MU-NLPC/Calc-aqua_rat huggingface dataset:
Set W consists of all the prime numbers between 10 and 25. What is the range of set W? Pick one:
A) 12	B) 13	C) 16.6	D) 17	E) 23

Solution: 12nswer of set W is 12.
Answer: A
Fake City has a population of 200,221 people and nine districts that are represented by nine members of the city council.They wish to redraw the district lines so that each district consists of the same amount of people. How many people would have to move into Fake City for them to achieve their goal? Choose the correct choice:
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: To figure this out, we use the divisibility rule of 9 to get our answer. We add the digits together and get a seven. Since we are adding people to the population, we add two(9 can be divided by 9) to people to the city to get a population of 200,223 people. Answer is option 2
Answer: B
The number of new words that can be formed by rearranging the letters of the word 'LIVE' is? Choose the correct choice from the following answers:
A) 15  B) 20  C) 25  D) 32  E) 23

Solution: Number of words which can be formed   = 4! - 1 = 24- 1= 
24- 1 = 23
23.   Answer:23
Answer: E
Three numbers are in the ratio 1:4:6 and their H.C.F is 9. The numbers are:	Choose the correct choice from the following choices:  A) 1,4,6  B) 12,24,36  C) 10, 20, 30  D) 12, 24, 36  E) 9,36,54.

Solution: Let the required numbers be x, 4x and 6x. Then, their H.C.F = x. So, x = 9.   The numbers are 9,36,54.   ANSW9,36,54.R:9,36,54.
Answer: E
If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Choose one
A) 33 1/8% B) 33 7/3% C) 33 1/3% D) 33 1/6% E) 32 1/3%

Solution: 1/4 33 1/3%P = 210 SP = 21*(80/100) = 168   SP = 840*(120/100)= 
840*(120/100) = 1_008
1008   1008 - 168= 
1008 - 168 = 840
840   3/4 SP= 630   Gain = 210   630 --- 210   100 --- ? => 33 1/3%   Answer:33 1/3%
Answer: C
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets 1000 more than D, what is B’s share?	Select the correct option:
A) 500	B) 1500	C) 2000	D) 1400	E) None of these

Solution: Let the shares of A, B, C and D be 5x, 2x, 4x, 3x respectively.   Then, 4x – 3x = 1000 ⇒ x = 1000   ∴ B’s Share = 2x = 2000   Answer 2000
Answer: C
Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and the remainder at 40 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator? Select
A) 110 B) 300 C) 24,000 D) 3,000 E) 30,000

Solution: total distance = d   total time taken = x/(100*60) + (100-x)/(100*40)   speed = distance / time   gives numerator = 24000   Answer : 24,000
Answer: C
The perimeter of a semi circle is 122 cm then the radius is?  Answers.
A) 17	B) 28	C) 24	D) 11	E) 12

Solution: 36/7 r = 122 => r   = 24   Answer: 24
Answer: C
Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 47 years. The age of E is?
Answers: A) 45 B) 47 C) 48 D) 35 E) 46

Solution: Solution   5 years ago average age of A,B,C,D = 45 years   => 5 years ago total age of A, B, C, D = 45 x 4 = 180 years   => Total present age of A, B, C, D = 180 + 5x4 = 200 years   If E's present age is x years = 200+x/5= 47   x=35 years. Answer 35
Answer: D
A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If15 were to be added to each score, which of these three statistics would change?  Answers.
A) The mean and the median  B) The median only  C) The standard deviation only  D) The mean only  E) The mean and the standard deviation

Solution: The correct answer is The mean and the median
Answer: A
A stock trader originally bought 300 shares of stock from a company at a total cost of m dollars. If each share was sold at 20% above the original cost per share of stock, then interns of m for how many dollars was each share sold?
Select the correct option:
A) a) 2m/300	B) b) m/300	C) c) m/200	D) d) 3m/250	E) e) 350/m

Solution: Let Cost of 300 shares be $ 3000   So, Cost of 1 shares be $ 10 =>m/300   Selling price per share = (100+20)/100 * m/300   Or, Selling price per share = 6/5 * m/300 => 3m/250   Hence answer will be (d) 3m/250)
Answer: D
If e is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of e ? Choose the correct choice.
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: Answer is C.   numbers in format of 3^k in the series from 1 to 30 inclusive e are: 3*1, 3*2, 3*3, 3*4, 3*5, 3*3*2, 3*7, 3*8, 3*3*3, 3*10. Total number of 3 = 13. So k=14.
Answer: C
An enterprising businessman earns an income of Re 5 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 10th day of business, he earns an income of: Answers.
A) 21
B) 22
C) 20
D) 45
E) 30

Solution: 2nd day he earns = 3(2 – 5)   3rd day he earns = 3(3 – 5)   On 20th day he earns 3(20 -5) = 45 rupees   ANSWER:45
Answer: D
2,345
2,354
2,435
.....
....
+5,432
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 2,3,4,5 exactly once in each integer. What is the sum of these 24 integers?
Choose the correct choice from the following choices
A) 81,218 B) 85,546 C) 89,928 D) 93,324 E) 97,716

Solution: In each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.   Then the sum equals 6(2222)+6(3333)+6(4444)+6(5555) = 93,324   The answer is 93,324.
Answer: D
A man sitting in a train which is travelling at 60 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?  Pick
A) 52 kmph. B) 62 kmph. C) 72 kmph. D) 80 kmph. E) None

Solution: Solution   Relative Speed	= (280 / 9)m/sec   = (280/9 x 18/5)   = 112 kmph.   Speed of the train	= (112 - 60)= 
(112 - 60) = 52
52 kmph.   52 kmph.nswer 52 kmph.
Answer: A
If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
Options.
A) 70%  B) 47%  C) 49%  D) 40%  E) 20%

Solution: 8 = (1*20*R)/100   R = 40%   Answer:40%
Answer: D
The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 40 feet wide by 150 feet long by 10 feet deep and is currently at 80% capacity, how long will it take to drain the pool? Choose the correct choice from the following answers:  A) 1000  B) 800  C) 600  D) 700  E) 500

Solution: volume of pool = 40*150*10 cu.ft , 80% full = 40*150*10*0.8 cu.ft water is available to drain.   draining capacity =60 cu.ft /min therefore time taken = 40*150*10*0.8/ 60= 
40*150*10*0.8/ 60 = 800
800 min   800
Answer: B
An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 4 miles per hour, then 5 miles per hour, then 6 miles per hour. If the test took 37 hours to complete, how many miles was the car driven during the entire test?	Answers.
A) 100	B) 120	C) 180	D) 200	E) 240

Solution: x is the segment to be traveled   x/4+x/5+x/6 =37   or 74x/120 =37   x = 60miles . total distance =3*60= 
3*60 = 180
180 miles   180
Answer: C
Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have?	Select.
A) 65 toys
B) 55 toys
C) 47 toys
D) 27 toys
E) 32 toys

Solution: If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys   49 - 5= 
49 - 5 = 44
44 for Tom and Bob   If distributed equally, each one will have   44 ? 2= 22 toys   Bob has 5 more toys than Tom, so Bob has     22 + 5= 
  22 + 5 = 27
27 toys   correct answer 27 toys
Answer: D
A certain store sells all maps at one price and all books at another price. On Monday the store sold 10 maps and 8 books for a total of $22.00, and on Tuesday the store sold 20 maps and 15 books for a total of $60.00. At this store, how much less does a map sell for than a book?	Pick.
A) $-5.4	B) $0.50	C) $0.75	D) $1.00	E) $l.25

Solution: 10x+8y=22   20x+15y=60   multiply eq 1 by 2 and eq 2 by 1   20x+16y=44   20x+15y=60   subtracting 1 from 2   y=-16   therefore   x=10.6   difference in price =-5.4   $-5.4
Answer: A
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 11000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is
Pick one: A) 14 B) 21 C) 22 D) 23 E) NONE

Solution: Sol.   Let the total number of workers be x. Then,   8000x = (10000 × 7) + 6000 ( x – 7)   ‹=› 2000x = 28000   ‹=› x = 14.   14nswer 14
Answer: A
Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 5 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive?
Choose the correct choice from the following
A) 20% B) 17% C) 4.0% D) 3.3% E) 2.8%

Solution: Share of each child(5 no) and (total share of grand children together)1 no= 1/(5+1)=1/6   As the grand children again equally share the part given to them:   Share of each grand child =[(1/6)/6]=1/36=2.8%   ANSW2.8%R:2.8%
Answer: E
3 men or 6 women can do a piece of work in 22 days. In how many days will 12 men and 8 women do the same work?  Choose the correct answer
A) 15/9 days	B) 15/4 days	C) 18/4 days	D) 11/4 days	E) 33/8 days

Solution: 3M = 6W ---- 22 days   12M + 8W -----?   24W + 8 W = 32W ---?   6W ---- 22 32 -----?   6 * 22  24  + 8= 
 24  + 8 = 32
32W ---?   6W ---- 22 32 -----?   6 * 22= 32 * x => x = 33/8 days   Answer:33/8 days
Answer: E
A rectangular floor that measures 15 meters by 18 meters is to be covered with carpet squares that each measure 3 meters by 3 meters. If the carpet squares cost $12 apiece, what is the total cost for the number of carpet squares needed to cover the floor?	Options
A) $200
B) $240
C) $360
D) $960
E) $1,920

Solution: The width of the rectangular floor(15 m) is a multiple of one side of the square(3 m), and the length of the floor(18 m) is also a multiple of the side of the square. So the number of carpets to cover the floor is (15/3)*(18/3)= 
(15/3)*(18/3) = 30
30.   The total cost is 30*12= 
30*12 = 360
$360.   The answer is, therefore, $360.
Answer: C
Which of the following is not divisible by 3?
Choose one:	A) 10,395	B) 41,714	C) 15,354	D) 30,708	E) 29,313

Solution: Divisibility rule of 3: The sum of the digits of the number should be divisible by 3   Option A: 10395, Sum = 18. Divisible by 3   Option B: 41714, Sum = 17, Not divisible by 3. Hence the number 41714 is also not divisible by 3   Option C: 15354, Sum = 18, Divisible by 3   Option D: 30708, Sum = 18, Divisible by 3   Option E: 29313, Sum = 18, Divisible by 3   Correct Option: 41,714
Answer: B
On my sister's birthday, she was 147 cm in height, having grown 5% since the year before. How tall was she the previous year? Choose the correct choice from the following options.
A) 145 cm B) 140 cm C) 142 cm D) 138 cm E) 135 cm

Solution: Let the previous year's height be x.   1.05x = 147   x = 140   The answer is 140 cm.
Answer: B
In how many different ways can the letters of the word LEADING be arranged in such a way that the vowels always come together ?  Choose the most appropriate option
A) 39600
B) 360
C) 40320
D) 720
E) None of these

Solution: LDNG V(EAI) so 5 letters can arrange in 5!=120 and 3 vowels can arrange in 3!=6. so Ans=120*6= 
120*6 = 720
720   ANSWER:720
Answer: D
By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?	Choose the correct choice from the following choices:	A) 8	B) 9	C) 7	D) 6	E) 5

Solution: 80% --- 12   120% --- ?     80/120 * 12= 
  80/120 * 12 = 8
8   8nswer: 8
Answer: A
Johny went up a certain hill at the rate of one and a half kilometers per hour and came down at the rate of four and a half kilometers per hour, so that it took just four hours to make the double journey. How far was it to the top of the hill ?  Choose one:
A) 3 km
B) 6 km
C) 4.5 km
D) km
E) none of the above

Solution: Assume the distance to the top of the hill (1 way) as: x   Now, speed=distance/time => time=distance/speed   So, for the first half of the journey, he traveled uphill at 1.5km/hr, so the time taken for the first leg of the journey is: x/1.5.   For the second half, he traveled downhill at 4.5km/hr, so the time taken for the second leg of the journey is: x/4.5   Now, the total time for the trip is given as 4 hrs.   Equating, (x/1.5)+(x/4.5)=4 => (3x+x)/4.5=4 => x=4.5 km   So, the distance one side is = 4.5 km.   The OA mentioned is 9km, which is exactly double of this distance, i.e., the total distance traveled during both legs of the journey, but the question only asked for the distance till the top of the hill, i.e., one way, so the answer should be 4.5km   4.5 kman someone assist me in understanding where am I wrong here?
Answer: C
Find the cost of fencing around a circular field of diameter 39 m at the rate of Rs.1.50 a meter?
Choose one:
A) 287
B) 132
C) 156
D) 158
E) 128.73

Solution: 2 * 22/7 * 19.5 = 122.6   122.6 * 1 1/2 = Rs.128.73   Answer: 128.73
Answer: E
a train 50 m from bridge going east to west with a speed 10m/sec another train which is other side of bridge and 100 m from the bridge going west to east.if both will come at the same time on bridge,train will collide.lenght of bridge is 50m.what could maximum speed of second train so that first train pass the bridge before reaching second train.neglect the length of train.
Options.
A) 20 B) 15 C) 12 D) 8 E) 10

Solution: time taken by first train to cross the bridge=(50+50)/10= 
(50+50)/10 = 10
10sec.   so this is the min. time which second train should take to reach the bridge,   max. speed of second train= 100/10= 
100/10 = 10
10m/sec   answer 10
Answer: E
Of the teams competing in the world archery championships, Forty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
Pick one.
A) 13/20 B) 15/20 C) 13/15 D) 7/20 E) 13/17

Solution: Half as manymeans half of EU, then   EU 40%   US 20%   AF 5%   the rest is 35%, answer 7/20
Answer: D
What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
Choose the most appropriate option:
A) 20 B) 21 C) 14 D) 1 E) 6

Solution: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.   Number of such number =14   Required percentage =14/70*100= 
14/70*100 = 20
20%   20NSWER 20
Answer: A
A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?	Answers
A) 2878	B) 2778	C) 1000	D) 2997	E) 2701

Solution: Along one edge, the number of small cubes that can be cut   = 100/10= 
100/10 = 10
10   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10= 
10 * 10 * 10 = 1_000
1000   Answer: 1000
Answer: C
If Sam goes to the store that was having a big sale and comes home saying he got a discount of Rs.140 from the original purchase price of Rs.400. What is the percentage of the rebate that Sam got from the store?  Choose the most appropriate option: A) 20% B) 25% C) 30% D) 35% E) 40%

Solution: Explanation:   Rebate = Rs.140; Original Price = Rs.400   % Rebate = Rs.140/Rs.400 = 0.35 .140/  .400= 
.140/  .400 = 0.35
0.35= 35%   Correct Option : 35%
Answer: D
The largest three digit number which is a perfect cube, is: Choose the most appropriate option.
A) 125	B) 999	C) 343	D) 512	E) 729

Solution: 729xplanation:     9*9*9= 
  9*9*9 = 729
729   Answer: 729
Answer: E
If the ratio of the areas of two squares is 225:256, then the ratio of their perimeters is :	Choose the correct choice from the following:
A) 15:12  B) 15:14  C) 15:16  D) 15:22  E) None of these

Solution: Explanation:   a2/b2=225/256=15/16   <=>4a/4b=4∗15/4∗16   =15/16=15:16   Option 15:16
Answer: C
In a apartment, 40% of the people speak English, 10% speak Hindi and 20% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?	Choose the correct choice from the following answers:
A) 1/3
B) 2/3
C) 3/5
D) 2/7
E) 2/9

Solution: P (E) = 40 / 100 = 4 / 10 , P (H) = 10 / 100 = 1 / 10 and P (E âˆ© H) = 20 / 100 = 2 / 10   P (E or H) = P (E U H)   = P (E) + P (H) - P (E âˆ© H)   = (4 / 10) + (1 / 10) - (2 / 10) = 4 / 10 = 3/5   3/5
Answer: C
Jane and Thomas are among the 9 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 9 people if at least one of either Jane or Thomas is to be selected? Choose the correct answer.
A) 67 B) 73 C) 79 D) 85 E) 91

Solution: The total number of ways to choose 4 people from 9 is 9C4 = 126.   The number of committees without Jane or Thomas is 7C4 = 35.   There are  126-35= 
 126-35 = 91
91 possible committees which include Jane and/or Thomas.   The answer is 91.
Answer: E
Which is better investment, 12% stock at par with an income tax at the rate of 5paise per rupee or 14 2/7 % stock at 120 free from income tax Choose one:
A) 12%	B) 142/7 %	C) Both are qually good	D) cannot compared	E) none of these

Solution: Let the investment in each (100*120)   Income in first case = (12/100*100*120)= 
(12/100*100*120) = 1_440
1440   Net income=(1440-5/100*1440)= 
(1440-5/100*1440) = 1_368
1368   Income in second case=((100/2*20)*100*120)=1428.57   Clearly, 14 2/7 % stock at 120 is better   ANSWER 142/7 %
Answer: B
It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010? Pick:	A) Tuesday	B) Saturday	C) Monday	D) Friday	E) Sunday

Solution: On 31st December, 2005 it was Saturday.   Number of odd days from 2006 to 2009 = (1 + 1 + 2 + 1)= 
(1 + 1 + 2 + 1) = 5
5 days.   On 31st December 2009, it was Thursday.   Thus, on 1st Jan, 2010 it is Friday   Answer is Friday.
Answer: D
The cost of one photocopy is $0.02. However, a 25% discount is offered on orders of more than 100 photocopies. If Arthur and David have to make 80 copies each, how much will each of them save if they submit a single order of 160 copies? Choose the correct answer.
A) $0.32	B) $0.40	C) $0.45	D) $0.48	E) $0.54

Solution: If Arthur and David submit separate orders, each would be smaller than 100 photocopies, so no discount. Each would pay (80)*($0.02) = $1.60, or together, a cost of $3.20 --- that's the combined no discount cost.   If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer  (80)*( 0.02)= 
 (80)*( 0.02) = 1.6
$1.60, or together, a cost of $3.20 --- that's the combined no discount cost.   If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer=($0.40).
Answer: B
Five friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount?  Choose one.
A) 14% B) 17% C) 20% D) 25% E) 33%

Solution: Let x be the original price of one ticket.   The total original cost is 5x.   The new cost is 6y, where y is the discounted price of one ticket.   5x = 6y   y = 5x/6 which is about 0.83x which is a discount of about 17%.   The answer is 17%.
Answer: B
0.009/x=0.02. find the value of X  Select the correct option
A) 0.045 B) 0.09 C) 0.9 D) 9 E) 90

Solution: x=0.009/0.045=0.9   0.045NSWER:0.045
Answer: A
A courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?
Choose the correct choice from the following answers:
A) 22877 B) 27778 C) 20000 D) 27999 E) 17799

Solution: Number of bricks =20000ourtyard area/1 brick area   =(2500×1600/20×10)=20000   Answer: 20000
Answer: C
If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?	Choose the correct answer
A) $30.60  B) $60.60  C) $70.60  D) $40.60  E) $50.60

Solution: The tip is 20% of what he paid for lunch. Hence   tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10   Total spent     50.50 + 10.10= 
  50.50 + 10.10 = 60.6
$60.60   correct answer $60.60
Answer: B
The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 30 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
Choices
A) 15
B) 30
C) 35
D) 45
E) 55

Solution: Let the number of students who wrote the exam be x.   Total marks of students = 80 x.   Total marks of (x - 5) students = 90(x - 5)   80x - (5 * 30) = 90(x - 5)   300 = 10x => x = 30   ANSWER:30
Answer: B
Eden drove an average speed of 15 miles per hour for the first 20 miles of a tripthen at a average speed of 30 miles/hr for the remaining 20 miles of the trip if she made no stops during the trip what was eden's avg speed in miles/hr for the entire trip
Choices: A) 35 B) 20 C) 45 D) 50 E) 55

Solution: Avg. speed = total distance / total time   Total distance = 40 miles   Total time = 20 / 15 + 15/30 = 2   Avg. speed = 20.   Answer - 20
Answer: B
If the probability that Brendon, Daniel and Kane score more than 700 on the GMAT is 0.4, 0.5 and 0.6 respectively, what is the probability that at least 2 of them score less than 700? Choose the correct answer:
A) 0.12
B) 0.38
C) 0.40
D) 0.5
E) 0.6

Solution: The probability that Brendon, Daniel and Kane score less than or equal to 700 on the GMAT is 0.4, 0.5 and 0.6 respectively,   All three score less than 700 = 0.6*0.5*0.4= 
0.6*0.5*0.4 = 0.12
0.12;   Brendon and Daniel score less than or equal to 700, while Kane scores more than 700= 0.6*0.5*0.6= 
0.6*0.5*0.6 = 0.18
0.18;   Brendon and Kane score less than or equal to 700, while Daniel scores more than 700= 0.6*0.4*0.5= 
0.6*0.4*0.5 = 0.12
0.12;   Kane and Daniel score less than or equal to 700, while Brendon scores more than 700= 0.5*0.4*0.4 = 0.08.   The sum of the above = 0.5.   Answer: 0.5.
Answer: D
A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is?
Choices
A) 12 B) 15 C) 72 D) 16 E) 11

Solution: Let son's age be x years. Then, father's age = (3x) years.   Five years ago, father's age = (3x - 5) years and son's age = (x - 5) years.   So, 3x - 5 = 4 (x - 5) 3x - 5 = 4x - 20 x = 15.   Answer: 15
Answer: B
Consider another example where a pack contains 4 blue, 2 red and 3 black pens. If a pen is drawn at random from the pack, replaced and the process repeated 2 more times, What is the probability of drawing 2 blue pens and 1 black pen? Pick.
A) 8/81 B) 9/81 C) 7/81 D) 6/81 E) None of these

Solution: EXPL8/81N8/81TION:   Here, total number of pens = 9   Probability of drawing 1 blue pen = 4/9   Probability of drawing another blue pen = 4/9   Probability of drawing 1 black pen = 3/9   Probability of drawing 2 blue pens and 1 black pen = 4/9 * 4/9 * 3/9 = 8/81   8/81NSWER IS 8/81
Answer: A
Find the unit digit in the product(2467)^153*(341)^72 Select the correct option
A) 7  B) 18  C) 25  D) 63  E) 98

Solution: Explanation:   Unit's digit in the given product=7^153*1^72   7^153 gives unit's digit =(1*7)= 
(1*7) = 7
7   1^72 unit's digit=1   Unit digit's in the product=(7*1)= 
(7*1) = 7
7   7nswer 7
Answer: A
Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? Choose one:
A) 22 B) 28 C) 99 D) 77 E) 66

Solution: Speed Ratio = 1:7/6 = 6:7   Time Ratio = 7:6   1 -------- 7   4 --------- ? è 28 m   Answer:77
Answer: D