 = 46
46   Total 5M 3W   8C3= 56   5C3 = 10   At least one women = total - with out women   At least one women = 56 - 10= 
56 - 10 = 46
46   46)
Answer: B
For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60?	Pick one:
A) 10
B) 15
C) 8
D) 12
E) 20

Solution: 4n+7 > 1   4n> -6   n > -(3/2)   n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)   From second constraint   4n+7 < 60   4n< 53   n < 13. 25   n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13)   Combining the two   -1.5 < n<13.25   n = 1 to 13 (48 integers)   and n = -1 and 0   so 15 integers.   15
Answer: B
The average (arithmetic mean) of four different positive integers is 13. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?
Select:
A) 4  B) 3  C) 2  D) 1  E) 0

Solution: Let the second integer be x and the fourth be a.   Then [3x + x + (x+2) + a]/4 = 13   => 5x + 2 + a = 52   => 5x + a = 50   => a = 50 - 5x   From the above equation we can see that a is minimum when x is maximum, provided both are positive   The maximum value that x can take in the above equation while still keeping a positive is x=10   This gives us a=50 - 50= 
50 - 50 = 0
0   Therefore the minimum value that the fourth integer can have is 0. Option 0
Answer: E
Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1111. Find the cost of each ice-cream cup?  Choices: A) 25 B) 66 C) 77 D) 50 E) 91

Solution: Let the cost of each ice-cream cup be Rs.x   16(6) + 5(45) + 7(70) + 6(x) = 1111   96 + 225 + 490 + 6x = 1111   6x = 300 => x = 50.   Answer: 50
Answer: D
Which of the following integers doesn't have a divisor greater than 1 that is the square of an integer?
Choose the correct choice.
A) 12 B) 36 C) 100 D) 61 E) 72

Solution: Prime Factorization   12=2*2*3=2^2*3. Includes a perfect square of 4.   36=2*2*3*3=2^2*3^2. Includes perfect squares of 4 and 9.   100=2*2*5*5=2^2*5^2. Includes the perfect squares 4 and 25.   61=61*1. 61 is prime, no perfect squares so a possibility.   72= 2*3*2*3*2=6^2*3. Includes perfect square of 36.   28=2*2*7=2^2*7. Includes a perfect square of 4.   All but 61 have a perfect square as a factor so the answer is D.   12=4*3. Perfect square of 4.   36=4*9. Perfect squares of 4 and 9.   100=4*25. Perfect squares 4 and 25.   61=61*1. No perfect squares.   72= 36*2. Perfect square of 36.
Answer: D
A card shop contains 10 birthday cards, 10 holiday cards, and 9 graduation cards. If three cards are purchased at random from the shop, what is the probability that the three cards will be of the same type?  Choose the correct choice from the following answers
A) 3/29  B) 12/58  C) 12/840  D) 7/841  E) 12/841

Solution: It doesn't matter which type of card you choose, so:   Probability of choosing 1st card: 1   Probability of choosing 2nd card of the same type: 4/29   Probability of choosing 3rd card of the same type: 3/29   Multiply and you get 12/841   Answer 12/841.
Answer: E
Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $1500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?  Choose the correct choice from the following answers
A) $3,750
B) $5,600
C) $13,500
D) $15,000
E) $22,500

Solution: x=8%   112/x years=112/8= 
112/8 = 14
14 years   Now, money triples every 14 years   Therefore, in 14 yrs , if $1500 triples to $4500, in 28 years, it will again triple to $4500*3=$13,500   Answer $13,500
Answer: C
One-fifth of Ramu’s expenditure is equal to one-half of his savings. If his monthly income is Rs.6300 how much amount does he save?  Choose the correct choice from the following choices:  A) Rs.1550  B) Rs.1800  C) Rs.2000  D) Rs.2350  E) Rs.2450

Solution: Let the saving be Rs. x   Therefore, Expenditure = Rs. (6300-x)   then, (6300-x)* 1/5 = x* 1/2   => 1260- x/5 = x/2   => 1260= x/2 + x/5   => 7x/10 = 1260   x= 1800   ANSWER:Rs.1800
Answer: B
If 1⁄8 of 2⁄3 of 4⁄5 of a number is 12 then 30 per cent of the number will be  Choose the correct option.
A) 48 B) 64 C) 54 D) 42 E) None of these

Solution: Let the number be x.   and 1⁄8 of 2⁄3 of 4⁄5 × x = 12   ∴ 3x⁄10 = 54   Answer 54
Answer: C
An article is bought for Rs.675 and sold for Rs.900, find the gain percent?	Choices
A) 33 1/9%
B) 33 1/6%
C) 33 1/3%
D) 33 8/3%
E) 31 1/3%

Solution: 675 ---- 225   100 ---- ? => 33 1/3%   Answer: 33 1/3%
Answer: C
How many numbers between 0 and 1370 have a prime tens digit and a prime units digit?
Pick one.
A) 204
B) 212
C) 220
D) 228
E) 236

Solution: From 1-9 there are 4 prime numbers {2, 3, 5, 7}. The 10s and 1s of the number must be made with these numbers. The total number of combinations is  4*4= 
 4*4 = 16
16. Thus every set of 100 consecutive positive integers has 16 such numbers.   From 0 to 1300, there  16*13= 
 16*13 = 208
208 such numbers.   From 1301 to 1370, the 10s units can only use 3 numbers {2, 3, 5}. 3*4=12.   The total number is then  208+12= 
 208+12 = 220
220   The answer is 220.
Answer: C
A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 50% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk? Pick.
A) 1:20
B) 1:10
C) 3:8
D) 3:4
E) 3:2

Solution: First of all, let's consider 1 liter of the stuff he is going to sell --- naive customers think it's pure milk, but we know it's some milk-water mixture. He is going to sell this liter of milk-water for $36.   This $36 should be a 50% increase over cost. Here, we need to think about percentage increases as multipliers.   Using multipliers   (cost)*1.50 = $36   cost = 36/1.5 = 360/12 = $24   If he wants a 20% increase over cost on the sale of one liter of his milk-water, the cost has to be $24.   Well, a liter of milk costs $33, so if he is going to use just $30 of milk in his mixture, that's 24/33 = 8/11 of a liter. If milk is 8/11 of the liter, then water is 3/11 of the liter, and the ratio of water to milk is 3:8. Answer choice(3:8)
Answer: C
What percentage of numbers from 1 to 50 have squares that end in the digit 5? Answers:  A) 1  B) 14  C) 10  D) 21  E) 22

Solution: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 5. Such numbers from 1 to 50 are 5,15,25,35,45.   Number of such numbers = 14.   Required percentage = (5/50 * 100)= 
(5/50 * 100) = 10
10%   ANSWER:10
Answer: C
A polygon has 35 diagonals. How many sides does it have?
Self made Choices:	A) 10	B) 13	C) 14	D) 15	E) 16

Solution: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals   n*(n - 3)/2 = 35   n*(n - 3) = 70   Substitute n from the answer choices. n = 10   10nswer: 10
Answer: A
Find the one which does not belong to that group ?	Pick.
A) 233 B) 288 C) 608 D) 287 E) 112

Solution: Explanation:   The sum of the digits in 508, 328, 706 and 148 is 13, but not in 608.   Answer:608
Answer: C
A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $1350 was the net sum to be paid for the entire work, what was the average daily wage of B?  Choices:
A) $144
B) $90
C) $60
D) $54
E) $48

Solution: The correct answer is $90.
Answer: B
For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 105 units raises the average to 55 units per day, what is the value of n? Choose one:
A) 8 B) 10 C) 12 D) 14 E) 16

Solution: The daily production was raised by 5 units for n days, which has a weighting of 5n.   5n = 105-55= 
105-55 = 50
50   n= 10   The answer is 10.
Answer: B
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 900 more than D, what is B's share?  Choose the correct choice from the following answers
A) Rs. 500 B) Rs. 1800 C) Rs. 2000 D) Rs. 2500 E) none of the above

Solution: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.   Then, 4x - 3x = 900   x = 900.   B's share = Rs. 2x = Rs. (2 x 900) = Rs. 1800.   Answer = Rs. 1800
Answer: B
A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? Choose the correct choice from the following choices:  A) 15,2  B) 15, 4  C) 15, 8  D) 15, 5  E) 15,7

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 20 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 30 => x = 15, y = 5.   Answer:15, 5
Answer: D
A man travels 100km by train at 40km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance?	Choose the correct choice from the following answers:
A) 35.3km/hr
B) 40km/hr
C) 48.9km/hr
D) 52.6km/hr
E) 27.6km/hr

Solution: Total distance traveled = 100+200+300+100= 
100+200+300+100 = 700
700km   Total time taken= 100/40 + 200/20 + 300/100 + 100/50= 
100/40 + 200/20 + 300/100 + 100/50 = 35/2 = around 17.5
17.5 hrs   Average speed= 700/17.5= 
700/17.5 = 40
40km/hr approximately ;   Answer is 40km/hr
Answer: B
A baker filled with a measuring cup with 3/4 cup water. He poured 1/2 of the water into the batter. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with? Pick one:  A) 1/8 cup  B) 3/8 cup  C) 1/4 cup  D) 1/2 cup  E) 6/8 cup

Solution: 3/4 is the original water in cup .half in batter.So left is 3/8.   so 50% more than what he started was = 3/4+1/2*(3/4)=9/8   Amount of water needed to add = 9/8 - 3/8=6/8   ANSW6/8 cupR:6/8 cup
Answer: E
How many Kg of sugar must be added to 30 Kg of 2% solution of sugar and water to increase it to a 10% solution?
Choose the correct choice from the following answers:
A) 2.6Kg	B) 4Kg	C) 3.4Kg	D) 1.8Kg	E) None of these

Solution: Explanation :   Solution: Amount of sugar in 30 Kg solution = (2/100 * 30)= 
(2/100 * 30) = 3/5 = around 0.6
0.6 Kg.   Let x Kg of sugar be added. Then, (0.6+x)/(30+x)= 10/100   60+100x = 300+10x   x = 240/90 = 8/3 = 2.6   2.6Kgnswer : 2.6Kg
Answer: A
A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 6t seconds, then what is the length of the platform?  Choose the correct choice from the following.
A) L	B) 3L	C) 5L	D) 7L	E) 9L

Solution: The train passes a pole in t seconds, so velocity v = L/t   (L+P)/v = 6t   (L+P) / (L/t) = 6t   P = 5L   The answer is 5L.
Answer: C
How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution?
Choose the correct choice from the following answers:
A) 45
B) 33 1/3
C) 27
D) 16 2/3
E) 15

Solution: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution?   3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x:   1.5/x = 1/20   x = 30   Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution.   45nswer is 45.
Answer: A
By selling 50 meters of dress. I gain the selling price of 15 meters. Find the gain percent?  Choose the correct choice from the following:
A) 52 6/9% B) 45 8/7% C) 42 6/7% D) 12 8/3% E) 56 6/7%

Solution: 42 6/7%   SP = 42 6/7%P + g   50 SP = 50 42 6/7%P + 15 SP   35 SP = 50 42 6/7%P   35 --- 15 42 6/7%P gain   100 --- ? => 42 6/7%
Answer: C
In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys? Choose the correct choice from the following options.
A) 384
B) 127
C) 276
D) 998
E) 267

Solution: 384verage mark scored by all the three boys =   [64/100 (800) + 36/100 (800) + 44/100 (800)] / 3 = 384.384nswer: 384
Answer: A
√{(8.2)(10^9)} is closest to which of the following?	Choose the correct option:
A) 6,000
B) 12,000
C) 30,000
D) 50,000
E) 90,000

Solution: √{(8.2)(10^9)} = √{(82)(10^8)} = √(82)√(10^8) = (√82) * 10,000 which is about 90,000.   The answer is 90,000.
Answer: E
A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?  Choose the correct choice
A) 126 B) 121 C) 165 D) 134 E) 123

Solution: Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]   = [1600 * 41/40(41/40 + 1)   = [(1600 * 41 * 81)/(40 * 40)]   = Rs. 3321.   C.I. = 3321 - 3200 = Rs.121.   Answer:121
Answer: B
If 9 is added to thrice a number and this sum is multiplied by 6, the result is the same as if the number is multiplied by 7 and 10 is added to the product. What is the number?	Choose the correct choice from the following answers:
A) -7
B) -8
C) -9
D) -10
E) -11

Solution: let the number be x;   6(9+3x)=7x+10;   x=-11   ANSW-11R:-11
Answer: E
At a company, the average wage of male employees is $6 per hour, and the average wage of female employees is $8 per hour. If the average wage of all employees is $7.5 per hour, what is the ratio of the number of male employees to the number of female employees?  Choose the correct choice from the following answers.
A) 1 to 3
B) 2 to 3
C) 3 to 2
D) 5 to 3
E) 2 to 1

Solution: 1 to 3verage hourly wage of male employees = 6 $   1 to 3verage hourly wage of female employees = 8 $   1 to 3verage hourly wage of all employees = 7.5 $   Let number of male employees = m   number of female employees = f   7.5 = (6m + 8f ) / m+f   =>7.5m + 7.5f = 6m + 8f   => .15m = .5f   => m/f = .5/.15 = 1/3   1 to 3nswer 1 to 3
Answer: A
There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more? Choose the correct answer.
A) 11
B) 40
C) 66
D) 55
E) 44

Solution: 760 ---- 22   760 ---- 20   x ----- 19   x*19 = 760*20   x = 800   760   -------   40   Answer:40
Answer: B
Find the odd pair of numbers
1) 55 - 42
2) 69 - 56
3) 48 - 34
4) 95 - 82
5) 45 - 32 Choose the correct choice from the following choices:	A) 55-42	B) 69-56	C) 48-34	D) 95-82	E) 45-32

Solution: minus the numbers   55-42= 
55-42 = 13
13   69-56= 
69-56 = 13
13   48-34= 
48-34 = 14
14   95-82= 
95-82 = 13
13   45-32= 
45-32 = 13
13   here   48-34= 
  48-34 = 14
14 which is not similar to the other, so 48 - 34 is the odd pair of numbers. correct answer (48-34)
Answer: C
An article costing rs.160 is sold at 20% discount on a mark-up price. What is the selling price after
discount?	Pick: A) 106 B) 116 C) 128 D) 136 E) 146

Solution: 160*80/100= 
160*80/100 = 128
128   ANSWER:128
Answer: C
Evaluate: 37 - 18÷3×2 =  Select:
A) 20
B) 25
C) 27
D) 22
E) 17

Solution: According to order of operations, 18÷3×2(division and multiplication) is done first from left to right   18÷3×2 = 6 × 2 = 12   Hence   37 - 18÷3×2 = 37 - 12= 
37 - 12 = 25
25   correct answer 25)25
Answer: B
Three dice are thrown together, Find the probability of getting a total of 5? Choose the correct option
A) 1/2
B) 1/5
C) 3/8
D) 3/14
E) 1/36

Solution: Three different dice are thrown at the same time.   Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.   Number of events of getting a total of 5 = 6   i.e. (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1), (2, 1, 2) and (1, 2, 2)   Therefore, probability of getting a total of 5   P(1/361) = Number of favorable outcomes/Total number of possible outcome   = 6/216   = 1/36
Answer: E
The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?  Choose the correct choice from the following answers.
A) 25  B) 20  C) 30  D) 35  E) 40

Solution: 39x = 5 + 12 + 15 + 19 + (x â€“ 4)44   x = 25   25NSWER 25
Answer: A
If xy > 0, 1/x + 1/y = 6, and 1/xy = 5, then (x+y)/6 = ?  Pick one.
A) 1/25 B) 1/6 C) 1/5 D) 5 E) 6

Solution: (1/X+1/Y)=6 canbe solved as {(x+y)/xy}=5. Substituting for 1/xy=5, we get   x+y=6/5   ==> (x+y)/6= 6/(5*6)=1/5.   1/5
Answer: C
A function g(n), where n is an integer, is defined as the product of all integers from 1 to n. How many of the followings must be a prime number?
g(12) + 2; g(12) + 3; g(12) + 4; and g(12) + 5?	Select:	A) 1	B) 2	C) 3	D) 4	E) none

Solution: g(12) is the product of all integers from 1 to 12, so g(12) = 12!   Thus g(12) is a multiple of all the integers from 1 to 12.   Then g(12) is a multiple of 2, 3, 4, and 5.   2 divides g(12)+2   3 divides g(12)+3   4 divides g(12)+4   5 divides g(12)+5   The answer is none.
Answer: E
A man sells a house for Rs.5,00,000 and loses something, if he had sold it for Rs.6,00,000, his gain would have been trible the former loss. Find the cost price of the horse?
Choose one: A) 5,50,000 B) 5,25,000 C) 5,20,000 D) 5,02,000 E) 6,00,200

Solution: CP = SP + 1CP = SP - g   5,00,000 + x = 6,00,000 - 3x   4x = 1,00,000=> x = 2000   CP = 5,00,000 +2000 = 5,02,,000   Answer: 5,02,000
Answer: D
Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 2. Which of the following operations would decrease the standard deviation of Set J?	Choose the correct choice from the following answers:
A) Divide each term by 2.2
B) Divide each term by b/c
C) Multiply each term by −1
D) Divide each term by d/e
E) Multiply each term by c

Solution: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.   1) It depends on the separation between the successive terms of the set   2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant   3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number   Divide each term by 2.2
Answer: A
Alan bought 180 packets of chocolate. He was able to sell 1/3 of them at a 5% profit, another 1/3 of them at zero profit and the remainder was sold at a 10% loss. Find the total profit or loss made by Alan after selling those 150 packets. A packet sold at a loss had a price of $9.
It's a bit confusing to say 5% of profit. Please provide an intuitive answer if possible. Thanks!!
Choose the correct choice from the following answers
A) 0	B) Profit of $20	C) Loss of $25	D) Profit of $30	E) Loss of $30

Solution: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.   60 packets was sold at a 5% profit --> gives profit of 10*0.05*60= 
10*0.05*60 = 30
$30.   60 packets was sold at a 10% loss --> gives loss of  10*0.1*60= 
 10*0.1*60 = 60
$60.   The overall loss is $30 - $60= $30.   Answer: Loss of $30.
Answer: E
Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 0 through 8 appears in one of these three integers, what is the minimum possible value of the sum of a, b, and c?  Choose the correct choice from the following choices:
A) 45
B) 666
C) 711
D) 801
E) 1368

Solution: According to the stem we should use the digits 0 through 7 to construct 3 three-digit integers, so that their sum is as small as possible.   To minimize the sum, minimize the hundreds digits of a, b, and c, so make them 1, 2, and 3.   Next, minimize tens digits. Make them 0, 4, and 5.   Use the remaining digits (6, 7, and 8) for units digits.   So, a would be 106, b would be 247 and c would be 358.   106 + 247 + 358= 
106 + 247 + 358 = 711
711.   Answer: 711.
Answer: C
what is sum of fist 10 prime numbers? Pick
A) 128  B) 129  C) 117  D) 123  E) 121

Solution: primes are of the form 6n+1 or 6n-1   1st 10 prime numbers are = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29   sum of above numbers = 129   129
Answer: B
Rahim bought 65 books for Rs.6500 from one shop and 35 books for Rs.2000 from another. What is the average price he paid per book ? Choose the correct choice from the following choices.
A) 80
B) 138
C) 100
D) 129
E) 85

Solution: Average price per book   = (6500+ 2000) / (65 + 35)   = 8500 / 100   = Rs.85   Answer:85
Answer: E
My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age of when my brother was born, then, what was the age of my father and mother respectively when my brother was born?  Choose the correct choice from the following answers:	A) 32 yrs, 23 yrs	B) 32 yrs, 29 yrs	C) 35 yrs, 29 yrs	D) 35 yrs, 33 yrs	E) none

Solution: Sol.   Clearly, my brother was born 3 years before I was born and 4 years after my sister was born.   So, father's age when brother was born = (28 + 4)= 
(28 + 4) = 32
32 years.   mother's age when was born= (26 - 3)= 
(26 - 3) = 23
23 years.   32 yrs, 23 yrsnswer 32 yrs, 23 yrs
Answer: A