MU-NLPC/Calc-aqua_rat huggingface dataset:
A daughter lent $750 to her mother to help pay her rent. At the end of the month, the daughter received y dollars more than than the amount that was lent due to interest. The mother also gave her daughter an additional $5 for goodwill. In terms of y, what fraction of the total amount that the daughter received was the goodwill amount?  Pick.
A) (5y-1)/(755-y)  B) 5/(755+y)  C) 5y/(755+y)-1  D) 5y/(755+y)  E) 5y

Solution: The amount of money the daughter received was (750 + 5+ y) dollars. The $5 goodwill gift as a fraction of the amount received was, therefore, 5/(755+y).   Answer: 5/(755+y).
Answer: B
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the
probability that it is neither blue nor green? Choose the correct choice.
A) 2/3
B) 8/21
C) 3/7
D) 9/22
E) None of these

Solution: Explanation:   Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(E) = 8/21.   Answer: 8/21
Answer: B
From a pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king ?  Choose the correct choice from the following:
A) 1/212
B) 1/223
C) 1/221
D) 2/213
E) 3/313

Solution: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.   ∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221   1/221
Answer: C
When p is divided by 9, the remainder is 8. All of the following are possible values of p, except for which of the following?	Choose the correct answer
A) 17 B) 35 C) 53 D) 61 E) 71

Solution: Four of these numbers can be expressed in the form of 9x+8, where x can be 0,1,2,3,4....   However, 61 = 9(6) + 7   The answer is 61.
Answer: D
A shop owner sells 30mtr of cloth and gains SP of 10 metres. Find the gain %?
Choose the correct choice from the following choices:
A) 30%
B) 40%
C) 50%
D) 65%
E) 72%

Solution: Here, selling price of 10 m cloth is obtained as profit.   Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)   Selling price of 20 m cloth = Selling Price of 30 m of cloth   Let cost of each metre be Rs. 100.   Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000   Profit% = 10 × 100 = 50%   20   Profit of 50 % was made by the merchant.   50%
Answer: C
The difference between the circumference and the radius of a circle is 37 cm. The area of the circle is:  Choices.
A) 111 cm2	B) 148cm2	C) 154cm2	D) 259cm2	E) 269cm2

Solution: 2πr-r=37 or (2π-1)r=37.   Or (2* 22/7 -1)r=37 or 37r/7=37 or r=7.   Therefore, Area= πr2= (22/7 *7*7)= 
(22/7 *7*7) = 154
154 cm2   ANSWER:154cm2
Answer: C
A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?	Choose the most appropriate option:
A) Rs.3919  B) Rs.3910  C) Rs.3997  D) Rs.3900  E) Rs.3902

Solution: Area = (l + b – d) d   (80 + 60 – 10)10 => 1300 m2   1300 * 3 = Rs.3900   Answer:Rs.3900
Answer: D
There are three prizes to be distributed among nine students. If no students gets more than one prize, then this can be done in?	Choose one.
A) 10
B) 45
C) 5
D) 84
E) None of these

Solution: Explanation :   3 prize among 9 students can be distributed in 9C3 ways = 84 ways.   Answer : 84
Answer: D
What percentage of numbers from 1 to 70 have squares that end in the digit 1?	Options.
A) 90% B) 28% C) 20% D) 23% E) 12%

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 numbers = 14.   Required percentage = (14/70 * 100)= 
(14/70 * 100) = 20
20%   Answer:20%
Answer: C
Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder Choices:
A) 1234  B) 1265  C) 1350  D) 1467  E) 1647

Solution: Let the smaller number be x. Then larger number = (x + 1375).   x + 1375 = 6x + 15   5x = 1360   x = 272   Large number = 272+1375= 
272+1375 = 1_647
1647   1647
Answer: E
An ant walks an average of 1000 meters in 30 minutes. A beetle walks 10% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h? Choose the most appropriate option.
A) 1.8	B) 1.6	C) 2.775.	D) 1.9	E) 3.5.

Solution: the ant walks an average of 1000 meters in 30 minutes   1000 meters in 1/2 hours   the beetle walks 10% less distance = 1000-10=900 meters in 30 minutes   0.900 km in 30/60 = 1/2 hours   speed = 0.900*2= 
0.900*2 = 1.8
1.8 km/h   I guess option 1.8 should be 1.8
Answer: A
A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days.If they get Rs 1500 for the whole work, the daily wages of B and C are?  Choose the correct choice from the following answers:	A) 225	B) 276	C) 126	D) 187	E) 1267

Solution: Explanation:   Let the total work = 30 units.   Then capacity of A = 3 units, B = 2 units. Now they worked for 5 days. So they must have completed 25 units. Rest of the work 5 units done by C in 2 days. So C capacity = 5/2= 
5/2 = 5/2 = around 2.5
2.5 units.   Given that toatal wages are Rs.1500 for 30 units. So for 1 unit of work they get Rs.50. Now B and C per day work= (2 + 2.5)= 
(2 + 2.5) = 4.5
4.5 units. So their daily wages= 4.5 × 50 = Rs.225   225nswer:225
Answer: A
In a nationwide poll, N people were interviewed. If 1/5 of them answered yes to question 1, and of those, 1/3 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?	Pick one:
A) N/8
B) 6N/7
C) 4N/15
D) 7N/15
E) 14N/15

Solution: The number of people who answered yes to both questions is (1/3)(1/5)N = N/15   The number of people who did not answer yes to both is 1 - N/15 = 14N/15   The answer is 14N/15.
Answer: E
Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend? Choose the correct choice from the following options.
A) $6.80
B) $8.40
C) $7.70
D) $4.70
E) $3.90

Solution: Linda spent   1.20 ? 3 = $3.60 on notebooks   The total amount of money that Linda spent is equal to    3.60 + 1.50 + 1.70= 
 3.60 + 1.50 + 1.70 = 6.8
$6.80   correct answer $6.80
Answer: A
The present ages of three persons are in proportions 4:7:9.Thirteen years ago, the sum of their ages was 81. Find their present ages.
Pick: A) 24, 42 B) 28, 36 C) 35, 45 D) 35, 55 E) of these

Solution: Let their present ages be 4x, 7x and 9x years respectively.   Then, (4x - 13) + (7x - 13) + (9x - 13) = 81   20x = 120 => x = 6   Their present ages are 24, 42 and 54 years respectively.   24, 42NSWER:24, 42
Answer: A
57+58=115. How many such 2 consecutive numbers are there less than 1500 when added gives a sum which is divisible by 5?  Choose the correct choice
A) 100  B) 200  C) 300  D) 400  E) 500

Solution: since 2+3= 
2+3 = 5
5 & 7+8= 
7+8 = 15
15   any combination with these no be will give u desirable result...   so total no in 100 will be 20 & that's why in 1000,it will be 20X15=300.   ANSWER:300
Answer: C
The average (arithmetic mean) monthly income of four workers is $1,000. After one worker’s income increases by 50 percent the new average income is $1,200. What was the original income of the worker whose monthly income increased?	Choose the correct choice from the following answers.
A) $1,800  B) $1,500  C) $1,300  D) $1,600  E) $1,100

Solution: Increase in total income was 200*4= 
200*4 = 800
$800, we know that this increase was 50% (1/2) of the workers original income, thus his/her original income was 800*2=$1,600.   Answer: $1,600
Answer: D
What is the largest 4 digit number exactly divisible by 35?
Choose the correct option
A) 4676 B) 4678 C) 9975 D) 9504 E) 9936

Solution: Largest 4 digit number = 9999   9999 ÷ 35 = 285, remainder = 24   Hence largest 4 digit number exactly divisible by 88   = 9999 - 24= 
9999 - 24 = 9_975
9975   answer :9975
Answer: C
The sum of 3 consecutive numbers is definitely  Choose the correct choice from the following answers:
A) Positive.
B) Divisible by 2.
C) Divisible by 4.
D) Divisible by 3.
E) Divisible by 5.

Solution: If 1st term is x:   x+(x+1)+(x+2)=3x+3--->Always divisible by 3   If 2nd term is x:   (x-1)+x+(x+1)  +( +1)+( +2)= 
  +( +1)+( +2) = 3
3x+3--->Always divisible by 3   If 2nd term is x:   (x-1)+x+(x+1)=3x--->Always divisible by 3   If 3rd term is x:   (x-2)+(x-1)+x=3x-3--->Always divisible by 3   Answer: Divisible by 3.
Answer: D
A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then
leaves. A alone can finish the remaining work in Choose the correct choice
A) 5 days B) 6 days C) 7.5 days D) 8.5 days E) None of these

Solution: Explanation:   B's 5 days work =   110   ∗   5=12Remaining work =1−12=12A can finish work =15   ∗   12=7.5days   Answer: 7.5 days
Answer: C
The average of marks obtained by 120 boys was 39. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?	Choose the correct choice from the following choices
A) 100
B) 110
C) 120
D) 130
E) 140

Solution: Let the number of boys who passed = X.   Then, 39 x X + 15 x (120 - X) = 120 x 39   24X = 4680 - 1800   => X = 2880/24= 
2880/24 = 120
120.   Hence, the number of boys passed= 120.   ANSWER:120
Answer: C
If the numerator of a fraction T is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?
Choose the correct choice from the following answers:
A) 16 1⁄6%	B) 25%	C) 33 1⁄3%	D) 50%	E) 66 2⁄3%

Solution: This question can be dealt with conceptually or by TESTing VALUES.   We're told that the numerator of a fraction T is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.   Let's TEST 2/1   If we triple the numerator and double the denominator, we end up with....   (2x3)/(1x2) = 6/2= 
6/2 = 3
3   Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2= 1/2 of itself = 50%   50%
Answer: D
At what rate percent on simple interest will Rs.750 amount to Rs.1125 in 5 years?	Options.
A) 2  B) 10  C) 4  D) 5  E) 6

Solution: 375 = (750*5*R)/100   R = 10%.Answer: 10
Answer: B
If 45% of a class averages 95% on a test, 50% of the class averages 78% on the test, and the remainder of the class averages 60% on the test, what is the overall class average? (Round final answer to the nearest percent). Pick:	A) 83%	B) 84%	C) 85%	D) 86%	E) 87%

Solution: This question is a Weighted Average question with a series of dependent variables.   The remaining portion of the class represents 100% - 45% - 50% = 5% of the class   85%onverting the portions of the class population to decimal weights, we find:   85%lass Average  100  - 45  - 50= 
 100  - 45  - 50 = 5
5% of the class   85%onverting the portions of the class population to decimal weights, we find:   85%lass Average= 0.45x95 + 0.50x78 + 0.05x60 = 84.75   The class average (rounded) is 85%   Final Answer   85%) 85%
Answer: C
John's Bank's saving amount is decreased 30% due to loan payment and current balance is Rs.7000. Find the actual balance before deduction?  Answers:	A) 8000	B) 8500	C) 9000	D) 9500	E) 10000

Solution: CP* (70/100) = 7000   CP= 100 * 100 => CP = 10000   Answer:10000
Answer: E
An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 2 ?
Choose the correct choice from the following choices:
A) 1/9	B) 1/3	C) 1/2	D) 2/3	E) 5/6

Solution: n(n+2) to be divisible by 2 either n or n+2 must be a multiples of 2.   In each following group of numbers: {1, 2, 3, 4}, {5, 6, 7, 8}, ..., {97, 98, 99, 100} there are EXACTLY 2 numbers out of 4 satisfying the above condition. For example in {1, 2, 3, 4} n can be: 2, or 4. Thus, the overall probability is 2/4 =1/2.   Answer: 1/2.
Answer: C
The sequence a1, a2, a3, ... , an, ... is such that an=an−1+an−2/2 for all n≥3n≥3. If a3=4 and a5=20, what is the value of a6 ?	Select the correct option:
A) 12 B) 16 C) 20 D) 24 E) 28

Solution: Since given that an=an−1+an−2/2, then:   a5=a4+a3/2 --> 20=a4+4/2 --> a4=36   a6=a5+a4/2 --> a6=20+36/2 --> a5=28   Answer: 28.
Answer: E
The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides.
Choose the correct choice from the following answers
A) 12, 9	B) 18, 3	C) 15.16, 6	D) 12, 12.37	E) 12, 15.16

Solution: CM=3   AREA=PM*CM/2, thus PM=12   By Pythagorean Theorem, we can now find the value of PC.   12, 12.37 is the correct option.
Answer: D
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 34 cm?
Choose the correct choice from the following choices
A) 680 sq.cm  B) 268 sq.cm  C) 618 sq.cm  D) 297 sq.cm  E) 600 sq.cm

Solution: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE = √(625 - 225)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 34= 
1/2 * 40 * 34 = 680
680 sq.cm.   680 sq.cmnswer:680 sq.cm
Answer: A
In a dairy farm, 46 cows eat 46 bags of husk in 46 days. In how many days one cow will eat one bag of husk?	Choose the correct choice from the following:
A) 1	B) 46	C) 20	D) 26	E) 30

Solution: Explanation :   One bag of husk = 46 cows per day   ⇒ 46 × 1 × 46 = 1 × 46 × x   For one cow = 46 days   Answer : 46
Answer: B
A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 488. What is the sum of the last 8 of the even integers?  Choices
A) 598
B) 604
C) 610
D) 616
E) 622

Solution: The sum of the first 8 numbers is: x + (x+2) +...+ (x+14) = 488   The sum of the next 8 numbers is: (x+16) + (x+2+16) +...+ (x+14+16) =   488 + 8(16) = 488 + 128= 
488 + 128 = 616
616   The answer is 616.
Answer: D
A boat travels 40 km downstream in 8 hours and 36 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.
Choose the correct answer
A) 8 km/hr, 1 km/hr B) 5 km/hr, 4 km/hr C) 1 km/hr, 6 km/hr D) 2 km/hr, 1 km/hr E) 4 km/hr, 1 km/hr

Solution: Downstream speed=40km/8hrs   =5kmph   upstream speed40  /8= 
40  /8 = 5
5kmph   upstream speed=36km/12hrs   =3kmph   speed of boat36  /12= 
36  /12 = 3
3kmph   speed of boat=avg of downstream and upstream speeds   speed of boat=(5+3)/2= 
(5+3)/2 = 4
4kmph.   current speed=half of the difference of downstream and upstream speeds   currend speed=(5-3)/2= 
(5-3)/2 = 1
1kmph   ans is 4km/hr,1km/hr   ANSW4 km/hr, 1 km/hrR:4 km/hr, 1 km/hr
Answer: E
During a given week A programer spends 1/4 of his time
preparing flow chart, 3/8 of his time coding and the rest of
the time in debugging the programs. If he works 48 hours
during the week , how many hours did he spend debugging the
program.	Select the correct option.
A) 15 hours
B) 16 hours
C) 17 hours
D) 18 hours
E) 19 hours

Solution: 1/4 of time for flow charts =48/4= 
48/4 = 12
12 hours   3/8 time for coding=48*3/8= 
48*3/8 = 18
18   so remaining time for debugging=48-12-18= 
48-12-18 = 18
18 hours   ANSWER:18 hours
Answer: D
Q. How many 6-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5?	Choose the correct choice from the following choices:
A) 180 B) 240 C) 210 D) 270 E) 300

Solution: the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2   i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _   case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6   when the units digit is 2 i.e 1 _ _ _ _ _ 2   number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60   when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30   case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6)   number of ways this can be done would be 5! / (2!) for 2 =60   and 5! / 2! for 6 ... = 60   adding all of these ... gives the answer 180 ...   the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat   180
Answer: A
In year Y imported machine tools accounted for 60 percent of total machine-tools sales in the United States, and Japanese imports accounted for 30 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars? Choices:
A) 55x/9  B) 50x/9  C) 60x/9  D) 65x/9  E) 75x/9

Solution: Sales of imported tools = 60% of the total sales = 0.60*{total} = 3{total}/5;   Sales of Japanese tools = 30% of the sales of imported tools = 3/10*3{total}/5 = 9{total}/50.   Since the sales of of Japanese tools was x, then 9{total}/50 = x -->9 {total} = 50x   {total} = 50x/9   Answer: 50x/9
Answer: B
30% of a number is more than 60% of 150 by 120. Find the number? Choose the correct answer:	A) 770	B) 712	C) 720	D) 740	E) 700

Solution: (30/100) * X – (60/100) * 650 = 190   2/7 X = 210   X = 700   Answer:700
Answer: E
5,9,17,29,49,__ Choose the most appropriate option: A) 79 B) 80 C) 81 D) 82 E) 83

Solution: (9+5) +3= 
(9+5) +3 = 17
17   (16+9) +4= 
(16+9) +4 = 29
29   (28+16)+5= 
(28+16)+5 = 49
49   (48+28)+6= 
(48+28)+6 = 82
82   ANSWER:82
Answer: D
If X and Y are positive integers such that (3X + 7Y) is a multiple of 11, then which of the following will be divisible by 11?	Options
A) 4X + 6Y  B) X + Y + 4  C) 9X + 4Y  D) 4X - 9Y  E) 9X - 4Y

Solution: by hit and trail, we put X = 5 and Y = 1 so that (3X + 7Y)   = ((3*5) + (7*1))= 
((3*5) + (7*1)) = 22
22, which is divisible by 11   (4X + 6Y)= 4*5 + 6*1= 
4*5 + 6*1 = 26
26, which is not divisible by 11   (X + Y + 4)= (5 + 1 + 4)= 
(5 + 1 + 4) = 10
10, which is not divisible by 11   (9X + 4Y)= (9*5 + 4*1)= 
(9*5 + 4*1) = 49
49 which is not divisible by 11   (4X - 9Y)= (4*5 - 9*1)= 
(4*5 - 9*1) = 11
11 which is divisible by 11   (9X - 4Y)= (9*5 - 4*1)= 
(9*5 - 4*1) = 41
41 which is not divisible by 11   So the Answer is 4X - 9Y
Answer: D
A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage.
I. The rate of X is Rs. 20 per kg.
II. The rate of Y is Rs. 13 per kg. Choose the correct choice from the following answers:
A) I alone sufficient while II alone not sufficient to answer	B) II alone sufficient while I alone not sufficient to answer	C) Either I or II alone sufficient to answer	D) Both I and II are not sufficient to answer	E) Both I and II are necessary to answer

Solution: EXPLANATION   The ratio, in which X and Y are mixed, is not given.   So, both I and II together cannot give the answer.   answer is (Both I and II are not sufficient to answer).
Answer: D
What percentage of numbers from 1 to 70 have squares that end in the digit 1?	Pick:
A) 1
B) 14
C) 20
D) 21
E) 22

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 numbers = 14.   Required percentage = (14/70 * 100)= 
(14/70 * 100) = 20
20%   ANSWER:20
Answer: C
A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,056. How much did she invest at 5%?
Options.
A) $500
B) $400
C) $700
D) $900
E) $950

Solution: et x be the portion invested at 5% and   Let (1-x) be the rest which is invested at 6%   The question states that the return after 1 year is (1056/1000)-1 = 0.053 = 5.3%   We want to find the dollar amount invested in X   Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)   0.05x+0.06(1-x)= 0.056   (0.05)x +0.06 - (0.06)x = 0.056   -0.01x = -0.004   x= -0.004/-0.01 = 4/10 = 40%   So X = 40% of the 1000 which is 400   ANSWER:$400
Answer: B
There are 100 apples in a bag of which 98% are green and the rest red. How many green apples do you need
to remove so that only 96% of the apples are green?  Pick:	A) 40	B) 8	C) 15	D) 25	E) 50

Solution: 98−x/100−x=96100   Or, 9800−100x=9600−96x   Or, 200=4x   Or, x=50   ANSW50R:50
Answer: E
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 answer:
A) 288
B) 660
C) 500
D) 267
E) 298

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
Answer: C
Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y?
Choose the correct answer
A) 15.5 sec
B) 8.4 sec
C) 33.6 sec
D) 31.11 sec
E) 16.8 sec

Solution: Z--------------------------------------|----------------------------Y   Car A(20mps)------------------------->P<---------------Car B(15mps)   Let 2 cars meet each other at point P in t seconds.   Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t.   From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.   so, 15t/20 = 10   So t=40/3 sec and total distance = (35*40)/3   Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.   Answer 31.11 sec
Answer: D
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -.
Choose one.
A) 7/18 B) 7/19 C) 7/11 D) 7/12 E) 7/15

Solution: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.   Similarly from eight white balls two can be drawn in ways.   7/15   Answer: 7/15
Answer: E
A box contains SEVEN bulbs out of which 3 are defective. If TWO bulbs are chosen at random, find the probability that atleast one bulb is good
Choose the correct answer
A) 5/6	B) 6/7	C) 7/8	D) 8/9	E) 9/8

Solution: Required probability ==1-3C2/7C2= 1 - 1/7 = 6/7.Answer:6/7
Answer: B
The sum of the ages of 4 children born at the intervals of 1 years each is 12 years. what is the age of the youngest child ?
Choose the correct option
A) 2.5  B) 1.5  C) 1  D) 3.5  E) 4.5

Solution: Let x = the youngest child. Each of the other four children will then be x+1, x+2, x+3   We know that the sum of their ages is 12   so, x+(x+1)+(x+2)+(x+3) = 12   therefore The youngest child is 1.5 years old   Answer: 1.5
Answer: B
In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?	Choose the correct choice from the following choices.
A) 187 B) 190 C) 192 D) 195 E) 213

Solution: The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:   (i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1   x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1= 
80 + 90 + 24 + 1 = 195
195   195
Answer: D
If (7)(x^2) has four different prime factors, at most how many different prime factors does x have? Choose the correct option
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: x can have at most 4 prime factors, namely the prime factor 7 plus 3 others.   If x had more than this number of prime factors, then (7)(x^2) would have more than 4 prime factors.   The answer is 4.
Answer: D