MU-NLPC/Calc-aqua_rat huggingface dataset:
The integer T has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of T and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?  Answers:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Let T be 67 and y be a8. Then the product of T and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.   So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9= 
3+7*9 = 66
66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.   So the answer is (5).
Answer: C
When a random experiment is conducted, the probability that event A occurs is 1/6. If the random experiment is conducted 4 independent times, what is the probability that event A occurs exactly twice?
Choose one:
A) 17/216  B) 19/216  C) 23/216  D) 25/216  E) 35/216

Solution: One case is: 1/6*1/6*5/6*5/6=25/1296   The total number of possible cases is 4C2 = 6   P(event A occurs exactly twice) = 6*(25/1296) = 25/216   The answer is 25/216.
Answer: D
A gunstore uses 400gm of powder in place of 1kg for their bullets. Find the actual % profit or loss, when the bullets are sold pending on 10% gain on cost price?
Choices: A) 32.5% B) 87.5% C) 35% D) 40% E) 50%

Solution: Selling price of 400gm = 100+10= 
100+10 = 110
$110   Profit= 110-40= 
110-40 = 70
$70   % of profit= 70*100/80= 
70*100/80 = 175/2 = around 87.5
87.5 %   Answer is 87.5%
Answer: B
For any triangle T in the xy–coordinate plan, the center of T is defined to be the point whose x–coordinate is the average (arithmetic mean) of the x–coordinates of the vertices of T and whose y–coordinate is the average of the y–coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (9,0) and center at the point (4,3), what are the coordinates of the remaining vertex? Select the correct option:
A) (3,4)	B) (3,6)	C) (4,9)	D) (3,9)	E) (9,6)

Solution: Let (a,b) be the remaining vertex.   x: 0 + 9 + a = 3*4. Then a = 3.   y: 0 + 0 + b = 3*3.= 
3*3. = 9
9.   The answer is (3,9).
Answer: D
If the radius of a circle is increased by 10% then the area is increased by: Choices:
A) 44%
B) 120%
C) 144%
D) 40%
E) 21%

Solution: initially A=pi*r2   now R2=110/100r   then area=Pi*(110R/100)2   area=121R/100   that is area increases from 100 to 121=increase in area=21%   ANSW21%R:21%
Answer: E
Last year, the price per transaction of certain company increases P percent from the year before, and the number of transactions increase N percent from the year before. Total revenue is simply the number of transactions times the price per transaction. Assume this one transaction is this company's only source of revenue. Which of the following is the percent increase in revenue last year, from the year before?	Choose the correct choice from the following answers:	A) P∗N %	B) (P+N)	C) (P+N+P∗N/100) %	D) (P+N-P∗N/100) %	E) (P+N+P∗N/100)^2 %

Solution: Assume   x = price per transaction for previous year   y = price per transaction for this year   Relationship between x and y   y =x (1+P/100)   Similarly, if   n1= no. of transactions for last year   n2 = no. of transactions for this year   n2 = n1(1+N/100)   Now, the question is [(n2y- n1x) /n1x] * 100   n2y = n1x(1+P/100)(1+N/100)   So, [(n2y - n1x)/n1x] * 100 = (n1x[(1+P/100) (1+N/100) - 1]/ n1x) * 100   (P+N-P∗N/100) % is the answer.
Answer: D
A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Choose the correct choice from the following answers
A) 33 4/3 % B) 33 1/7 % C) 50 % D) 32 1/3 % E) 60 %

Solution: The total number of mangoes bought by the shopkeeper be 18.   If he buys 6 a rupee, his 50 %P = 3   He selling at 3 a rupee, his SP = 6   Profit = SP - 50 %P = 6 - 3= 
6 - 3 = 3
3   Profit Percent= 3/6 * 100= 
3/6 * 100 = 50
50 %   Answer:50 %
Answer: C
In 1937, the ship of the great sailor SINBAD left an Egyptian port heading Ivory coast at E mile/month .
One month later another ship of the greatest pirate ever CHENG I SAO was 5000 miles due south of the same Egyptian port and heading due north at Y miles/month. Six months later after the leaving of Sinbad’s ship from Egyptian port, how far apart were the ships? [Ivory coast is in the west of Egypt]  Pick one:	A) { (6E)^2 + (5000-5y)^2 }^1/2	B) { (36x)^2 + (5000-7y)^2 }^1/2	C) { (16x)^2 + (5000-7y)^2 }^1/2	D) { (7x)^2 + (5200-7y)^2 }^1/2	E) { (2x)^2 + (300-7y)^2 }^1/2

Solution: The chinese ship sailed for 5 months i.e. 5Y miles @Y miles/month, therefore distance from Egyptian port is 5000-5Y. Since { (6E)^2 + (5000-5y)^2 }^1/2 is the only option with this value ...therefore { (6E)^2 + (5000-5y)^2 }^1/2 is the answer
Answer: A
Nitin ranks 24th in a class of 58 students. What is rank from the last ? Choices.
A) 33 B) 34 C) 32 D) 28 E) 19

Solution: Explanation:   Number students behind the nitin in rank = (58 - 24)= 
(58 - 24) = 34
34   Nitin is 34nd from the last   Answer: 34) 34
Answer: B
The captain of a cricket team of 11 members is 24 years old and the wicket keeper is 7 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
Choose one:
A) 21	B) 22	C) 23	D) 24	E) 25

Solution: Let the average age of the whole team be x years.   11x - (24 + 31) = 9 (x - 1)   11x - 9x = 46   2x = 46   x = 23.   The average age of the team is 23 years.   The answer is 23.
Answer: C
Train A and Train B began traveling towards each other from opposite ends of a 540-mile long track at 1:00 PM. If Train A traveled at 35 miles per hour and Train B traveled at 25 miles per hour, at what time did the trains meet?
Choices.
A) 5:40 PM B) 10:00 PM C) 7:20 PM D) 8:00 PM E) 9:20 PM

Solution: This question tests your concepts of relative speed:   If two trains are moving in opposite direction, then distance will reduce at a rate of (Speed of 1 + Speed of 2)   If two trains are moving in same direction, then distance will reduce at a rate of (Speed of 1 - Speed of 2)   Here the trains are moving towards each other, hence in opposite direction.   Trains will cover the 500 mile track in a time of 500/(25 + 35) = 540/60= 
540/60 = 9
9 hours   Trains started at 1:00 PM, there they will meet at 10:00 PM   Option 10:00 PM
Answer: B
If n and k are integers whose product is 1600, which of the following statements must be true? Choose the correct choice from the following answers
A) n+k>0  B) n does not equal k  C) Either n or k is a multiple of 10  D) If n is even, then k is odd  E) If n is odd, then k is even

Solution: If n is odd and k is odd, then the product is odd.   The answer is If n is odd, then k is even.
Answer: E
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 272 runs?
Choices:
A) 6.25	B) 6.22	C) 6.29	D) 6.39	E) 6.0

Solution: Required run rate   = [272 - (3.2 * 10)]/40   = 240/40= 
240/40 = 6
6.00   Answer: 6.0
Answer: E
Think of a number, divide it by 5 and add 10 to it. The result is 21. What is the number thought of?
Choices:
A) 24 B) 55 C) 297 D) 267 E) 29

Solution: Explanation :   21-10= 
21-10 = 11
11   11 x 5= 55   Answer : 55
Answer: B
Ajay and Sasi start walking towards each other at 6am at speed of 4kmph and 5kmph. They were initially 20km apart. At what time do they meet?	Pick one
A) 6am	B) 8am	C) 10am	D) 9am	E) 12pm

Solution: Time of meeting = distance / relative speed = 20/6+4 = 20/10= 
20/10 = 2
2 hrs after 6am= 8am   Answer is 8am
Answer: B
A bought 100kg of rice for Rs 1100 and sold it at a loss of as much money as he received for 2o kg of rice. At what price did he sell the rice?
Choose the correct choice from the following answers:	A) 800	B) 880	C) 900	D) 920	E) 940

Solution: 100Kg of rice for 1100/-   then 1kg rice cost must be 1100/100= 
1100/100 = 11
11   then 20kg rice cost is  20*11= 
 20*11 = 220
220/---------------->this is loss    1100-220= 
 1100-220 = 880
880   then sell price=880   ANSWER:880
Answer: B
March 11, 2003 is a Tuesday. What will be the day on which march 11 2004 comes??  Pick one:
A) Thursday
B) wednesday
C) friday
D) sunday
E) monday

Solution: 2004 is a leap year that means 29 days in feb.   so march 11,2003 to march 11, 2004 will be 366 days.   366/7=52 weeks + 2 days. Hence Thursday   ThursdayNSWER:Thursday
Answer: A
If two sides of a triangle are 3 and 12, respectively, which of the following could NOT be the area of this triangle?
Choose the correct option:
A) 1
B) 6
C) 17
D) 29
E) 16

Solution: For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 3 and 12.   We know that the area of a triangle will be maximized when two sides are perpendicular to each other (consult Bunuel's drawing above). Thus we have a max area being equal to one half the base times the height, either (.5)12 * 3 -or- (.5)3 * 12 will result in a maximum area of 18 for the triangle; therefore, the triangle could never have an area of 29.   29
Answer: D
The measure of the side of a square is doubled. If x represents the perimeter of the original square, what is the value of the new perimeter?  Pick:
A) 2x  B) 4x  C) 9x  D) 12x  E) 27x

Solution: Original perimeter = x   Hence original side = x/4   New side = 2x/4   New perimeter = 4*2x/4 = 2x   Correct Option: 2x4*2 /4= 
4*2 /4 = 2
2x   Correct Option: 2x
Answer: A
3 pig’s and 10 goats are brought for Rs.1100. If the average price of a goat be Rs.50. What is the average price of a pig.
Options:
A) 275 B) 300 C) 200 D) 250 E) 225

Solution: Explanation:   Average price of a goat = Rs.50   total price of 10 goats = 10*50 = Rs.500   But total price of 3 pigs and 10 goats = Rs. 1100   Total price of 3 pigs is = 1100 - 500= 
1100 - 500 = 600
600   Average price of a pig= 600/3   = Rs. 200   Answer: 200
Answer: C
If a man buys 10 lollipops for $80 and sold them for $3 dollars determine his loss.  Choose the most appropriate option:
A) 50  B) 60  C) 70  D) 80  E) 90

Solution: Cost of 10 lollipops = $80   Sold each lollipop for $3   So he sold 10 lollipops for $(10 × 3) = $30   Loss = $(80 – 30) = $50   answer :50   Therefore, loss = $ 50.
Answer: A
A thief goes away with a SANTRO car at a speed of 50 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start?
Pick.
A) A)2  B) B)5  C) C)7  D) D)5  E) E)8

Solution: Explanation:   |-----------20--------------------|   60 50   D = 20   RS = 60 – 50 = 10   T = 20/10= 
20/10 = 2
2 hours   2nswer: Option 2
Answer: A
If you roll a fair-sided die twice, what is the probability of getting 1 ,1 ?	Choose the correct answer.
A) 1/3!
B) 1/36
C) 1/18
D) 1/24
E) 1/12

Solution: total no. in two dice (1,1) ,(2,2) .....(6,)   Total number of events= 6*6   Total events of getting same pair(1, 1) = 6   Probability= 6/6*6= 1/6=1/3!   1/3!
Answer: A
A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is : Choose the correct choice from the following:  A) 45%  B) 56%  C) 67%  D) 75%  E) None of these

Solution: Explanation:   We will first subtract the cone volume from wood volume to get the wood wasted.   Then we can calculate its percentage.   Sphere Volume =4/3πr3   Cone Volume =1/3πr2h   Volume of wood wasted =(4/3π∗9∗9∗9)−(1/3π∗9∗9∗9)=π∗9∗9∗9cm3   Required Percentage =π∗9∗9∗9 /4/3π∗9∗9∗9∗100%=3/4∗100%=75%   Option 75%
Answer: D
The length of the bridge, which a train 130 metres long and travelling at 108 km/hr can cross in 30 seconds, is:
Choose the correct option
A) 200 m  B) 225 m  C) 245 m  D) 170 m  E) 240 m

Solution: Speed = [108 X 5/18] m/sec = 30 m/sec   Time = 10 sec   Let the length of bridge be x metres.   Then, (130 + x)/30 = 10 => 130 + x = 300 => x = 170 m.   ANSWER:170 m
Answer: D
The speed of a car is 90 km in the first hour and 50 km in the second hour. What is the average speed of the car?	Options
A) 70	B) 75	C) 88	D) 54	E) 15

Solution: S = (90 + 50)/2= 
(90 + 50)/2 = 70
70 kmph   70nswer: 70
Answer: A
A man can row upstream at 26 kmph and downstream at 30 kmph, and then find the speed of the man in still water?  Choose the correct choice:
A) 29 B) 28 C) 30 D) 32 E) 23

Solution: US = 26   DS = 30   M = (30 + 26)/2= 
(30 + 26)/2 = 28
28   Answer:28
Answer: B
A train 520 meters long is running with a speed of 52 kmph. The time taken by it to cross a tunnel 160 meters long is?
Choose the correct choice from the following:
A) 287 sec
B) 288 sec
C) 47 sec
D) 16 sec
E) 17 sec

Solution: D = 520 + 160= 
520 + 160 = 680
680   S= 52 * 5/18 = 14.4 mps   T = 680/14.4 = 47 sec   Answer: 47 sec
Answer: C
If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the second part is?
Choose the correct choice from the following answers.
A) A)426  B) B)526  C) C)207  D) D)204  E) E)272

Solution: Given ratio   = 1/2:2/3:3/4 = 6:8:9   1st part = 782 * 8/23   = Rs. 272   Answer:272
Answer: E
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?	Choose the correct choice:
A) 33  B) 299  C) 36  D) 88  E) 21

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec.   Answer:36
Answer: C
A number when divided by 221 gives a remainder 43, what remainder will be obtained by dividing the same number 17?  Choose the most appropriate option
A) 9 B) 11 C) 15 D) 5 E) 20

Solution: 221 + 43= 
221 + 43 = 264
264/17= 9   9NSWER 9
Answer: A
The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $60 less. What was the total cost cost of the vacation? Choose the correct choice from the following:
A) $200
B) $300
C) $400
D) $720
E) $600

Solution: C for cost.   P price per person.   C= 3*P   C=4*P-240   Substituting the value of P from the first equation onto the second we get P = 240.   Plugging in the value of P in the first equation, we get C= 720. Which leads us to answer choice $720
Answer: D
Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?  Choose one:
A) 17/26
B) 17/21
C) 17/92
D) 17/20
E) 17/18

Solution: n(S) = 20   n(Even no) = 10 = n(E)   n(Prime no) = 8 = n(P)   P(EᴜP) = 10/20 + 8/20 - 1/20   = 17/20   Answer:17/20
Answer: D
The average (arithmetic mean) of 20, 40, and 60 is 4 more than the average of 10, 70, and what number?  Choose one
A) 28 B) 25 C) 35 D) 45 E) 55

Solution: a1 = 120/3= 
120/3 = 40
40   a2= a1 -4 = 36   sum of second list = 36*3= 
36*3 = 108
108   therefore the number= 108 -80= 
108 -80 = 28
28   28NSWER:28
Answer: A
A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?	Choose the correct choice from the following options: A) Rs. 380 B) Rs. 600 C) Rs. 420 D) Rs. 400 E) Rs. 480

Solution: Explanation :   Amount of work A can do in 1 day = 1/6   Amount of work B can do in 1 day = 1/8   Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24   Amount of work A + B + C can do = 1/3   Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24   work A can do in 1 day: work B can do in 1 day: work C can do in 1 day   = 1/6 : 1/8 : 1/24 = 4 : 3 : 1   Amount to be paid to C = 3200 × (1/8) = 400   Answer : Option Rs. 400
Answer: D
Boy sells a book for Rs. 720 he gets a loss of 10 %, To gain 10%, what should be the SP?  Choose the correct choice from the following choices:
A) 430
B) 880
C) 550
D) 590
E) 600

Solution: Cost price = 720/90 x 100 = 800   To gain 10% = 800 x 10/100 = 80   SP = CP + gain = 800 + 80= 
800 + 80 = 880
880   Answer : 880
Answer: B
What Least number should be added to 1056,so that the sum is completely divisible by 23? Choose one.
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: That is 1056/23=45   Remainder=21   =>21+2= 
21+2 = 23
23   Hence 2 should be added to 1056 so that the sum will be divisible by 23   Answer is option 2
Answer: B
Pipe A fills a tank of capacity 900 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?
Choose the correct choice from the following answers.
A) 42 minutes	B) 14 minutes	C) 54 minutes	D) 40 minutes 20 seconds	E) None of these

Solution: In one cycle they fill 40+30-20= 
40+30-20 = 50
50 liters   900= 50*n => n = 18   here n = number of cycles.   total time = 18*3= 
18*3 = 54
54 as in one cycle there are 3 minutes.   thus 54 minutes   ANSWER:54 minutes
Answer: C
For any positive x, y and z if x is n% of y and z is m% of y then what percentage W must x be of z?  Choose the correct option
A) (n/m)%
B) (m × n)%
C) (100 / [m × n]) %
D) (100 × m/n)%
E) (100 × n/m)%

Solution: x is n% of y M(100 × n/m)%ANS x= (n/100 )* y------------------------eq1   z is m% of y M(100 × n/m)%ANS z= (m/100 )* y------------------------eq2   Find equation of xz   substitute value of y from 2nd equation into Ist equation   so x= (n/100)*(100z/m)   so x= (n/m)z   or x= (100n/m)z/100   so answer W is 100n/m %.(100 × n/m)%
Answer: E
If a*b*c=195, b*c*d = 65, c*d*e=1000 and d*e*f=250 the (a*f)/(c*d) = ? Answers.
A) 1/2
B) 1/4
C) 3/4
D) 2/3
E) None of these

Solution: Explanation :   aâˆ—bâˆ—c/bâˆ—câˆ—d= 195/65 => a/d = 3   dâˆ—eâˆ—f/câˆ—dâˆ—e= 250/1000 => f/c = 1/4   a/d* f/c = 3 * 1/4 = 3/4   Answer : 3/4
Answer: C
A retailer bought a machine at a wholesale price of $80 and later on sold it after a 20% discount of the retail price. If the retailer made a profit equivalent to 20% of the wholesale price, what is the retail price of the machine? Choose the correct choice from the following choices.
A) $80  B) $100  C) $120  D) 135  E) 160

Solution: The price after the discount was 1.2*80= 
1.2*80 = 96
$96   Let x be the retail price.   0.8x= $96   x = 96/0.8= 
96/0.8 = 120
$120   The answer is $120.
Answer: C
A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? Choose one:
A) 14700
B) 14500
C) 14900
D) 14300
E) 14000

Solution: Total amount invested = 50000   Assume that investment of C =x.   Then investment of B =5000+x,   Investment of 14700 =4000+5000+x=9000+x   x+5000+x+9000+x=50000   ⇒3x+14000=50000   ⇒3x=50000–14000=36000   ⇒x=36000/3= 
36000/3 = 12_000
12000   Investment of C=x=12000   Investment of B =5000+x=17000   Investment of 14700 =9000+x=21000   Ratio of the investment of 14700, B and C   =21000:17000:12000   =21:17:12   Share of 14700 = Total profit ×21/50   =35000×21/50=700×21=14700   14700nswer is 14700.
Answer: A
Find the differece between largest and smallest number formerd by the digits 0,1,2,3,5  Choose the correct answer.
A) 41375  B) 42975  C) 42775  D) 43565  E) 43589

Solution: Explanation:   53210   01235   ---------   41975   Answer: Option 42975
Answer: B
A corporation paid $8 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?  Choose the correct answer
A) 6% B) 14% C) 20% D) 23% E) 86%

Solution: Difference in Ratios = (30/150) - (8/50) = (6/50)   % Change = (Change (6/50) / Original ratio (7/50)) *100 = 86%   Answer - 86%
Answer: E
A man can row with a speed of 10 kmph in still water. If the stream flows at 55 kmph, then the speed in downstream is? Choose the correct choice from the following
A) 29  B) 65  C) 20  D) 27  E) 121

Solution: M = 10   S = 55   DS = 10 + 55= 
10 + 55 = 65
65   Answer: 65
Answer: B
The number of real roots of the equation A2/x + B2/(x-1) = 1, where A and B are real numbers not equal to zero simultaneously is Choose the correct choice from the following options:
A) None	B) 1	C) 2	D) 1 or 2	E) 3

Solution: Explanation :   => A2/x + B2/(x-1) = 1,   => A2 (x-1) + B2x = x2 - x.   This is a quadratic equation.   Hence, number of roots = 2 or 1 (1 in the case when both roots are equal )   Nonenswer : None
Answer: A
It costs $4 for the first 1/4 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $12 per hour. If a certain customer uses the laundry machine for 3 hours and 25 minutes, how much will it cost him?	Select the correct option
A) $25  B) $32  C) $36  D) $40.  E) $42.

Solution: 3 hrs 25 min = 205 min   First 15 min ------> $4   Time left is 190 min...   Now, 60 min costs $ 12   1 min costs $ 12/60   190 min costs $  12/60*190= 
 12/60*190 = 38
> $ 38   So, Total cost will be $38 + $4 => $ 42   Hene answer will be ($42.) $ 4238 +  4= 
38 +  4 = 42
> $ 42   Hene answer will be ($42.) $ 42
Answer: E
A student chose a number, multiplied it by 8, then subtracted 138 from the result and got 102. What was the number he chose?
Choose the correct choice from the following:  A) 30  B) 120  C) 130  D) 140  E) 150

Solution: Solution:   Let xx be the number he chose, then   8⋅x−138=102   8x=240   x=30   30nswer 30
Answer: A
Two trains 120 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?  Options:	A) 7.16	B) 7.16	C) 7.07	D) 7.15	E) 7.11

Solution: T = (120 + 165)/ (80 + 65) * 18/5   T = 7.07   Answer: 7.07
Answer: C
How many figures are required to number the pages the pages of a book containing 1210 pages?
Choose the correct choice from the following answers:
A) 3533
B) 3833
C) 3333
D) 3633
E) 3733

Solution: 1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 999= 900 * 3= 
900 * 3 = 2_700
2700   1000 to 1210= 211 * 4= 
211 * 4 = 844
844   -----------   3733   ANSW3733R:3733
Answer: E
Eleven years ago Tina was half as old as Ike will be in 4 years. If Ike is m years old now, how old is Tina now, in terms of m?
Choose the correct answer:
A) 4m - 11 B) m/2 + 13 C) 1/(2m - 22) D) (4m + 11)/2 E) 2m-7

Solution: Ike's current age = m   Ike's age after 4 years = m + 4   Tina age 11 years ago =(m+4)/2   Tina's current age = (m+4)/2 + 11 = (m+4+22)/2= m/2+13   Ans m/2 + 13
Answer: B
If x and y are integers and x + y = 4, which of the following must be true?  Answers.
A) x and y are consecutive integers. B) Both x and y are even. C) If x > 0, then y < 0. D) If x < 0, then y > 0. E) Both x and y are less than 5.

Solution: In option C if x > 0,then y<0 means x is +ve and y is -ve   In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.   How option If x < 0, then y > 0. is right could you explain
Answer: D
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: Answers:
A) 14
B) 67
C) 56
D) 89
E) 34

Solution: Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years.   14nswer:14
Answer: A
Of all the homes on Gotham Street, 1/3 are termite-ridden, and 7/10 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing? Choose the correct choice.
A) 1/4	B) 1/6	C) 1/8	D) 1/9	E) 1/10

Solution: The fraction of homes which are termite-infested but not collapsing is 3/10*1/3 = 1/10   The answer is 1/10.
Answer: E