MU-NLPC/Calc-aqua_rat huggingface dataset:
A children's gift store sells gift certificates in denominations of $3 and $5. The store sold 'm' $3 certificates and 'n' $5 certificates worth $93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take?  Choose one
A) 5 B) 7 C) 6 D) 31 E) 18

Solution: Explanatory Answer   Step 1: Key data   1. Total value of all certificates sold = $93.   2. Certificates sold were in denominations of $3 and $5.   3. Both 'm' and 'n' are natural numbers.   Step 2: Approach   The value of all certificates sold, 93 is divisible by 3.   So, a maximum of 31 $3 certificates and no $5 certificates could have been sold.   However, the question states that both 'm' and 'n' are natural numbers.   Hence, at least 1 $5 certificate should have been sold.   Let us reduce the number of $3 certificates from theoretical maximum count of 31 by say 'x' and correspondingly increase $5 certificates by 'y'.   Evidently, 3x = 5y because the value of $3 certificates reduced should be the same as the value of $5 certificates increased.   It means that x has to be a multiple of 5 and y has to be a multiple of 3.   Or $3 certificates reduce in steps of 5 certificates.   Step 3: List down possibilities   The following combinations are possible   1. m = 26, n = 3   2. m = 21, n = 6   3. m = 16, n = 9   4. m = 11, n = 12   5. m = 6, n = 15   6. m = 1, n = 18   An alternative way to think of the same concept - Replacing five $3 certificates with three $5 certificates leads to no change in the overall value of certficates sold and gives us a new combination each time. We need to see how many such combinations are possible.   Answer 6
Answer: C
A pump can fill a tank with a water in 2 hours. Because of a leak, it took 3 and 1/3 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?  Select.
A) 5 hrs	B) 7 hrs	C) 12 hrs	D) 14 hrs	E) 16 hrs

Solution: The rate of the pump + leak = 3/10   1/2 - leak's rate = 3/10   leak's rate = 1/5   The leak will empty the tank in 5 hours.   The answer is 5 hrs.
Answer: A
A man counted his animals, 80 heads and 250 legs (ducks and goats). how many goats are there?  Choose the correct choice from the following answers.
A) 30 B) 40 C) 50 D) 45 E) 70

Solution: let no of ducks=d and no of goat=g   d+g=80(heads)----------> eq 1   each duck has 2 legs and goat has 4 legs   2d+4g=250 and divide 2d+4g=250 by 2 we get d+2g=125 -----------> eq2   subtract eq1 from eq2   we get no of goats=45   ANSWER:45
Answer: D
To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 8 hours a day?
Select.
A) 40  B) 36  C) 42  D) 44  E) 46

Solution: Man-hours required to asphalt 1 km road=30*12*8= 
30*12*8 = 2_880
2880   Man-hours required to asphalt 2 km road=2880*2= 
2880*2 = 5_760
5760   Man-hours available per day=20*8= 
20*8 = 160
160   Therefore number of days=5760/240=36 days   Ans=36
Answer: B
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?	Pick one
A) 1000
B) 2288
C) 2777
D) 2999
E) 2711

Solution: 90%   104%   --------   14% ---- 140   100% ---- ? => Rs.1000   1000nswer:1000
Answer: A
During the second quarter of 1984, a total of 4,976,000 domestic cars were sold. If this was 24% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ? Choose the correct choice from the following.
A) 714,240 B) 2,261,760 C) 2,400,000 D) 3,690,240 E) 4,012,903

Solution: Let number of cars sold in 1st quarter = x   Number of cars sold in 2nd quarter = 24% greater than the number sold during the first quarter = (1 + 24/100)= 
(1 + 24/100) = 31/25 = around 1.24
1.24 x   1.24 x= 4,976,000   => x = 4,012,903   So, answer will be 4,012,903
Answer: E
One-fourth of certain journey is covered at the rate of 25 km/h, one-third at the rate of 30 km/h and the rest at 50 km/h. Find the average speed for the whole journey. Pick one
A) 600/53km/h	B) 1200/53 km/h	C) 1800/53 km/h	D) 1600/53 km/h	E) None of these

Solution: Solution: Let distance be 120 KM, hence 30 KM is covered by @ 25 kmph and 40 km covered by @ 30 kmph and rest 50 km has been covered@ 50 km.   Now, average = (120/total time taken);   = {120/[(30/25)+(40/30)+(50/50)}]   = 3600/106 = 1800/53 km/h.   Answer: Option 1800/53 km/h
Answer: C
I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last?  Choose the correct answer:
A) 4 hours
B) 2 hours
C) 3 hours
D) 2 hours 24 minutes
E) None

Solution: Explanatory Answer   The total time of journey = 5 hours.   Let 'x' hours be the time that I traveled at 40 kmph   Therefore, 5 - x hours would be time that I traveled at 60 kmph.   Hence, I would have covered x*40 + (5 - x)60 kms in the 5 hours = 240 kms.   Solving, for x in the equation 40x + (5 - x)*60 = 240, we get   40x + 300 - 60x = 240   => 20x = 60 or x = 3 hours.   Answer 3 hours
Answer: C
A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7,8,9}. If no digit may be repeated and each password must be at least 8 digits long, how many passwords are possible?  Choose the correct option:
A) 8! + 9!  B) 2 x 9!  C) 8! x 9!  D) 17!  E) 18!

Solution: If we choose the 9 different digits then they can be arranged in 9! ways.   The number of possible 8-digit passwords is 9*8*...*2 = 9!   The total number of passwords is 9! + 9! = 2*9!   The answer is 2 x 9!.
Answer: B
A woman sold 300 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 4 for 85 cents. How many were sold at the first rate?	Choose the correct choice from the following choices.
A) 45
B) 21
C) 9
D) 16
E) 13

Solution: This can be solved like a classical mixture problem but numbers are awkward to deal with.   It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 7 at the second rate. You simple subtract the answer choices for the first rate from 100 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 4.   100 - 45 = 255 => not a multiple of 4 so exclude   100 - 21 = 279 => not a multiple of 4 so exclude   100 -9 = 291 => not a multiple of 4 so exclude   100 - 16 = 284 => a multiple of 4 so keep   100 - 13 = 287 => not a multiple of 4 so exclude   Hence, answer choice 16 is correct.   16
Answer: D
The price of an item is discounted 5 percent on day 1 of a sale. On day 2, the item is discounted another 5 percent, and on day 3, it is discounted an additional 10 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
Choose one:
A) 80%	B) 82.5%	C) 83%	D) 84%	E) 85.5%

Solution: Let initial price be 100   Price in day 1 after 5% discount = 95   Price in day 2 after 5% discount = 90.25   Price in day 3 after 10% discount = 81.23   So, Price in day 3 as percentage of the sale price on day 1 will be = 81.23/95*100 => 85.5%   Answer will definitely be (85.5%)
Answer: E
If 8 boys can color 48 m long cloth in 2 days, then 6 boys can color 36 m long cloth in	Choose the correct option.
A) day B) days C) days D) days E) days

Solution: The length of cloth painted by one boy in one day = 96 / 8 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 boys = 36/ 6 × 6 = 1 day.   day)
Answer: A
If the price of a certain computer increased 20 percent from d dollars to 351 dollars, then 2d = Choose the correct choice from the following answers
A) 540 B) 585 C) 619 D) 649 E) 700

Solution: Before Price increase Price = d   After 30% Price increase Price = d+(20/100)*D = 1.2d = 351 (Given)   i.e. d = 351/1.3 = $292,5   i.e. 2d = 2*292.5= 
2*292.5 = 585
585   Answer: option 585
Answer: B
an article with cost price of 280 is sold at 30% profit. what is the selling price?	Select the correct option:  A) 198  B) 364  C) 369  D) 207  E) 210

Solution: sp=1.30*280= 
1.30*280 = 364
364   ANSWER:364
Answer: B
After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6500. Find the actual price of the good.
Choices.
A) s. 6000 B) s. 9000 C) s. 10800 D) s. 9503 E) s. 9980

Solution: Let actual price was 100.   After three successive discount this will become,   100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4   Now Compare,   68.4 = 6500   1 = 6500/68.4   100 = (6500*100)/68.4 = Rs. 9503.   Answer: Option s. 9503
Answer: D
In the gure below, arc SBT is one quarter of a circle with center R and radius
r. The length plus the width of rectangle ABCR is 8, and the perimeter of the shaded region
is 10 + 3. Find the value of r. Answers:
A) 6
B) 6:25
C) 6:5
D) 6:75
E) 7

Solution: Set x = RC and y = AR. It must then be x+y = 8 (by hypothesis) and x2+y2 = r2   (since the rectangle ABCR has one vertex in the circle). The perimeter of the shaded area is   then AS + SBT + TC + AC = (r 􀀀 y) + r=2 + (r 􀀀 x) +   p   x2 + y2 = 3r + r=2 􀀀 (x + y) =   3r + r=2 􀀀 8. All we need to so is solve for r in the equation 18 + 3 = (3 +   2 )r.   correct answer 6
Answer: A
If k, (k+200), (k+350), and 15*K are all multiples of V, then V could equal which of the following ?  Pick one:  A) 20  B) V=25  C) V=75  D) 100  E) 150

Solution: {Multiple of V} - {Multiple of V} = {Multiple of V}.   (K+200) - k = 200 = {Multiple of V}.   (K+350) - k = 350 = {Multiple of V}.   Both 200 and 350 are multiples of only option B.   Answer: V=25.
Answer: B
list of salaries of 8 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $33,000	Pick one.
A) $32,000 B) $28,500 C) $30,200 D) $30,800 E) $31,500

Solution: Ordering the data from least to greatest, we get:   $27,000, $29,000, $30,000, $31,000, $33,000, $35,500, $40,000, $43,000   Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.   $31,000 + $33,000 = $64,000   The median salary is $32,000.   $32,000nswer : $32,000
Answer: A
Tharak covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?  Choose the correct choice:
A) 3 hours 12 minute
B) 2 hours
C) 4 hours 40 minutes
D) 3 hours 20 minutes
E) 3 hours 18 minute

Solution: Let x be no. Of hours, and he travelled at 20kmph.   And balance distance (8-x)hr at 70kmph.   Total distance=20x+(8-x)hr =400   20x+(8-x)70=400   20x+560-70x=400   20x-70x=400-560   -50x=-160   x=3.2 =3 hr 12minutes   3 hours 12 minuteNSWER:3 hours 12 minute
Answer: A
In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate?  Choose one:
A) 576
B) 425
C) 215
D) 321
E) None of these

Solution: Explanation :   In a circle, 5 boys can be arranged in 4! ways   Given that the boys and the girls alternate.   Hence there are 4 places for girls which can be arranged in 4! ways   Total number of ways = 4! x 4! = 24 x 24 = 576. 576nswer : Option 576
Answer: A
Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?	Select
A) Rs. 1851  B) Rs. 1941  C) Rs. 1951  D) Rs. 1961  E) Rs. 1861

Solution: P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.   Amount = [15625 * (1 + 4/100)3]   = (15625 * 26/25 * 26/25 * 26/25) = Rs. 17576 C.I. = 17576 - 15625 = Rs. 1951.   ANSWER:Rs. 1951
Answer: C
In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:  Choose the correct choice.
A) Rs. 3100  B) Rs. 6240  C) Rs. 6500  D) Rs. 9600  E) Rs. 8600

Solution: To get Rs. 10, Investment is 96   To get Rs. 650, investment is (96/10)*650= 
(96/10)*650 = 6_240
6240   ANSWER:Rs. 6240
Answer: B
Find the product of place value and face value of 5 in 65231  Choose one.
A) 28000 B) 25000 C) 27000 D) 26000 E) 28000

Solution: Place value of 5 in 65231 = 5 x 1000 = 5000   Face value = 5   required product = 5000 x 5 = 25000   Answer :25000
Answer: B
The average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student. The weight of the student is	Choose the correct choice from the following options:
A) 62 kg
B) 60 kg
C) 64 kg
D) 72 kg
E) None of these

Solution: Explanation :   Let the weight of student be x kg.   Given, Difference in average weight = 8 kg   => (96-x)/4 = 8   => x = 64   Answer : 64 kg
Answer: C
The cost of 4 bags and 12 purses is Rs.1520, what is the cost of 10 bags and 30 purses?  Select:	A) Rs.3600	B) Rs.3500	C) Rs.3800	D) Rs.3900	E) None of these

Solution: Explanation:   Cost of 4 bags + 12 purses = Rs.1520   Multiply each term by 5/2, we get,   Cost of 10 bags + 30 purses = Rs.3800.   Answer: Option Rs.3800
Answer: C
Johnny travels a total of one hour to and from school. On the way there he jogs at 4 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour. How far is it to the school? Choose the correct choice from the following answers.
A) 2 miles B) 6.6 miles C) 4.8 miles D) 8 miles E) 10 miles

Solution: Answer: B) 6.6 miles.   Average speed for round trip = 2*a*b/(a+b), where a,b are speeds   so, average speed was = 2*4*20/(4+20) = 6.6m/hr   the distance between schoolhome should be half of that. ie. 6.6 miles   answer 6.6 miles
Answer: B
If two numbers are in the ratio 4:7. If 10 is added to both of the numbers then the ratio becomes 6:10 then find the largest number?	Choose the correct choice from the following.
A) 80 B) 40 C) 140 D) 100 E) None of these

Solution: Explanation:   4:7   4x + 10 : 7x + 10 = 6 : 10   10[4x + 10] = 6[7x + 10]   40x + 100 = 42x + 60   100 – 60 = 42x – 40x   2x = 40   X = 20   Then the first number is = 4   7x = 140   Short cut method:   a:b = 4:7   c:d = 6:10   1.Cross multiplication with both ratios   a * d ~ b * c = 4 * 10 ~ 7 * 6 = 40 ~ 42 = 2   2. If 10 is added both the number means   10 * 6= 
  10 * 6 = 60
60 and   10 * 10= 
  10 * 10 = 100
100,   Then 60 ~ 100= 40   ===> 2 -----> 40   ===> 1 -----> 20   ==> 7 -----> 140   Answer: Option 140
Answer: C
The price of 80 apples is equal to that of 120 oranges. The price of 60 apples and 75 oranges together is Rs.1320. The total price of 25 apples and 40 oranges is	Choose the correct choice from the following options
A) Rs. 660  B) Rs. 620  C) Rs. 820  D) Rs. 780  E) Rs. 960

Solution: Explanation :   Let the price of one apple = a and price of one orange = b   The price of 80 apples is equal to that of 120 oranges   80a = 120b   => 2a = 3b   ⇒b=2a3-----(Equation 1)   price of 60 apples and 75 oranges together is Rs.1320   =>60a + 75b = 1320   => 4a + 5b = 88   ⇒4a+5(2a)3=88(∵ Substituted the value of b from equation 1)   => 12a + 10a = 88 × 3   => 6a + 5a = 44 × 3   => 11a = 44 × 3   => a = 4 × 3 = 12   b=2a3=2×123=8   Total price of 25 apples and 40 oranges   = 25a + 40b = (25 × 12) + (40 × 8) = 300 + 320= 
300 + 320 = 620
620   Answer : Rs. 620
Answer: B
A cylinder is being filled with sand weighing 200 kg per cubic foot. The cylinder has a diameter of 1 foot and is 5 feet tall. How much sand is being used??  Options:
A) 250pi kg B) 500pi kg C) 500pi^2 kg D) 1000pi kg E) 1000pi^2 kg

Solution: Answer is A.   Volume of Cylinder = Pi*r^2 *h --------> Pi * (1/2)^2 * 5 --------> Pi * (1/4) * 5 --------> (5/4)Pi cubic feet.   1 cubic feet = 200 kg. so (5/4)Pi cubic feet = ((200*5)/4)Pi ---------> 250Pi   Regards,   250pi kgbhijit answer is 250pi kg
Answer: A
How many 3-digit numbers are completely divisible 6 ?  Choose the correct answer
A) 25
B) 78
C) 93
D) 150
E) 14

Solution: Explanation:   3-digit number divisible by 6 are: 102, 108, 114,... , 996   This is an A.P. in which a = 102, d = 6 and l = 996   Let the number of terms be n. Then tn = 996.   a + (n - 1)d = 996   102 + (n - 1) x 6 = 996   6 x (n - 1) = 894   (n - 1) = 149   n = 150   Number of terms = 150.   150)
Answer: D
Speed of a boat in standing water is 10kmph and speed of the stream is 1.5kmph. A man can rows to a place at a distance of 105km and comes back to the starting point. The total time taken by him is?	Select
A) 20.48hours  B) 21.48hours  C) 22.48hours  D) 23.48hours  E) 24.48hours

Solution: Speed upstream = 8.5kmph   Speed downstream = 11.5kmph   Total time taken = 105/8.5 + 105/11.5 = 21.48 hours   Answer is 21.48hours
Answer: B
An escalator moves towards the top level at the rate of 11 ft.sec and its length is 126 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length.  Options: A) 14 sec B) 10 sec C) 12 sec D) 8 sec E) 9 sec

Solution: Time taken to cover the entire length = tot.dist/resultant speed   = 126/ (11+3)= 
126/ (11+3) = 9
9 sec   ANSW9 secR:9 sec
Answer: E
How many seconds will a 750 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ? Choose the correct option
A) 48
B) 36
C) 26
D) 11
E) 45

Solution: Explanation:   Here distance d = 750 mts   speed s = 63 - 3= 
63 - 3 = 60
60 kmph= 60 x 5/18 m/s   time t = = 45 sec.   Answer: 45
Answer: E
Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 34 years old, and she stopped baby-sitting 12 years ago. What is the current age of the oldest person for whom Jane could have baby-sat? Pick:
A) 20 B) 21 C) 22 D) 23 E) 25

Solution: Check two extreme cases:   Jane = 18, child = 9, years ago = 34-18= 
34-18 = 16
16 --> child's age now= 9+16= 
9+16 = 25
25;   Jane= 22, child = 11, years ago = 34-22= 
34-22 = 12
12 --> child's age now= 11+12= 
11+12 = 23
23.   Answer: 25.
Answer: E
The average of first seven prime numbers which are odd is?  Choose the correct choice.
A) 15.5
B) 15.7
C) 15.2
D) 15.8
E) 10.7

Solution: Sum of first 7 prime no. which are odd = 75   Average = 75/7 = 10.7   Answer:10.7
Answer: E
A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? Choose one:
A) 7500 B) 2028 C) 2775 D) 5496 E) 6851

Solution: 35%-----------L   65%-----------W   ------------------   30%----------2250   100%---------? => 7500   7500nswer:7500
Answer: A
John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
Choose the correct choice from the following answers:
A) 10 B) 11 C) 12 D) 14 E) 15

Solution: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)   and Rupesh + 6 = | (Ravi + 6) ...(ii)   Solving both the equations we get,   Ravi = 12 years.   12
Answer: C
It takes Avery 3 hours to build a brick wall while Tom can do it in 5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
Choose the correct choice from the following choices:
A) 100  B) 110  C) 120  D) 130  E) 140

Solution: Avery takes 3 hours   Tom takes 2 hours   Efficiency of Avery is 1/3 units/hr   Efficiency of Tom is 1/5 units/hr   Combined efficiency of Tom and Avery is 1/3 +1/5 = 8/15 units/hr   Since they worked for 1 hour they completed 8/15 units of work and 7/15 units of work is left which is to be completed by Tom ( Since Avery left )   So Time taken by Tom to complete the remaining work will be 7/15/1/5 hours => 7/3*60= 
7/3*60 = 140
140 minutes...   Answer will be (140)
Answer: E
A restaurant meal cost $32.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:	Choose the correct option
A) $40 and $42	B) $39 and $41	C) $38 and 40	D) $37 and $39	E) $36 and $38

Solution: let tip=t   meal cost=32.50   range of tip = from 10% of 32.5 to 15% of 32.5 = 3.55 to 5.325   hence range of amount paid= 32.5+T= 36.05 to 37.825   ANSW$36 and $38R:$36 and $38
Answer: E
On what dates of April, 2001 did Wednesday fall?  Choices
A) 2nd, 9th, 16th, 23rd
B) 4th, 11th, 18th, 25th
C) 3rd, 10th, 17th, 24th
D) 1st, 8th, 15th, 22nd, 29th
E) 3rd, 8th, 15th, 17th, 23rd

Solution: Explanation:   We need to find out the day of 01-Apr-2001   01-Apr-2001 = (2000 years + period from 1-Jan-2001 to 01-Apr-2001)   We know that number of odd days in 400 years = 0   Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)   Days from 1-Jan-2001 to 01-Apr-2001 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 1(Apr) = 91   91 days = 13 weeks = 0 odd day   Total number of odd days = (0 + 0)= 
(0 + 0) = 0
0 odd days   0 odd day= Sunday. Hence 01-Apr-2001 is Sunday.   Hence first Wednesday of Apr 2011 comes in 04th and successive Wednesdays come in 11th, 18th and 25th   Answer: Option 4th, 11th, 18th, 25th
Answer: B
Rs 1000 is invested at 5% pa simple interest. If interest is added to principal after every 10 yr. Then we will get amount 2000 after how many year?	Choose the correct choice from the following options
A) 12 years. B) 13.66 years. C) 14 years. D) 16.66 years. E) 15 YEARS

Solution: P = 1000.   R = 5%.   T = 10 years.   I = PTR/100 = (1000 * 5*10)/100= 
(1000 * 5*10)/100 = 500
500.   Now,   Principal= 1000 + 500= 
1000 + 500 = 1_500
1500.   A= 2000   I = 500   R = 5%   T = (100 * I)/PR = (100 * 500)/(1500 *5) = 6.66 Years.   Total Time = 10 + 6.66= 
10 + 6.66 = 16.66
16.66 years.   ANSWER : OPTION 16.66 years.
Answer: D
Which of the following functions does not intersect with T = 3x^2 + 2x + 1  Options.
A) T = 3x^2 + 3x + 1	B) T = 2x^2 + 3x + 1	C) T = 3x^2 + 2x + 3	D) T = 4x^2 + 2x - 3	E) T = x^2 + 2x + 3

Solution: Let’s find the actual intersecting point of given function and each choice T.   A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0   B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1   C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.   D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2   E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.   So only choice (C) has no intersecting point. The answer is (T = 3x^2 + 2x + 3).
Answer: C
If x and y are different integers, both divisible by 6, then which is not necessarily true?
Choose the correct choice from the following:
A) x^2 + y^2 is divisible by 6 B) x - y is divisible by 6 C) xy is divisible by 6 D) x + y is divisible by 6 E) x + y is divisible by 12

Solution: Let x = 6k and let y = 6j.   Then x+y = 6(k+j) and k+j could be even or odd.   Thus 6(k+j) is not necessarily divisible by 12.   The answer is x + y is divisible by 12.
Answer: E
40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?  Choose the correct answer:
A) 76
B) 56
C) 56
D) 90
E) 15

Solution: Given, 40% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.   Given, marks of Robert = 80   30% of 80 = 30/100 * 8 = 24   Given, 40% of Ram's marks = 24.   => Ram's marks = (24 * 100)/40= 
(24 * 100)/40 = 60
60   Also, 20% of Rahim's marks= 24   => Rahim's marks   = (24 * 100)/20= 
(24 * 100)/20 = 120
120   Average marks of Ram and Rahim= (60 + 120)/2= 
(60 + 120)/2 = 90
90.   Answer: 90
Answer: D
A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? Options
A) 7  B) 9  C) 10  D) 12  E) 14

Solution: Explanation:   7 * 8 : 9 * x = 8:9 => x= 7   7)
Answer: A