MU-NLPC/Calc-aqua_rat huggingface dataset:
IF 2+3=31 ; 3+5=134 ; 5+7=368 Then 7+11=?
Choices
A) 1250  B) 1360  C) 1270  D) 1380  E) 1290

Solution: 2^2 + 3^3= 4 + 27= 
4 + 27 = 31
31   3^2 + 5^3= 9 + 125= 
9 + 125 = 134
134   5^2 + 7^3= 25 + 343= 
25 + 343 = 368
368   and   7^2 + 11^3= 49 + 1331= 
49 + 1331 = 1_380
1380   ANSWER:1380
Answer: D
In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 700 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Choose the correct choice from the following
A) 511  B) 546  C) 552  D) 562  E) 570

Solution: Number of newborns that can die in first month = 1/10 * 700= 
1/10 * 700 = 70
70   Survived= 630   Number of newborns that can die in second month = 1/10 * 630= 
1/10 * 630 = 63
63   Survived= 567   Number of newborns that can die in third month = 1/10 * 567 = 56   Survived = 511   511nswer:511
Answer: A
If 250!/10^n is an integer, what is the largest possible value of n?  Choose the correct option.
A) 65 B) 66 C) 62 D) 69 E) 97

Solution: The question actually asks the highest power of 10 which divides 250! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)   10 = 2 x 5   250 factorial will have 62 as -   250/5= 
250/5 = 50
50   50/5= 
50/5 = 10
10   10/5= 
10/5 = 2
2   So answer will be (62) 62
Answer: C
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:	Answers:  A) 28 sec  B) 36 sec  C) 48 sec  D) 52 sec  E) 56 sec

Solution: Relative speed = (60+ 90) km/hr   = 150x5/18   = 120/3 m/sec   Distance covered = (1.10 + 0.9)= 
(1.10 + 0.9) = 2
2 km= 2000 m.   Required time = 2000 x 3/125 = 48 sec.   Answer : 48 sec.
Answer: C
Nobel played a cricket series. His 7 innings score as {50, 75, 90, 115 120, 135, 150 }, find the mean and median of cricket scores of Nobel respectively ?  Choose one
A) 105,115  B) 100,120  C) 143,90  D) 115,105  E) 100,130

Solution: This is a good question to understand the difference between mean and median.   Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)   Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median   Coming to this question,   Mean = (50+ 75+ 90+ 115+ 120+ 135+ 150 )/7= 
(50+ 75+ 90+ 115+ 120+ 135+ 150 )/7 = 105
105   Median= 115   Option 105,115
Answer: A
In how many different ways can the letters of the word 'BANANA' be arranged?
Select
A) 10 ways
B) 120 ways
C) 30 ways
D) 60 ways
E) 40 ways

Solution: Totally there are 6 letters on the word BANANA. it contains 1B,3A,2N.   The no of ways is 6!/3!2!=120 ways.   ANSWER:120 ways
Answer: B
The average age of a group of people were 60 person aged 40 exits the group and average increases to 65. How many people were in the group initally?	Answers
A) 3 B) 4 C) 5 D) 6 E) 8

Solution: Let n be the number of people in the group   the new average;   65=60n-40/(n-1) => 65n-65=60n-40 => 5n=25 => n=5   Answer: 5
Answer: C
What is the dividend. divisor 18, the quotient is 9 and the remainder is 5?
Answers
A) A)130 B) B)134 C) C)148 D) D)158 E) E)167

Solution: D = d * Q + R   D = 18 * 9 + 5   D = 162 + 5= 
162 + 5 = 167
167   Answer 167
Answer: E
Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?  Options.
A) 2:9  B) 2:7  C) 1:6  D) 1:4  E) 1:3

Solution: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)   => Ratio of A / Ratio of B = (4 - 3)/(10 - 4) = 1/6   So they should be mixed in the ratio 1:6   Answer - 1:6
Answer: C
At a circular table for eleven will sit nine adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the eleven people be arranged around the table.	Choose the correct option
A) 12,720 B) 16,120 C) 20,160 D) 24,240 E) 28,080

Solution: Consider the two parents and two children as one unit.   Then there are seven adults and one family unit.   The number of ways 8 can form a line is 8!   Around a circular table, there would be 8 rotations so we divide this number by 8.   There are 7! ways for 8 to sit around the circular table.   Then the two children have two options and the two parents have two options.   Then the total number of ways is 7!*2*2= 20,160   The answer is 20,160.
Answer: C
In a set of integers, one-half of the numbers are multiples of 7 and one-third of the numbers are multiples of 3. If one-fifth of the numbers are multiples of both 3 and 7, then what percentage of the number are multiples of 7 but not multiples of 21? Pick one:
A) 9	B) 15	C) 30	D) 33.3	E) 60

Solution: Say there are 210 number in the set (LCM of 2, 3, 5, and 7).   Multiples of 7 = 1/2*210= 
1/2*210 = 105
105;   Multiples of both 3 and 7, so multiples of 21= 1/5*210= 
1/5*210 = 42
42.   Multiples of 7 but not 21= 105 - 42= 
105 - 42 = 63
63.   The percentage= 63/210 = 3/10.   Answer: 30.
Answer: C
If the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is? Choose the correct choice from the following answers.
A) 18	B) 11.2	C) 14	D) 12	E) 91

Solution: 2 * 22/7 * 15 * x = 1056 => x   = 11.2   Answer: 11.2
Answer: B
A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
Choose the correct choice from the following options: A) 1/13 B) 2/13 C) 1/26 D) 1/52 E) 1/23

Solution: Explanation:   Total number of cases = 52   Favourable cases = 2   Probability = 2/56 = 1/26   ANSWER IS 1/26
Answer: C
if (64)^2 - (36)^2 = 10x, then x = ?  Select the correct option.
A) 280  B) 210  C) 330  D) 220  E) 200

Solution: a^2−b^2=(a−b)(a+b)   (64)^2 - (36)^2 = (64 - 36)(64 + 36) = 28 × 100   Given that (64)^2 - (36)^2 = 10x   => 28 × 100 = 10x   => x = 280   280nswer is 280
Answer: A
How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 30 percent butterfat to obtain milk that is 20 percent butterfat? Choose the correct choice from the following:
A) 6
B) 8
C) 14
D) 16
E) 28

Solution: Equate the fat:   0.1x + 0.30*8 = 0.2(x + 8) --> x = 8.   Answer: 8.
Answer: B
If 2^4, 3^3, and 10^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w? Options:  A) 198  B) 288  C) 363  D) 360  E) 484

Solution: I will go with 360 (pending elements to match is 2^2*3^2*10^1 = 360
Answer: D
In how many different ways can 4 physics, 4 math, and 4 chemistry books be arranged in a row so that all books of the same subject are together?	Choose the correct choice from the following answers.
A) 76,366  B) 78,488  C) 80,122  D) 82,944  E) 84,500

Solution: Let's think of each subject as a group so there are 3 groups.   The number of ways to arrange these 3 groups is 3!   Within each subject the books can be re-arranged.   So we need to multiply 3! by 4!*4!*4! which is 3!*4!*4!*4! = 82,944   The answer is 82,944.
Answer: D
Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is:	Choices:
A) A)3
B) B)98
C) C)34
D) D)35
E) E)62

Solution: (3x-9):(5x-9) = 3:2   x = 1 => 3x = 3   3nswer:3
Answer: A
Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 6 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
Choose one
A) 2 hours B) 3 hours C) 5 hours D) 1 hour E) None of these

Solution: Explanation :   Tap A can fill the tank completely in 6 hours   => In 1 hour, Tap A can fill 1⁄6 of the tank   Tap B can empty the tank completely in 12 hours   => In 1 hour, Tap B can empty 1⁄12 of the tank   i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank   => In 6 hours, Tank A and B can effectively fill 1⁄12 × 6 = 1⁄2 of the tank.   Time taken to fill the remaining 1−(1/2) = 1/2 of the tank = (1/2)/(1/6)= 
(1/2)/(1/6) = 3
3 hours. Answer : Option 3 hours
Answer: B
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 5 cm? Choose the correct answer:
A) 827 cm2
B) 216 cm2
C) 95 cm2
D) 80 cm2
E) 176 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (5)   = 95 cm2   Answer:95 cm2
Answer: C
Albert invested an amount of $8000 in a fixed deposit scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit? Choose the correct choice from the following answers:  A) $8100  B) $8820  C) $8800  D) $8810  E) $8825

Solution: Amount = 8000 x (1 + 5/100)^2)   = 8000 x 21/20 x 21/20   =8820.   Answer $8820)$8820
Answer: B
Two persons start running simultaneously around a circular track of length 600 m from the same point at speeds of 20 km/hr and 10 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ? Choose the correct choice from the following answers.
A) 27 sec B) 87 sec C) 67 sec D) 72 sec E) 37 sec

Solution: Explanation:   Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 600 / (20 + 10)5/18 = 600 x 18 / 30 x 5 = 72 seconds.   Answer: 72 sec
Answer: D
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 170 runs and his average excluding these two innings is 58 runs, find his highest score.  Select:
A) 179  B) 367  C) 189  D) 177  E) 191

Solution: Explanation:   Total runs scored by the batsman = 60*46= 
60*46 = 2_760
2760 runs   Now excluding the two innings the runs scored= 58*44= 
58*44 = 2_552
2552 runs   Hence the runs scored in the two innings= 2760 â€“ 2552 = 208 runs.   Let the highest score be x, hence the lowest score = x â€“ 170   x + (x - 170) = 208   2x = 378   x = 189 runs   ANSWER: 189
Answer: C
At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 10 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank? Select.
A) 3/25  B) 5/6  C) 7/12  D) 2/3  E) 25/36

Solution: Gas used = (5 hours)*(50 miles/hour)*(1 gallon/30 miles) = 8+1/3 gallons   Portion used = (8+1/3) / 10 = 5/6   Ans 5/6
Answer: B
Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 36 meter head start. If Cristina runs at a pace of 6 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?  Choose the correct option: A) 15 seconds B) 18 seconds C) 25 seconds D) 30 seconds E) 12 seconds

Solution: used pluging in method   say t is the time for cristina to catch up with Nicky, the equation will be as under:   for Nicky=N=3*t+36   for Cristina=C=6*t   @t=12, N=72 C=72 right answer   ans:12 seconds
Answer: E
Two sets of 3 consecutive positive odd integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
Select the correct option:
A) 4  B) 7  C) 8  D) 12  E) it cannot be determined from the information given.

Solution: A=(1,3,5), sum of this=9   B=(5,7,9), sum of this=21,   The differenct between   21-9= 
  21-9 = 12
12   Hence,12 is the answer i.e.12
Answer: D
How many real roots does the equation x^3y+16xy+64y=0 have if y < 0?
Choose the correct choice from the following choices.
A) 0 B) 1 C) 2 D) 3 E) Infinite

Solution: x^3y+16xy+64y=0   => y ( x^2 + 16x + 64) = 0   => y (x+8)^2 = 0   if y<0 , then x=-8   So although there are 2 factors , they are the same x=-8 .   The equations has 1 distinct real root .   Answer 1
Answer: B
Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
Choose one:
A) Rs.28,028 B) Rs.28,002 C) Rs.28,028 D) Rs.28,000 E) Rs.28,039

Solution: 3:1   2:1   ------   6:1   1 ----- 4000   7 ----- ? => Rs.28,000   Answer: Rs.28,000
Answer: D
If 244,312 football shoes need to be placed in boxes and each box can contain at most 5 pair of football shoes. How many pair of football shoes will be in the last unfilled box?
Options:	Select the correct option:
A) 1football shoes
B) 3 football shoes
C) 4 football shoes
D) 2 football shoes
E) 9 football shoes

Solution: The number of football shoes that can be placed in boxes of 5 football shoes is the first number that is divisible by 5 that occurs before 244,312.   In order to divide the sum in 5 parts, the amount must be divisible by 5   Divisibility rule of 5: the last digit is 5 or 0.   last digit of digits of 244,312 is 2 and 2 is not divisible by 5   Hence, we need to remove 2 to this number for it to be divisible by 5   Correct Option: 2 football shoes
Answer: D
If a square mirror has a 20-inch diagonal, what is the approximate perimeter W of the mirror, in inches?  Select the correct option.
A) 40	B) 60	C) 80	D) 100	E) 120

Solution: if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.   And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter W must be less than 80, so we can eliminate answer choice C, D and E.   so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.   Now we are left with is 60
Answer: B
Find the simple interest on Rs. 69,000 at 16 2/3% per year for 9 months.	Choose the correct answer.
A) 7500
B) 6500
C) 8625
D) 9500
E) None of them

Solution: P = Rs.69000,R = 50/3% p.a and T = 9/12 years = 3/4years.   Simple Interest = (P*R*T)/100 = Rs.(69,000*(50/3)*(3/4)*(1/100))= Rs.8625   Answer is 8625.
Answer: C
The sum of three consecutive numbers is 252. The greatest among these three number is: Answers:  A) 45  B) 80  C) 85  D) 55  E) 40

Solution: Let the numbers be x, x + 1 and x + 2   Then,   x + (x + 1) + (x + 2) =252   3x = 252   x = 83   Greatest number, (x + 2) = 85   ANSWER:85
Answer: C
Solution A is 20% salt and Solution B is 60% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?	Pick: A) 6:4 B) 6:14 C) 4:4 D) 4:6 E) 1:3

Solution: Forget the volumes for the time being.   You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use   w1/w2 = (A2 - Aavg)/(Aavg - A1)   w1/w2 = (60 - 50)/(50 - 20) = 1/3   So the volume of the two solutions will be equal. Answer has to be 1:3   1:3.
Answer: E
A certain club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly J new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y? Answers:
A) 5^1/12	B) 3^11 * 5^11	C) 3^12 * 5^12	D) 3^11 * 5^12	E) 60^12

Solution: At the end of the first week, there are 5 new members;   At the end of the second week, there are 5J new members (since each 5 new members from the previous week brings J new members);   At the end of the third week, there are 5J^2 new members (since each 5J new members from the previous week brings J new members);   ...   At the end of the twelfth week, there are 5J^11 new members (since each 5J^10 new members from the previous week brings J new members).   We are given that 5J^11=y. Out of the answers only D yields integer value for J: 5J^11=3^11 * 5^12 --> J=3*5= 
3*5 = 15
15.   Answer: 3^11 * 5^12.
Answer: D
The difference between a number and its two-fifth is 510. What is 60% of that number? Pick.
A) 512
B) 510
C) 514
D) 516
E) 518

Solution: Let the number be x. Then,   x - 2/5 x = 510   x = (510 * 5)/3= 
(510 * 5)/3 = 850
850   60% of 850= 510.   Answer:510
Answer: B
Find the principle on a certain sum of money at 5% per annum for 4 years if the amount being Rs.1120? Pick
A) 933	B) 1067	C) 1977	D) 1056	E) 1097

Solution: 1120 = P [1 + (5*4)/100]   P= 933   933nswer: 933
Answer: A
A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the s um of the profits of B and C. Find the total profit. Choose one:
A) s.4500
B) s.5200
C) s.1800
D) s.Rs.3000
E) s.5000

Solution: A:B:C = 5:6:4   Let the total profit = 100 - 30= 
100 - 30 = 70
70   5/15 * 70= 70/3   A share = 70/3 + 30 = 160/3   B + C share = 100 - 160/3 = 140/3   A-(B+C) = 160/3 - 140/3 = 20/3   20/3 ---- 200   100 ---- ? => 3000   ANSWER:s.Rs.3000
Answer: D
Solution A is 20% pottasium and Solution B is 80% pottasium. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% pottasium solution?
Options: A) 6:4 B) 6:14 C) 4:4 D) 4:6 E) 3:7

Solution: Forget the volumes for the time being.   You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use   w1/w2 = (A2 - Aavg)/(Aavg - A1)   w1/w2 = (80 - 50)/(50 - 20)= 
(80 - 50)/(50 - 20) = 1
1/1   So the volume of the two solutions will be equal. Answer has to be 4:4=4:4
Answer: C
A team bought a total of 567 balls. If each player on the team bought at least 24 balls, then what is the greatest possible number of players on the team? Choose the correct choice from the following choices:
A) 21
B) 22
C) 23
D) 24
E) 25

Solution: 567/24=23 plus remainder.   The answer is 23.
Answer: C
P is 6 times greater than Q then by what per cent is Q smaller than P?
Pick one
A) 84%
B) 85.5%
C) 80%
D) 83.33%
E) None

Solution: Solution: Let Q = 10.   Then, P = 60.   Q is 50 less than P.   Q, % less than P = (50 /60)*100 = 83.33%.   Alternative Method   10 (Q)==(6 times greater)==> 60(P)==x%↓(Less than Q)==>10 (Q).   Now, x = 50*100/60 = 83.33%.   Answer: Option 83.33%
Answer: D
Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 38 years. What is Molly's age right now?
Choose the correct option:
A) 15	B) 18	C) 21	D) 24	E) 27

Solution: Now, Sandy is  38 - 6= 
 38 - 6 = 32
32   Molly's age is (3/4) * 32= 
(3/4) * 32 = 24
24   The answer is 24.
Answer: D
The least number which should be added to 2520 so that the sum is exactly divisible by 5,6,4 and 3 is :
Choose the correct choice from the following.
A) 3  B) 18  C) 23  D) 33  E) 43

Solution: Solution   L.C.M. of 5,6,4 and 3 = 60. on dividing 2520 by 60, the remainder is 42.   ∴ Number to be added = (60-42)= 
(60-42) = 18
18. Answer 18
Answer: B
If a profit of Rs.12000 is to be divided among three partners A,B and C in the ratio 5:3:4 then share of B is  Choices:
A) Rs.2000 B) Rs.4000 C) Rs.3000 D) Rs.5000 E) Rs.7000

Solution: B=3/12*12000= 
3/12*12000 = 3_000
3000   ANSWER:Rs.3000
Answer: C
If m > 1 and n = 2^(m+2), then 4^m =
Choose the most appropriate option
A) 16n^2	B) 4n^2	C) n^2	D) n^2/4	E) n^2/16

Solution: n = 2^(m+2) = 2^m*4   2^m = n/4   4^m = (2^m)^2 = (n/4)^2 = n^2/16   The answer is n^2/16.
Answer: E
Two out of five employees are capable of doing a certain task. Sixty percent of the five employees, including the two who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable?	Choose the most appropriate option.
A) 43.33%  B) 33.33%  C) 13.33%  D) 38.33%  E) 23.33%

Solution: Given 60% of 5 employees including 2 who are capable of doing task.   60% of 5 employeees   = 60/100 * 5= 
60/100 * 5 = 3
3 employees===> 2 employees who are capable of doing the task and one employee who is not capable.   percentage of employees assigned who are not capable   = 1/3 * 100   = 33.33%   ANSWER:33.33%
Answer: B
What is the ratio of (1/4 )to the power 3 and (1/4) to the power4  Select the correct option:
A) 1:2	B) 1:3	C) 1:4	D) 2:1	E) 4:1

Solution: 1/4^3/1/4^4=4/1= 
4/1 = 4
4:1   ANSW4:1R:4:1
Answer: E
A thief steels a car at 8a.m. and drives it at 50kmph. The theft is discovered at 9a.m. and the owner sets off in another car at 70 kmph. When will he overtake the thief?
Choices
A) 9a.m.  B) 9.30a.m.  C) 1130a.m.  D) 11.45a.m.  E) 10.15a.m.

Solution: Suppose the thief overtakes x hours after 8a.m.   Distance covered by the thief in x hrs = distance covered by the owner in (x-1 hours)   50x = 70(x-1)   20x = 70   x = 7/2 hrs   Thief is overtaken at 11.30a.m.   Answer is 1130a.m.
Answer: C
Two persons starting from the same place walk at a rate of 5kmph and 7kmph respectively. What time will they take to be 24km apart, if they walk in the same direction?  Choose the correct answer
A) 17 hrs  B) 22 hrs  C) 25 hrs  D) 12 hrs  E) 14 hrs

Solution: The relative speed of the boys = 7kmph â€“ 5kmph   = 2 kmph   12 hrsistance between them is 24 km   Time= 24km / 2 kmph = 12 hrs   Answer : 12 hrs.
Answer: D
a, b are positive integers. The remainder of a to be divided by 8 is 3 and the remainder of b to be divided by 6 is 5.
Which is possible to be the remainder of a*b to be divided by 48
Choose the correct choice from the following options
A) a) 2
B) b) 6
C) c) 8
D) d) 15
E) e) 20

Solution: Two ways to do it...   a=8x+3..   b=6y+5..   1) convenient way..   Take x and y as 0, and you will get a*b as   3*5= 
  3*5 = 15
15   Answer : d) 15
Answer: D
Perimeter of an equilateral and isosceles is 45 and 40 respectively. At least one of the sides of isosceles is equal to the equilateral. What's the base of isosceles triangle?  Choose the correct choice from the following options.
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: 10 units   as other 2 sides will be 15,15 units.   ANSWER:10
Answer: D
For any non-zero a and b that satisfy |ab| = -ab and |a| = a, |b-3| + |ab-b| =  Choose the correct choice from the following choices:
A) ab-4	B) |ab|+4	C) 2a-4b	D) b-3ab	E) ab+2ab+1

Solution: given |ab|=-ab a*b is negative , |a|=a, so a is positive hence b is negative since ab is negative.   assume a=1,b=-1 |b-3|= 4, |ab-b|=2; |b-3|+|ab-b|=6.   test case :c)   2a-4b= 6   test a) |-1|-4= -3   test b) 1+4=5   hence corect answer: 2a-4b
Answer: C
If 4+X < (2+5X)/3, which of the following is correct? Choices.
A) X < -5.	B) X > -5.	C) X > 5.	D) -5 < X < 0.	E) 0 < X < 5.

Solution: 4+X < (2+5X)/3   12+3X < 2+ 5X   10 < 2X   5<x x=""> 5. is the answer</x>
Answer: C