MU-NLPC/Calc-aqua_rat huggingface dataset:
A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent Pick:
A) 90%
B) 40%
C) 100%
D) 75%
E) 25%

Solution: MP = 100   100%P = 75   SP = 150   ------   75 ---- 75   100 ---- ? => 100%   Answer: 100%
Answer: C
Which of the following could be the value of x, if |14x – 56| = 196?
Choose the correct choice from the following choices:
A) -14	B) -18	C) -10	D) 10	E) 1/4

Solution: |14x – 56| = 196   => 14x - 56 = 196   or 14x - 56 = -196   => 14x = 252 or 14x = -140   => x = 18 or x = -10   Answer -10
Answer: C
What is the remainder when 54487^(42787035) is divided by 5?	Pick:
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: We need to find the units digit of the number.   The units digit of powers of seven repeats 7, 9, 3, and 1 cyclically.   Since 42787035 has the form 4a + 3, the units digit is 3.   Then the remainder when dividing by 5 is 3.   The answer is 3.
Answer: D
How many pieces of 85 cm length can be cut from a rod of 42.5 meters long?  Pick one:
A) 50 B) 40 C) 30 D) 20 E) 10

Solution: Number of pieces = 4250/85=850/17= 
850/17 = 50
50   50nswer is 50.
Answer: A
What is the difference between the greatest and the smallest five digit numbers formed using the digits 7, 0, 3, 4 and 2 without repeating the digits? Pick one:  A) 53978  B) 53916  C) 53961  D) 56781  E) None of these

Solution: Explanation:   The greatest 5 digit number that can be formed using the given digits = 74320   The smallest 5 digit number that can be formed using the given digits = 20342   .: The required difference = 74320 - 20342= 
74320 - 20342 = 53_978
53978   53978nswer: Option 53978
Answer: A
How many ounces of a 60% salt solution must be added to 60 ounces of a 20 percent salt solution so that the resulting mixture is 40% salt?	Choose the correct choice
A) 16.67  B) 30  C) 50  D) 60  E) 70

Solution: let x=ounces of 60% salt solution to be added   .2*60+.6x=.4(60+x)   x=60   Answer 60
Answer: D
The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?
Choose the correct option:
A) 30, 40
B) 25, 30
C) 50, 60
D) 20, 40
E) 35, 45

Solution: Explanation:   Their present ages be 3X and 4X.   5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7   X = 35 - 25 => X = 10.   Their present ages are: 30, 40.   30, 40NSWER IS 30, 40
Answer: A
If -4 < x < 4 and -6 < y < 3, which of the following specifies all the possible values of xy?
Answers.
A) -42 < xy < 21
B) -42 < xy < 24
C) -28 < xy < 18
D) -24 < xy < 24
E) -24 < xy < 24

Solution: The least value of xy is a bit more than 4*(-6)=-24 and the largest value of xy is a bit less than (-4)*(-6)= 
(-4)*(-6) = 24
24.   Therefore -24 < xy < 24.   Answer: -24 < xy < 24.
Answer: D
9.009/2.002 =	Choose one:
A) 4.05  B) 4.50045  C) 4.501  D) 4.5045  E) 4.5

Solution: 9.009/2.002 = 9009/2002 = 9(1001)/2(1001) = 9/2= 
9/2 = 9/2 = around 4.5
4.5   The answer is 4.5.
Answer: E
Mike, Jim and Bob are all professional fisherman. Mike can catch 33 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour? Choose the correct choice:
A) 154.  B) 172.  C) 186.  D) 98.  E) 142.

Solution: All of them catch fishes in relation to number 33....   2/3*33+2*33+2*1.5*33*2/3= 
2/3*33+2*33+2*1.5*33*2/3 = 154
154   154.nswer is 154.
Answer: A
Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 4 of the slips are the drawn, without replacement, what is the probability that all 4 have a even number written on it?  Choices:
A) 1/12 B) 1/10 C) 1/8 D) 1/42 E) 5/9

Solution: Key is that there is no replacement, so each successive choice will become more skewed towards picking a neg (i.e. the pool of positives decreases, while the pool of negatives stay the same)   P(+ on 1st pick) = 5/10   P(+ on 2nd pick) = 4/9   P(+ on 3rd pick) = 3/8   P(+ on 4rd pick) = 2/7   5/10*4/9*3/8*2/7=1/42   1/42
Answer: D
If a man crosses a 800 m long street in 5 minutes. What is his speed? Options:	A) 7 km/hr	B) 7.1 km/hr	C) 7.2 km/hr	D) 8 km/hr	E) 9.6 km/hr

Solution: distance = 800 meter   time = 5 minutes = 5 x 60 seconds = 300 seconds   Speed = distance/time=800/300=2.67m/s=2.67×18/5 km/hr=9.6 km/hr   9.6 km/hr
Answer: E
A number exceeds by 40 from its 3/8 part. Then the number is?  Choose the correct choice from the following choices:	A) A)32	B) B)24	C) C)64	D) D)40	E) E)45

Solution: x – 3/8 x = 40   x = 64   ANSWER:64
Answer: C
1/0.06 is equal to  Choose the correct choice from the following:
A) 25.5	B) 16.7	C) 25	D) .25	E) None of these

Solution: Explanation:   1/0.06 = (1 * 100)/6 = 100/6 = 16.7   Option 16.7
Answer: B
AQ + CD = AAA, where AQ and CD are two-digit numbers and AAA is a three digit number; A, Q, C, and D are distinct positive integers. In the addition problem above, what is the value of C? Choices:
A) 1
B) 3
C) 7
D) 9
E) Cannot be determined

Solution: Since AQ and CD are two-digit integers, their sum can give us only one three digit integer of a kind of AAA: 111.   So, A=1 and we have 1Q+CD=111   Now, C can not be less than 9, because no two-digit integer with first digit 1 (1Q<20) can be added to two-digit integer less than 90, so that to have the sum 111 (if CD<90, so if C<9, CD+1Q<111).   Hence C=9.   Answer: 9.
Answer: D
The sum of three consecutive numbers is 87. The greatest among these three numbers is :  Choices.
A) 22
B) 24
C) 26
D) 30
E) 44

Solution: Sol.   Let the numbers be x, x + 1 and x + 2.   Then, x + (x + 1) + (x + 2) = 87 ⇔ 3x = 84 ⇔ x = 28.   Greatest number = (x + 2) = 30.   Answer 30
Answer: D
P and Q started a business investing Rs 50000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.  Choose the most appropriate option
A) 12:5
B) 17:3
C) 10:6
D) 17:7
E) 10:3

Solution: Explanation:   In this type of question as time frame for both investors is equal then just get the ratio of their investments.   P:Q = 50000:15000   = 50:15   = 10:3   Option 10:3
Answer: E
Having scored 98 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?
Choose the correct choice from the following choices.
A) 28	B) 27	C) 26	D) 22	E) 24

Solution: Explanation :   Let the average score of the first 18 innings be n   18n + 98 = 19(n+4)=> n = 22   So, Average score after 19th innings = x+4 =26.   Answer : 26
Answer: C
Bradley owns b video game cartridges. If Bradley’s total is one-eighth the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?	Options.
A) 33b / 4 B) 35b / 4 C) 37b / 4 D) 39b / 4 E) 41b / 4

Solution: b = Bradley’s total   8b = Andrew’s total   b/4 = 37b / 4harlie’s total   The total number of cartridges is:   b + 8b+ b/4 = (4b + 32b + b) / 4 = 37b / 4   The answer is 37b / 4.
Answer: C
There are 4 magazines lying on a table; 2 are fashion magazines and the other 2 are sports magzines. If 1 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?  Choose one:
A) 1 B) 1/2 C) 1/4 D) 1/6 E) 1/8

Solution: 1- (2c1/4c1) = 1-1/2 = 1/2   Answer: 1/2
Answer: B
We bought a total of 80 books at the store. Math books cost $4 and history books cost $5. The total price was $373. How many math books did we buy?
Select:
A) 23 B) 27 C) 31 D) 35 E) 39

Solution: M + H = 80   H = 80 - M   4M + 5H = 373   4M + 5*(80 - M) = 373   M = 27   The answer is 27.
Answer: B
In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive difference W between n and m?  Pick:
A) 1  B) 3  C) 5  D) 7  E) 9

Solution: We have equation 2n + 5m = 50   We have factor 2 in first number and we have factor 5 in second number.   LCM(2, 5) = 10   So we can try some numbers and we should start from 5 because it will be less list than for 2   2 * 5= 
2 * 5 = 10
10 and n should be equal 20   4 * 5= 
4 * 5 = 20
20 and n should be equal 15   6 * 5= 
6 * 5 = 30
30 and n should be equal 10   8 * 5= 
8 * 5 = 40
40 and n should be equal 5   10 * 5= 
10 * 5 = 50
50 and n should be equal 0   third variant give us the mininal difference   n - m= 10 - 6= 
10 - 6 = 4
4   And there is some mistake in my way of thinking because we don't have such answer )   If we change the task and will seek for difference between m and n   than minimal result W will be 8 - 5= 
8 - 5 = 3
3   And answer 3
Answer: B
Joan and Karl each bought a TV and the sum of their purchases was $500. If twice of what Joan paid was $40 more than what Karl paid, what did Joan pay for her TV? Choose the correct choice from the following answers.
A) $165 B) $170 C) $175 D) $180 E) $185

Solution: J+K=500 so K=500-J   2J=K+40   2J=(500-J)+40   3J=540   J=180   The answer is $180.
Answer: D
Sakshi can do a piece of work in 20 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work : Answers
A) 15	B) 16	C) 18	D) 25	E) 10

Solution: Solution   Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 .   Suppose Tanya taken x days to do the work.   5 : 4 : : 20 : x ⇒ x = (20x4/5) ⇒ x = 16 days.   Hence,Tanya takes 16 days is complete the work.   Answer 16
Answer: B
In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected? Choose the correct choice from the following options.
A) 508 B) 500 C) 800 D) 570 E) 503

Solution: We can select one boy from 20 boys in 20 ways.   We select one girl from 25 girls in 25 ways   We select a boy and girl in 20 * 25 ways i.e., = 500 ways.   Answer:500
Answer: B
A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?  Choose the correct answer:
A) 1.0	B) 1.9	C) 1.6	D) 1.5	E) 1.1

Solution: M = 4.5   S = x   1.5S = 4.5 + x   US = 4.5 + x   4.5 + x = (4.5 - x)2   4.5 + x = 9 -2x   3x = 4.5   x = 1.5   Answer: 1.5
Answer: D
Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer T between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?  Choose the correct choice from the following choices.
A) 12
B) 15
C) 17
D) T=18
E) 20

Solution: Since we are concerned with integers between 1 and 20, write down the primes till 40.   2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37   (you should be very comfortable with the first few primes... )   2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)   2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)   2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)   2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)   2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.   Answer (T=18).
Answer: D
How many of the integers between 45 and 105 are even ?
Choose the correct option
A) 21	B) 30	C) 11	D) 10	E) 9

Solution: Number start between 45 to 105 is 60 numbers   half of them is even..which is 30   ANSWER:30
Answer: B
John takes 15 hours to complete a certain job, while Bill takes only 5 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job? Choose the correct choice.
A) 2 hours, 5 minutes B) 2 hours, 40 minutes C) 3 hours, 20 minutes D) 3 hours, 45 minutes E) 4 hours, 10 minutes

Solution: The rate of John plus Bill is 1/15 + 1/5 = 4/15 of the job completed per hour.   If Steve worked at the same rate as John, the rate would be 4/15 + 1/15 = 1/3   The slowest possible time would be 3 hours.   If Steve worked at the same rate as Bill, the rate would be 4/15 + 1/5 = 7/15   The fastest possible time would be 15/7 hours = 2 hours + 1/7 hours.   The actual time is somewhere between these two extreme points.   The answer is 2 hours, 40 minutes.
Answer: B
A manâ€™s current age is (2/5) of the age of his father. After 5 years, he will be (1/2) of the age of his father. What is the age of father at now?	Choose the correct choice from the following:	A) 40	B) 25	C) 38	D) 50	E) 39

Solution: Let, fatherâ€™s current age is A years.   Then, Manâ€™s current age =[ (2/5)A ]years.   Therefore, [ (2/5)A + 5 ]= (1/2)(A + 5)   2(2A + 25) = 5(A + 8)   A = 25   25
Answer: B
If the numbers 1 to 97 are written on 97 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?
Choose the correct choice from the following answers: A) 1/50 B) 1/25 C) 1/97 D) 1 E) 2

Solution: There are 25 primes, 71 composite numbers from 1 to 97. The number   which is neither prime nor composite is 1.   Therefore, required probability = 1/97.   ANSWER:1/97
Answer: C
Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?  Pick one.
A) 21 cm B) 19 cm C) 32 cm D) 18 cm E) 28 cm

Solution: 93 + 123 + 153 = a3 => a = 18   ANSWER:18 cm
Answer: D
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Euro 1000 more than D, what is B's share?	Options.
A) Euro 500 B) Euro 1500 C) Euro 2000 D) None of these E) Cannot be determined

Solution: Explanation: Let the shares of A, B, C and D be Euro 5x, Euro 2x, Euro 4x and Euro 3x respectively.   Then, 4x - 3x = 1000   x = 1000.   B's share = Euro 2x = Euro (2 x 1000) = Euro 2000.   Answer: Option Euro 2000
Answer: C
The total of company C's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Options:
A) 7N
B) 8N
C) 9N
D) 10N
E) 20

Solution: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.   In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:   $100 + 4x$100 = $100 + $400 =$500   In 1994, the total assets were 100% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993:   $500 + 1x$500 100 +  400= 
100 +  400 = 500
$500   In 1994, the total assets were 100% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993:   $500 + 1x$500= $500 + $500 =$1000   This is 10 times the 1992 number, so the correct answer is 10N.   10N500 +  500= 
500 +  500 = 1_000
$1000   This is 10 times the 1992 number, so the correct answer is 10N.   10N
Answer: D
A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? Choose the correct choice from the following options.
A) 176 m B) 179 m C) 500 m D) 169 m E) 576 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (800 + x)/60 = 65/3   x = 500 m.   Answer:500 m
Answer: C
Eric throws 2 dice,and his score is the sum of the values shown.Sandra throws one dice and her score is the square of the value shown. what is the probabilty that Sandras score will be strictly higher than Erics score??  Select:
A) 137/216	B) 137/218	C) 137/217	D) 136/216	E) 138/216

Solution: sandra score can be like 1,4,9,16,25,36   eric score less then 1-->0   eric score less then 4=(1,1),(1,2)(2,1)-->3   eric score less then 9 are (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(4,1)(4,2)(4,3)(4,4)(5,1)(5,2)(5,3)(6,1)(6,2)-->26   eric score will always be less then 16--->36   eric score will always be less then 25--->36   eric score will always be less then 36--->36   total favorable outcomes=3+26+36+36+36= 
3+26+36+36+36 = 137
137   total possible outcomes=216(36*6)   probability=137/216   137/216NSWER:137/216
Answer: A
Sides of a rectangular park are in the ratio 3: 2 and its area is 1536 sq m, the cost of fencing it at 50 ps per meter is? Pick one
A) 51  B) 1287  C) 125  D) 988  E) 271

Solution: 3x * 2x = 1536 => x = 16   2(48 + 32) = 102 m   102 * 1/2 = Rs.51   51nswer: 51
Answer: A
A 270-metre-long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 secs. What is the length of the other train?	Choose the most appropriate option:
A) 240 metres
B) 320 metres
C) 260 metres
D) 230 metres
E) None of these

Solution: Relative speed = 120 + 80= 
120 + 80 = 200
200 × 5⁄18 m/sec   t= 230 metresistance/Speed=(270+x)×9/500   or 270 + x = 9×500/9x = 500 – 270 = 230 m   Answer 230 metres
Answer: D
Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 7790, then what will be the share of Sameer in the profit?
Choose the correct choice from the following answers.
A) s.2323  B) s.2380  C) s.2329  D) s.2660  E) s.2312

Solution: Kamal : Sameer = (9000 * 12) : (8000 * 7)   = 108:56 = 27:14   Sameer's share = 7790 * 14/41   = Rs.2660.   Answer: s.2660
Answer: D
There is a road beside a river. Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 12 km/hr, while the other sails on a boat at a speed of 10 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends will return to place A first? Choose one
A) 5.4 km /hr B) 7.2 km /hr C) 8.4 km/hr D) 9.6 km /hr E) None

Solution: Solution   Clearly, the cyclist moves both ways at a speed of 12 km/hr.   So, average speed of the cyclist	= 12 km/hr.   Average speed	= (2x14x6/14+6) km/hr   = 42/5= 
42/5 = 42/5 = around 8.4
8.4 kmph   Since the average speed of the cyclist is greater, he will return to A first.   Answer 8.4 km/hr
Answer: C
Find out the wrong number in the series.
6, 12, 48, 104, 384, 768, 3072
Choose one:
A) 768	B) 384	C) 104	D) 488	E) 12

Solution: Each even term of the series is obtained by multiplying the previous term by 2.   2nd term = (1st term) x 2 = 6 x 2 = 12   4th term = (3rd term) x 2 = 48 x 2 = 96.   6th term = (5th term) x 2 = 384 x 2 =768.   4th term should be 96 instead of 104.   ANSWER:104
Answer: C
Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter? Choose the correct option:
A) Rs.150
B) Rs.132
C) Rs.100
D) Rs.125
E) Rs.225

Solution: 2 * 22/7 * 14= 
2 * 22/7 * 14 = 88
88   88 * 1 1/2= Rs.132   ANSWER:Rs.132
Answer: B
What is the number of different committees of 6 people that can be selected from a group of 10 people?	Choose the correct choice from the following answers:
A) a) 20	B) b) 40	C) c) 80	D) d) 120	E) e) 210

Solution: 10c6 = 210   Answer is e) 210.
Answer: E
Two pipes A and B can separately fill a tank in 12 minutes and 15 minutes respectively. Both the pipes are opened together but 8 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?	Answers.
A) 5min B) 9min C) 7min D) 6min E) 8min

Solution: 8/12 + x/15 = 1   x = 5   5minNSWER:5min
Answer: A
A certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 11 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke? Options
A) A.72
B) B.50
C) C.48
D) D.46
E) E.23

Solution: At 6:00 it'll chime 6 times. If we assume that the time taken to chime is x, then time between chimes is also x. So you have 6 chimes, which is 6x and 5 time intervals between chimes. This means that 11x = 11 seconds. Thus x = 1 seconds.   By a similar logic, at 12:00, there are 12 chimes and 11 intervals so the total time is   (12+11)= 
  (12+11) = 23
23x= 23 seconds.   Answer E.23
Answer: E
The probability that a number selected at random from the first 50 natural numbers is a composite number is -. Choose the correct answer:
A) 17/25 B) 17/27 C) 17/18 D) 17/22 E) 17/09

Solution: The number of exhaustive events = ⁵⁰C₁ = 50.   We have 15 primes from 1 to 50.   Number of favourable cases are 34.   Required probability = 34/50 = 17/25.   17/25nswer:17/25
Answer: A
Dividing by 3⁄8 and then multiplying by 5⁄8 is the same as dividing by what number?
Choose the most appropriate option:
A) 31⁄5  B) 16⁄5  C) 20⁄9  D) 9⁄20  E) 5⁄3

Solution: say X/3/8*5/8 = x*8/3*5/8 = x*5/3   5⁄3
Answer: E
The average age of a family of four members is 25 years. If the age of the youngest member be 15 years then what was the average age of the family at the time of the birth of the youngest member?
Choose the correct choice from the following answers:	A) 13.5	B) 14	C) 15	D) 13.33	E) 16

Solution: Explanation :   At present the total age of the family = 4 * 25= 
4 * 25 = 100
100   The total age of the family at the time of the birth of the youngest member= [100-15-(15*3)= 
100-15-(15*3) = 40
40   Therefore, average age of the family at the time of birth of the youngest member= 40/3   = 13.33   Answer : 13.33
Answer: D
Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 100kmph, find the rate at which the train B runs.  Pick one:
A) 40 B) 60 C) 150 D) 80 E) 100

Solution: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:   Sa/Sb = √(b/a)   i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.   Sa/Sb = √(4/9) = 2/3   This gives us that the ratio of the speed of A : speed of B as 2:3.   Since speed of A is 100 kmph, speed of B must be   100*(3/2)= 
  100*(3/2) = 150
150 kmph   Answer 150
Answer: C
In the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 5:4:1, respectively. If the total amount allocated to these three categories is $1,800, what is the amount allocated to food?  Select.
A) $900	B) $720	C) $675	D) $450	E) $225

Solution: To solve this question, it will be best to first express the given ratio using variable multipliers. Thus, we have:   Household Expenses : Food : Miscellaneous = 5x : 4x : x   Since we are told that the TOTAL amount allocated to these categories is $1,800 we can set up the equation:   5x + 4x + x = 1,800   10x = 1,800   x = 180   Thus, the total amount allocated to food is 4 x 180 = $720.   Answer $720.
Answer: B
If Rs. 578 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively?  Pick.
A) s.300	B) s.408	C) s.389	D) s.368	E) s.323

Solution: (A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4   A:B = 2:3 and B:C = 1:4 = 3:12   A:B:C = 2:3:12   A;s share = 578 * 2/17 = Rs. 68   B's share = 578 * 3/17 = Rs. 102   C's share = 578 * 12/17 =Rs.408.   Answer:s.408
Answer: B
Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=3/4, what is the ratio of rectangle A’s area to rectangle B’s area? Select:
A) 3/4 B) 9/16 C) 16/3 D) 4/3 E) 3/16

Solution: The area of rectangle A is ab.   c=4a/3 and d=4b/3.   The area of rectangle B is cd=16ab/9.   The ratio of rectangle A's area to rectangle B's area is ab / (16ab/9) = 9/16.   The answer is 9/16.
Answer: B