MU-NLPC/Calc-aqua_rat huggingface dataset:
How many positive integers less than 10,000 are such that the product of their digits is 30?
Choose the correct choice from the following answers:  A) 12  B) 24  C) 36  D) 38  E) 50

Solution: 30 = 1 * 30, 2 * 15, 3* 10, 5 *6   We have the option of using single digits 1,2,3,5 and 6   No : of four digit numbers such that the product is 30   The possible combinations are using digits (1,2,3,5) & (1,1, 5, 6) such that the product 30.   No: of different combinations possible using (1,2,3,5) = 4! = 24   No: of different combinations possible using (5,6,1,1) = 4!/2! = 12 ('1' is repeated twice)   Total 4 digit numbers so that the product is 30 is  24+12= 
 24+12 = 36
36   No: of three digit numbers such that the product is 30   The possible combinations are using digits (2,3, 5) & (1,5,6)   No: of different combinations possible using (2,3,5)= 3! = 6   No: of different combinations possible using (1,5,6) = 3! = 6   Total 3 digit numbers so that the product is 30 is  6+6= 
 6+6 = 12
12   No: of 2 digit numbers such that the product is 30 is 2 (56 and 65)   Total numbers under 10000 such that the product is 30 is  36+12+2= 
 36+12+2 = 50
50   50
Answer: E
Dawson has to secure 30% marks to clear his exam of class 8th.
He got 30 marks and failed by 36 marks.
What is the maximum marks ? Pick one.
A) 180
B) 190
C) 200
D) 210
E) 220

Solution: E   220   To pass the exam ravish needs 30 + 36= 
30 + 36 = 66
66 marks.=> (66/30) *100= 
(66/30) *100 = 220
220
Answer: E
Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
Choose the most appropriate option: A) 226 B) 992 rs C) 665 D) 771 E) 211

Solution: (800*3*3)/100= 
(800*3*3)/100 = 72
72   920 + 72= 
920 + 72 = 992
992   Answer: 992 rs
Answer: B
A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 50 minutes. The total distance is? Choose the correct choice from the following answers
A) 1 km B) 2 km C) 3.19 km D) 4 km E) 5 km

Solution: C   3 km   Let the total distance be 3x km.   Then, x/3 + x/4 + x/5 = 50/60   47x/60 = 50/60 => x = 1.06.   Total distance = 3 * 1.06 = 3.19 km.
Answer: C
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 7x boxes?  Choose one
A) 3 minutes
B) 4 minutes
C) 5 minutes
D) 14 minutes
E) 12 minutes

Solution: Rate = Work / Time   Given Rate of Machine A = X / 10 min   Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .   Rate of Machine B = 4x / 10   we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates   let's first find the combined Rate of Machine A and B   Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10   Now combine Time = combine work needs to be done / Combine Rate = 7x/5x * 10 = 14 Min   Ans: 14 minutes7 /5  * 10= 
7 /5  * 10 = 14
14 Min   Ans: 14 minutes
Answer: D
A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,750 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?	Choose one
A) 25%
B) 30%
C) 35%
D) 40%
E) 45%

Solution: E for me.   Let managers comminsion rate be M.   m*5000+ 2*0.05*5000=2750   5000*m=2250   m=45/100=45%
Answer: E
If you write down all the numbers from 1 to 100, then how many times do you write 3 ? Select the correct option:
A) 33
B) 38
C) 20
D) 88
E) 28

Solution: Explanation:   Clearly, From 1 to 100, there are ten numbers with 3 as the unit's digit - 3, 13, 23, 33, 43, 53, 63, 73, 83, 93 and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.   So, required number = 10 + 10= 
10 + 10 = 20
20.   Answer: 20) 20
Answer: C
R is a set containing 8 different numbers. S is a set containing 7 different numbers, all of which are members of R. Which of the following statements CANNOT be true?	Pick.
A) The range of R is less than the range of S. B) The mean of R is greater than the mean of S. C) The range of R is equal to the range of S. D) The mean of R is less than the mean of S. E) The mean of R is equal to the mean of S.

Solution: The range of a set is the difference between the largest and smallest elements of a set.   So, the answer is straight A: the range of a subset cannot be more than the range of a whole set: how can the difference between the largest and smallest elements of a subset bemorethan the difference between the largest and smallest elements of a whole set.   As for D:   Consider set R to be {-3, -2, -1, 0, 1, 2, 3, 4} --> mean=0.5.   (D) The mean of R is less than the mean of S --> remove the smallest term -3, then the mean of S will be 1, so more than 0.5. The range of R is less than the range of S.NSWER IS The range of R is less than the range of S.
Answer: A
A certain list has an average of 6 and a standard deviation of B (B is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than B?	Choose one.
A) (-6;0) B) (0;0) C) (0;6) D) (0;12) E) (6;6)

Solution: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.   So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.   According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.   Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.   (6;6))
Answer: E
In a jar there are 20 white balls, 25 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 22 balls of the same color?
Choose one:	A) a)	23	B) b)	46	C) c)	57	D) d)	63	E) e)	67

Solution: Here, we need to find minimum number of marbles to be taken out to get 22 marbles of same color.   For a instance, if we take 20 white marbles 1st and followed by 21 Green and then 21 Blue.   Total will be   20 + 21+ 21= 
  20 + 21+ 21 = 62
62 draws.   If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 22.   So Minimum we need to take 62+1= 
62+1 = 63
63 Times to get 22 marbles of same color(either Green or Blue).   Answer : d)	63.
Answer: D
If the sides of a square are doubled in length, the area of the original square is now how many times as large as the area of the resultant square?	Options:
A) 25%  B) 50%  C) 100%  D) 200%  E) 400%

Solution: Let the original square have sides of length L and the new square have sides of length 2L.   The resulting areas are L^2 for the original square and 4L^2 for the new square (as the length of the side is square to get the area).   The original square's area is L^2/4L^2 or 25% of the new square's area. Choice 25%
Answer: A
The price of cooking oil has increased by 25% . The percentage of reduction that a family should effect in the use of cooking oil so as not to increase the expenditure on this account is :
Choose the correct option:
A) 15%
B) 20%
C) 25%
D) 30%
E) None

Solution: Explanation:   Reduction in consumption:   =(25/125×100)%=20%   Correct Option: 20%
Answer: B
A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 11% below the cost price of the claimed weight.  Choose the correct choice from the following answers: A) 19.81% B) 22.38% C) 37.5% D) 25% E) 37.5%

Solution: There is a one step calculation method too. It requires more thought but is faster.   The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer $110. Hence, in effect, there is a 10% mark up.   While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only $80 for it. So this is again a mark up of $20 on $80 which is 25%.   22.38%ut he also sells at 11% less   (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)   11/10 * 5/4 * 89/100 = (1 + p%)   profit % = 22.38%   22.38%
Answer: B
The perimeter of a semi circle is 144 cm then the radius is?	Options.
A) 29 B) 28 C) 277 D) 24 E) 21

Solution: 36/7 r = 144 => r = 28   Answer:28
Answer: B
Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 35 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?  Choose the correct choice:
A) 2:5  B) 5:15  C) 3:5  D) 4:7  E) 14:5

Solution: Answer = B) 5:15   ........................ Rum ..................... Coke ................. Total   First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)   Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)   Total .................. 10 ............................. 28 .................... 38   Ratio = 10:30 = 5:15   5:15
Answer: B
How many pages the book have, if total 306 digits are used to form the page numbers?
Options:  A) 135 pages  B) 136 pages  C) 137 pages  D) 138 pages  E) 139 pages

Solution: First 9 pages .. 9 digits   next 90 pages .. 180 digits   next 39 pages ... 117 digits   ----------------------   Total ...138 pages ...300 digits   ANSWER:138 pages
Answer: D
Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?	Choose the correct choice:
A) 2197 feet
B) 2420 ft
C) 2500 feet
D) 2629 feet
E) None of these

Solution: Distance =(1100*11/5)= 
(1100*11/5) = 2_420
2420 feet.   Correct Option: 2420 ft
Answer: B
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 36 times, A has killed:
Options
A) 60 birds B) 72 birds C) 30 birds D) 80 birds E) 40 birds

Solution: Let the total number of shots be x. Then,   Shots fired by A =(5/8)x   Shots fired by B =(3/8)x   Killing shots by A =(1/3)of	(5/8)x=(5/24)x   Shots missed by B =(1/2) of (3/8)x	=(3/16)x   3x/16= 36 or x =(36 x 16)/3= 192.   Birds killed by A =(5x/24)	=(5/24*192)= 
(5/24*192) = 40
40.   Answer is 40 birds
Answer: E
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is?	Choose the most appropriate option:
A) 35
B) 50
C) 88
D) 66
E) 22

Solution: Speed of the train relative to man   = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr   = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5   = 30 ==> x   = 35 km/hr.   35nswer:35
Answer: A
On a store counter are exactly two boxes containing only purple marbles and yellow marbles. Box A has 30 purple marbles and 20 yellow marbles; box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one of the boxes and then randomly selects one marble from the box, what is the probability that the marble selected will be purple?
Choose the correct answer.
A) 3/20	B) 3/10	C) 9/20	D) 3/5	E) 9/10

Solution: We are given that box A has 30 purple marbles and 20 yellow marbles and that box B has 15 purple marbles and 35 yellow marbles. We need to determine the probability, when selecting one marble from the box, of selecting a purple marble. Since we have two boxes, A and B, there are multiple scenarios to account for when selecting the marbles. We must account for the probability of first selecting either box and then secondly for selecting a purple marble. Let’s start with Box A.   P(selecting box A) = ½   P(selecting a purple marble in box A) = 30/50 = ⅗   Thus, the probability of selecting a purple marble from box A is ½ x ⅗ = 3/10   Next we can determine the probability of selecting a purple marble from box B.   P(selecting box B) = ½   P(selecting a purple marble in box B) = 15/50 = 3/10   Thus, the probability of selecting a purple marble from box B is ½ x 3/10 = 3/20   Now we can determine the probability of selecting a purple marble from box A or box B:   3/10 + 3/20 = 6/20 + 3/20 = 9/20.   Answer: 9/20
Answer: C
$ represents addition and * represents subtraction,what is the value of the following expression?
15 * 5 $ 15 $ 10 $ 30 * 25 * 35 * 25 $ 20 * 25 * 20  Pick:
A) -15 B) -35 C) -55 D) -45 E) -65

Solution: 15-5+15+10+30-25-35-25+20-25-20   =10+15+10+30-25-35-25+20-25-20   =25+10+30-25-35-25+20-25-20   =35+30-25-35-25+20-25-20   =65-25-35-25+20-25-20   =40-35-25+20-25-20   =5-25+20-25-20   =-20+20-25-20   =0-25-20   =-45   ANSWER:-45
Answer: D
In a tournament prize of 1st, 2nd, and 3rd is given in same interval.If total amount of prize Rs 4800 and prize of 1st is Rs 2000, find the interval??	Choose the correct answer:
A) 600 B) 450 C) 350 D) 550 E) 400

Solution: Let the interval is x.   prize of 2nd and 3rd is 2000-x and 2000-2x   2000+2000-x+2000-2x = 4800   x = 400   Answer :400
Answer: E
A player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many diamonds as spades and twice as many hearts as diamonds. How many clubs does he hold  Choose one:
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: Explanation:   Clearly, the black cards are either clubs or spades while the red cards are either diamonds or hearts.   Let the number of spades be x. Then, number of clubs = (7 - x).   Number of diamonds = 2 x number of spades = 2x;   Number of hearts = 2 x number of diamonds = 4x.   Total number of cards = x + 2x + 4x + 7 - x = 6x + 7.   Therefore 6x + 7 = 13 6x  6  + 7= 
 6  + 7 = 13
13 6x= 6 x - 1.   Hence, number of clubs = (7 - x) = 6.   Answer: 6
Answer: C
The length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is: Pick one: A) 239 B) 277 C) 215 D) 88 E) 232

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30   = 25/2 ==> 2(160 + X) = 750 ==> X = 215 m.   Answer: 215
Answer: C
If x = 9/3 and y = 4/3, what is the value of the expression -2x – y^2?	Choose the correct choice from the following
A) -28/51	B) -70/9	C) 45/87	D) 13/21	E) 14/40

Solution: x = 9/3 and y = 4/3   ==> -2(9/3) - (4/3)^2 = -18/3 - 16/4 = -70/9   Ans: -70/9
Answer: B
A rower can row upstream at 22 kph and downstream at 34 kph. What is the speed of the rower in still water?
Options: A) 28 B) 29 C) 30 D) 31 E) 32

Solution: Let V be the rower's speed in still water.   Let S be the speed of the current in the stream   V-S = 22   V+S = 34   When we add the two equations, we get: 2V = 56   Then V = 28 kph.   The answer is 28.
Answer: A
A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,000 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
Choose the correct choice from the following choices
A) 25 B) 30 C) 35 D) 39 E) 45

Solution: 39ay 1   2t+3=21   t=9   39ay 2   t+3   9+3= 
9+3 = 12
12   9r+12(r+15)=1000   r=39   Answer:39
Answer: D
If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability R that their product will be of the form of x^2-(by)^2, where b is an integer?  Choose the most appropriate option:
A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) R=1/6

Solution: Only (X+y)(x-y) pair will give the form x^2-(by)^2   The probability of selecting these two pairs are 1/4 * 1/3 = 1/12, assuming x+y is picked first, then x-y, but x-y can be picked first followed by x+y. So the probability R= 1/12 * 2 = 1/6   Ans R=1/6
Answer: E
A man sells a horse for Rs.140 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse? Options:
A) 420
B) 299
C) 277
D) 860
E) 771

Solution: CP = SP + 1CP = SP - g   140 + x = 980 - 2x   3x = 840=> x = 280   CP = 280 + 140= 
280 + 140 = 420
420   420nswer: 420
Answer: A
A student travels from his house to school at 10 km/hr and reaches school 1 hour late. The next day he travels 12 km/hr and reaches school 1 hour early. What is the distance between his house and the school?	Choose the correct answer: A) 100 B) 105 C) 110 D) 115 E) 120

Solution: Let x be the distance from his house to the school.   x/10 = x/12 + 2   6x = 5x + 120   x = 120 km   The answer is 120.
Answer: E
A box contains 3 red balls and 4 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?	Pick.
A) 7/4  B) 1/2  C) 1/2  D) 5/8  E) 2/3

Solution: My complicated version of your simple approach   Let the 5 black balls be BBBBB and 3 Red Balls be RRR   They can be arranged in 8 slots _ _ _ _ _ _ _ _   in (7!)/ (4!x3!)   If the fourth slot is Black ball then the arrangement will be to fill   _ _ _ B _ _ _ _   we have 7 slots and 3 Black (BBB) and 3 Red (RRR)   They can be arranged in (6!)/ (3!x3!)   Hence required probability = [(7!)/ (4!x3!)]/[(6!)/ (3!x3!)]   7/4ns = 7/4   7/4
Answer: A
A sum fetched total simple interest of 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?	Choose the correct choice from the following answers: A) 8925 B) 8032.5 C) 4462.5 D) 8900 E) None of these

Solution: Let the sums be P.   Now, 45% of P = 4016.25   or, P = 8925   8925nswer 8925
Answer: A
When a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $112.70, what was the total value of the item? Select the correct option:
A) $2420	B) $2610	C) $2860	D) $3050	E) $3270

Solution: Let x be the value of the item.   0.07*(x-1000) = 112.70   x = 2610   The answer is $2610.
Answer: B
A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?
Choose the correct option: A) 1/720 B) 1/80 C) 1/10 D) 1/9 E) 1/5

Solution: Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the treasurer is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/10+1/10=2/10.   Answer: 1/5.
Answer: E
On a two-dimensional coordinate plane, the line z = x^2 - x^3 touches the x-axis in how many places?
Pick.
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Apparently it's z = x^2 - x^3 instead of z = x^2 - z^3.   In this case: the x-intercept is the value(s) of x for z = 0.   0 = x^2 - x^3;   0 = x^2(1 - x);   x = 0 or x = 1.   Answer: 2.
Answer: C
. In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 80 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
Pick one.
A) 50%
B) 53%
C) 54%
D) 55%
E) 56%

Solution: Registered voters = 100   D = 60   R = 40   80% of D ( 60) = 48   20% of R ( 40 ) = 8   Total voter% of registered voters = 56 / 100   56% Ans 56%
Answer: E
A string of 50 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.05, what is the probability that the string of light bulbs will fail during the time period T? Choices.
A) 0.05  B) (0.05)^50  C) 1 - (0.96)^50  D) 1 - (0.95)^50  E) (0.95)^50

Solution: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.   The opposite event is when none of the 50 light bulbs fails, since the probability of each light bulb not to fail is 1-0.05= 
1-0.05 = 0.95
0.95 the the probability that none of the 50 light bulbs fails is 0.95^50.   Hence, the probability that at least one light bulb fails is 1-0.95^50.   Answer: D.   Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 50, then according to your logic the probability that the string of light bulbs will fail would be 100*0.05= 
100*0.05 = 5
5, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: D
You own thirteen pairs of socks, all different, and all of the socks are individually jumbled in
a drawer. One morning you rummage through the drawer and continue to pull out socks until
you have a matching pair. How many socks must you pull out to guarantee having a matching
pair? Choose the correct choice from the following
A) 3 B) 12 C) 13 D) 14 E) 25

Solution: You might be unlucky and have the first thirteen socks all different, but then the 14th   has to match one of them.   correct answer 14
Answer: D
A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse? Options:
A) 188
B) 786
C) 991
D) 860
E) 121

Solution: CP = SP + 1CP = SP - g   800 + x = 980 - 2x   3x = 180 => x = 60   CP = 800 + 60= 
800 + 60 = 860
860   Answer: 860
Answer: D
A new savings account offers 6 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000? Choose the correct option:  A) $80.00  B) $84.40  C) $360.00  D) $6,360.00  E) $6,365.40

Solution: Solution -   At the end of the first 6 months, the interest earned is (1/2)*6000*(6/100)= 
(1/2)*6000*(6/100) = 180
180. (6 months is 1/2 in the equation since 6% is a yearly rate, not for six months).   Since the interest is compounded, the second six months of the year is getting interest on original and first six months interest i.e.,6180.   The interest earned during the final 6 months of the year is   (1/2)*6180*(6/100)= 
  (1/2)*6180*(6/100) = 927/5 = around 185.4
185.4   The total balance at the end of the year is   6000+180+185.4= 
  6000+180+185.4 = 6_365.4
6365.4   Answer: $6,365.40
Answer: E
A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 30 meters apart,then at what speed is the train traveling? Choose the most appropriate option.
A) 100km/hr
B) 110km/hr
C) 50km/hr
D) 150km/hr
E) 90km/hr

Solution: Number of gaps between 51 telephone posts = 50   Distance traveled in 1 minute = 50*30= 
50*30 = 1_500
1500m= 1.5km   Speed = 60*1.5=900km/hr   Answer is 90km/hr
Answer: E