MU-NLPC/Calc-aqua_rat huggingface dataset:
In a college the ratio of the numbers of boys to the girls is 8:5. If there are 190 girls, the total number of students in the college is?  Pick one:
A) 562
B) 356
C) 452
D) 494
E) 512

Solution: Let the number of boys and girls be 8x and 5x   Then , 5x = 190   x= 38   Total number of students = 13x = 13*38= 
13*38 = 494
494   Answer is 494
Answer: D
A sum was put at simple interest at a certain rate for 9 years Had it been put at 5% higher rate, it would have fetched 1350 more. Find the sum.  Choose the correct choice from the following options.
A) 3000  B) 3100  C) 3200  D) 3300  E) 3400

Solution: Difference in S.I. = P×T/100(R1−R2)   ⇒ 1350 = P×9x5/100(∵ R1 - R2 = 2)   ⇒ P = 1350×100/9x5=3000   3000nswer 3000
Answer: A
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? Choose the correct choice:	A) 76 sec	B) 88 sec	C) 48 sec	D) 44 sec	E) 33 sec

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.9= 
1.10 + 0.9 = 2
2 km= 2000 m.   Required time = 2000 * 3/125= 
2000 * 3/125 = 48
48 sec.   Answer: 48 sec
Answer: C
Find the least square number which is exactly divisible by 10,12,15 and 18. Pick one:  A) 900  B) 120  C) 103  D) 140  E) 217

Solution: L.C.M. of 10, 12, 15, 18 = 180. Now, 180 = 2 * 2 * 3 * 3 *5 = 22 * 32 * 5.   To make it a perfect square, it must be multiplied by 5.   Required number = (22 * 32 * 52) = 900.   900NSWER 900
Answer: A
Currently apples cost 75 cents/pound. Due to a disease affecting the apple trees it is expected that next month apples will cost 150% more than they do currently. How much are apples expected to cost next month?  Choose one
A) 195 cents /pound B) 192 cents /pound C) 187.50 cents /pound D) 187 cents /pound E) 190 cents /pound

Solution: If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).   In this case, (new cost) = 75 cents/pound + (150/100)(75 cents/pound)   = 75 cents/pound + 112.50 cents/pound   = 187.50 cents /pound   Answer : 187.50 cents /pound
Answer: C
Find the number of ways in which 10 different beads can be arranged to form a necklace.  Choose the correct choice from the following options:
A) 181440
B) 245890
C) 457890
D) 124560
E) 231560

Solution: Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,10 beads can be arranged to form a necklace in(10-1)! /2 ways   = 9!/2 = 181440ways   181440nswer is 181440
Answer: A
A person takes 5hrs 45 min in walking to a place and ridingback. He would have gained 2hrs by riding both ways. The time he would take to walk both ways is?
Choose the correct choice from the following choices
A) 5 hours 45 min  B) 6 hours 30min  C) 4 hours 50 min  D) 7 hours 45 min  E) 8 hours

Solution: ----------------------------------------------------------------   Solution 1   ----------------------------------------------------------------   Given that time taken for riding both ways will be 2 hours lesser than   the time needed for waking one way and riding back   From this, we can understand that   time needed for riding one way = time needed for waking one way - 2 hours   Given that time taken in walking one way and riding back = 5 hours 45 min   Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min   In fact, you can do all these calculations mentally and save a lot of time   which will be a real benefit for you.   7 hours 45 min
Answer: D
If ab+bc+ca=0,What is the value of a^2+b^2+c^2?	Pick
A) (a^2+b^2+c^2)/2  B) (a+b+c)^2  C) (a^2+b^2+c^2)^2  D) a+b+c  E) c+a+b

Solution: The option B is correct.   The formula (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca).   (a+b+c)^2=a^2+b^2+c^2+2(0).   a^2+b^2+c^2=(a+b+c)^2 is the answer
Answer: B
A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 12 men leave the bus and six women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?
Choose the correct choice from the following answers:
A) 15
B) 30
C) 36
D) 45
E) 54

Solution: Explanation:   Originally, let number of women = x. Then, number of men = 2x.   So, in city Y, we have : (2x - 12) = (x + 6) or x = 18.   Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 54.   Answer: 54
Answer: E
A and B can finish a work 30 days if they work together. They worked together for 20 days and then B left. A finished the remaining work in another 20 days. In how many days A alone can finish the work? Pick:	A) 60	B) 50	C) 40	D) 30	E) 20

Solution: Explanation :   60mount of work done by 60 and B in 1 day = 1/30   60mount of work done by 60 and B in 20 days = 20 × (1/30) = 20/30 = 2/3   Remaining work – 1 – 2/3 = 1/3   60 completes 1/3 work in 20 days   60mount of work 60 can do in 1 day = (1/3)/20 = 1/60   => 60 can complete the work in 60 days   60nswer : Option 60
Answer: A
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 46 years now, the son's age five years back was	Choose the correct option
A) 16years B) 17years C) 18years D) 19years E) 20years

Solution: Let the son's present age be x years. Then, (46 - x) = x   2x = 46.   x = 23.   Son's age 5 years back (23 - 5)= 
(23 - 5) = 18
18 years.   18years)
Answer: C
A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?  Pick one.
A) 18  B) 87  C) 26  D) 27  E) 29

Solution: Let the present age of the person be x years.   Then, 3(x + 3) - 3(x - 3) = x   3x + 9 - 3x + 9 = x => x = 18'   18nswer: 18
Answer: A
8^100 is divisible by 17. Find the remainder?	Pick one
A) 8  B) 12  C) 16  D) 18  E) 20

Solution: This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.   So divide 100 by 16 and find the remainder. Remainder = 4   Therefore, 100 = (16 × 6) + 4   Now this problem can be written as 810017 = 816×6+417 = (816)6×8417   Now this problem simply boils down to (1)6×8417 = 8417   84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.   16
Answer: C
Four of the five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.  Choices:  A) 371.587 + 46.32 – 217.907  B) 4 × 125 – 75 × 4  C) 58.25 × 4.5 – 65.875  D) 25 × 12 – 2 × 5 × 10  E) 121 × 3.5 – 2 × 111.75

Solution: The other parts are equal to 200.   Answer 58.25 × 4.5 – 65.875
Answer: C
For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many multiples of 4 are there between 4* and 5*, inclusive? Answers.
A) 5  B) 6  C) 20  D) 24  E) 25

Solution: here, 4* = 4! and 5* = 5!   question is asking no. of terms in an AP whose first term is 24(4!), last term is 120(5!) and common difference is 4.   last term OR nth term = first term +(no. of tems -1)(common difference)   Tn = a + (n-1)d   120 = 24 + (n-1)4   96/4 = n-1   n = 25 .....25
Answer: E
Two buses and a van were employed to transport a class of students on a field trip. 3/5 of the class boarded the first bus. 1/2 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
Choose one.
A) a) 1/2
B) b) 7/10
C) c) 11/15
D) d) 23/30
E) e) 4/5

Solution: This is a pure ratio question (we aren't given any numbers for anything), so you can just choose any starting number you like, and use it to solve the problem. The best number to pick is almost always the product of all the denominators of your fractions, so here we could start with 30 students. Then we have:   • 3/5 of these, or 18 students, board the first bus   • there are 12 students left. 1/2 of these, or 6 students, board the second bus   • this bus breaks down, and 1/2 of the 6 students, or 3 students, board the first bus   • the first bus now contains 21 out of the original 30 students, so the answer is 21/30 = 7/10   Answer b) 7/10
Answer: B
The average of 11 numbers is 30. If the average of first six numbers is 17.5 and that of last six is 42.5, then what is the sixth number?
Choose the most appropriate option:  A) 30  B) 36  C) 45  D) 47  E) 43

Solution: Given: Average of 11 numbers = 30   Step 1: Calculate total of 11 numbers by multiplying it by average value 30 = 11 x 30 = 330   Step 2: Calculate total of first six members by multiplying it by average value 17.5 = 17.5 x 6 = 105   Step 3: Calculate total of last six members by multiplying it by average value 42.5 = 42.5 x 6 = 255   Therefore, we can find sixth number by adding value of first six and last six numbers and subtracting it from the total value of 11 numbers.   Sixth number =(105 + 255)- 330= 
(105 + 255)- 330 = 30
30   30NSWER IS 30
Answer: A
Mrs. Evans gave a test to her freshmen economics class, which has 40 students enrolled and 30 of them answered question 1 correctly. If 29 answered question 2 correctly and 10 did not take the test then how many answered both questions correctly?	Choices
A) 24  B) 27  C) 29  D) 31  E) 33

Solution: Total number of enrolled students = 40   Number of students who did not take test = 10   Hence, number of students who took test = 40 - 10= 
40 - 10 = 30
30   Number of students who answered Q2 correctly=29, therefore, all students who took test answered Q2 correctly.   So, number of students who answered Q1 correctly, also answered Q2 correctly = 29.   Number of students who answered both Q1 & Q2 correctly = 29.   ANSWER:29
Answer: C
For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -7, -6 ?  Select the correct option.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Given sequence: {1, -3, 2, 5, -4, -6}   The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative.   1*(-3)=-3=negative;   -3*2=-6=negative;   2*5= 
2*5 = 10
10=positive;   5*(-4)=-20=negative;   (-4)*(-6)= 
(-4)*(-6) = 24
24=positive.   So there are 5 pairs of consecutive terms of the sequence for which the product is negative.   Answer: 5.
Answer: E
Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much? Choose the correct choice from the following answers
A) 9680 B) 2338 C) 1278 D) 1098 E) 1279

Solution: (8000*3*2)/100= 
(8000*3*2)/100 = 480
480   9200   --------   9680   9680nswer: 9680
Answer: A
What is the units digit of the expression 14^7−19^4?	Choose the correct answer:
A) 0
B) 3
C) 4
D) 6
E) 8

Solution: I think answer on this one should be E too. Since we know that 14^7>19^4, as Will said one should always check if the number is positive.
Answer: E
If x < y < 0, which of the following must be true? Choose the correct answer.
A) 2xy/3x is a negative integer B) x-y is a positive integer C) (-x)+ (-y) is positive integer D) x/y is a negative integer E) 2x+y is a negative integer

Solution: Given x, y are less than 0. So both will be negative integers   negative + negative = negative   negative * negative = positive   negative / negative = positive   x-y is false since xSo, option (-x)+ (-y) is positive integer is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers)   Answer : (-x)+ (-y) is positive integer
Answer: C
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0014)? Options.
A) 13.86 B) 14.86 C) 15.86 D) 12.86 E) 11.86

Solution: You get 10^2 (100-1) (.0014)   we know   14/10000= 
  14/10000 = 7/5_000 = around 0.0014
.0014   10^2 (99) * (14/10000)   10^2= 100 and 100^2 = 10000   Cancel out the 100 with the 10^2   Left with 99(14/100).   .99*14= 
.99*14 = 13.86
13.86   13.86nswer : 13.86
Answer: A
In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (11, 0), (0, -3.5), (-11, 0)?  Choose the correct answer.
A) 56 B) 77 C) 112 D) 116 E) 120

Solution: Area of rhombus= 1/2* D1 *D2   Length of 1st diagonal = 11+11= 
11+11 = 22
22   Length of 2nd diagonal= 3.5+3.5= 
3.5+3.5 = 7
7   Area= 1/2*22*7= 
1/2*22*7 = 77
77   77 is the answer
Answer: B
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?	Pick.
A) 15 minutes.	B) 17 minutes.	C) 12 minutes.	D) 10 minutes.	E) 11 minutes.

Solution: Part filled by A in 1 min =1/20   Part filled by B in 1 min =1/30	.   Part filled by (A + B) in 1 min =1/20+1/30=1/12	.   Both pipes can fill the tank in 12 minutes.   Answer is 10 minutes.
Answer: D
A certain company reported that the revenue on sales increased 40 % from 2000 to 2003, and increased 60 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? Choose the correct choice.
A) 50 %  B) 40 %  C) 14 %  D) 32 %  E) 29 %

Solution: Assume the revenue in 2000 to be 100. Then in 2003 it would be 140 and and in 2005 160, so from 2003 to 2005 it increased by (160-140)/140=20/140=1/7=~14%.   Answer: 14 %
Answer: C
radius of a circle is 5cm , if we draw a rectangle of maximum size, what is the area of rectangle?
Choose the correct choice
A) 30 B) 40 C) 50 D) 60 E) 70

Solution: Area of rectangle of max size inside circle will be a square with diagonal equal to 10 cms.   Then side of square = Root (100/2)= 
(100/2) = 50
Root 50   Area of square= Root 50 * root 50 = 50 sq cms.   ANSWER:50
Answer: C
If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an even number
II. P is a multiple of 17
III. P is a multiple of 24
Choose the correct choice from the following choices:
A) I only
B) II only
C) III only
D) None of the above
E) All of the above

Solution: I onlynswer = I only) Ionly
Answer: A
Together, Andrea and Brian weigh p pounds; Brian weighs 14 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds? Select:	A) p/2 - 10	B) 3p/4 - 7	C) 3p/2 - 5	D) 5p/4 - 10	E) 5p - 5

Solution: Together, Andrea and Brian weigh p pounds --> A + B = p.   Brian weighs 10 pounds more than Andrea --> B = A + 14 --> A + (A + 14) = p --> A = (p - 14)/2 = p/2 - 7.   Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea --> C = A + p/4 = (p/2 - 7) + p/4 = 3p/4 -7.   Answer: 3p/4 - 7.
Answer: B
45% of the employees of a company are men. 60% of the men in the company speak French and 40% of the employees of the company speak French. What is % of the women in the company who do not speak French?	Choose the correct option.
A) 4%  B) 10%  C) 76.36%  D) 90.16%  E) 20%

Solution: No of employees=100(say)   Men=45   Women=55   Men speaking french=0.6*45= 
0.6*45 = 27
27   Employees speaking french=0.55*100= 
0.55*100 = 55
55   Therefore women speaking French=55-42= 
55-42 = 13
13   And women not speaking French=55-13= 
55-13 = 42
42   % of women not speaking French=42/55*100=76.36%   Answer 76.36%
Answer: C
How many five digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 10, without any of the digits repeating?
Select.
A) 100
B) 216
C) 96
D) 81
E) 72

Solution: 0,1,2,3,4,5   One digit will have to remain out for all 5 digit numbers;   if 0 is out; Leftover digits will be 1,2,3,4,5 = Sum(1,2,3,4,5)=15. ignore   if 1 is out; Leftover digits will be 0,2,3,4,5 = Sum(0,2,3,4,5)=14. Ignore   if 3 is out; Leftover digits will be 0,1,2,4,5 = Sum(0,1,2,4,5)=12. ignore   if 4 is out; Leftover digits will be 0,1,2,3,5 = Sum(0,1,2,3,5)=11. Ignore   if 5 is out; Leftover digits will be 0,1,2,3,4 = Sum(0,1,2,3,4)=10. =96   Total count of numbers divisible by 10 = 96 = 96   Ans:96
Answer: C
x =3 1 5
y= 27 7 81 then what is the relation between x and y	Choose the correct choice from the following.
A) 3*X)^1	B) 3*X)^2	C) 3*X)^4	D) 3*X)^3	E) 3*X)^5

Solution: Y=(3*X)^2   81=(3*3)^2   81=81   ANSWER:3*X)^2
Answer: B
The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is: Choose the correct choice from the following answers.
A) 1677 B) 1683 C) 2523 D) 3363 E) 3656

Solution: L.C.M. of 5, 6, 7, 8 = 840.   Required number is of the form 840k + 3   Least value of k for which (840k + 3) is divisible by 9 is k = 2.   Required number = (840 x 2 + 3) = 1683.   Answer: Option 1683
Answer: B
On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday two of his spiders, Wednesday would then have three times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley one of her spiders, Pugsley would now have two fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences?
Options:	A) 4	B) 5	C) 6	D) 8	E) 9

Solution: If Pugsley were to give Wednesday two of his spiders, Wednesday would then have three times as many spiders as Pugsley does:   (w + 2) = 3(p - 2)   If Wednesday were to give Pugsley one of her spiders, Pugsley would now have three fewer spiders than Wednesday had before they traded:   p + 1 = w - 3   Solving gives p =6 and w = 10.   Answer: 6.
Answer: C
The simple interest on a certain sum of money for 2 l/2 years at 12% per year is Rs. 40 less than the simple interest on the same sum for 3 ½ years at 10% per year. Find the sum.
Choose the correct choice.
A) 800
B) 700
C) 600
D) 500
E) None of them

Solution: Let the sum be Rs. x Then, ((x*10*7)/(100*2)) – ( (x*12*5)/(100*2)) = 40   = (7x/20)-(3x/10)=40   x = (40 * 20)= 
(40 * 20) = 800
800.   Hence, the sum is Rs. 800.   800nswer is 800.
Answer: A
Half a number plus 5 is 13.What is the number? Choose the correct choice from the following:	A) 8	B) 16	C) 10	D) 11	E) 12

Solution: Let x be the number. Always replace "is" with an equal sign   (1/2)x + 5 = 13   (1/2)x = 13 - 5   (1/2)x = 8   x = 16   correct answer is 16
Answer: B
If 9 gallons of gasoline are added to a tank that is already filled to 3/4 of its capacity, the tank is then filled to 9/10 of its capacity. How many gallons does the tank hold?
Select the correct option:
A) 20
B) 24
C) 36
D) 40
E) 54

Solution: Let the Capacity of the tank=C   (3/4)C + 9 = (9/10)C   =>(9/10)C - (3/4)C = 9   =>(3/20)C = 9   =>C = (9*20)/3= 
(9*20)/3 = 60
60   Number of gallons of gasoline that the tank currently holds= 3/4*C +9 = 45+9= 
45+9 = 54
54   Answer 54
Answer: E
What will be the fraction of 30% Choose the correct choice:
A) 1/4
B) 1/5
C) 3/10
D) 1/11
E) None of above

Solution: Explanation:   It will 30*1/100 = 3/10   Option 3/10
Answer: C
Robert left from a Pvt Company. Management hold his salary Rs. 15000/- for one month. Earlier Robert earned a performance incentive Rs. 7280/- from company. But Robert forgot that. After one month Robert asked his salary and accountant gives Rs.18500/- to him. What is the bonus amount given to Robert?	Select.
A) A)9500 B) B)12500 C) C)10780 D) D)10500 E) E)8600

Solution: Total Salary = Rs.15000/-   Incentive earned earlier = 7280/-   Balance Salary = 15000-7280= 
15000-7280 = 7_720
7720   Paid amount= 18500/-   Bonus = 18500-7720= 
18500-7720 = 10_780
10780/-   Answer is 10780
Answer: C
Souju's age is 118% of what it was 10 years ago, but 86 2/3% of what it will be after 10 years. What is her present age? Choose the correct choice from the following answers
A) 56 years  B) 65 years  C) 60 years  D) 66 years  E) 75 years

Solution: Let the age before 10 years =x. Then,   118x/100=x+10   â‡’118x=100x+1000   â‡’x=1000/18=55   Present age =x+10=55+10= 
55+10 = 65
65   ANSWER:65 years
Answer: B
A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?	Answers
A) 227
B) 269
C) 270
D) 277
E) 112

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 250)/26 = 20   x = 270 m. Answer:277
Answer: D
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?  Options: A) 5 B) 4 C) 3 D) 6 E) 8

Solution: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3   All the three pipes together will fill the tank in 3 hours.   Answer:3
Answer: C
A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 18 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?
Choices.
A) 14 B) 45 C) 54 D) 65 E) 42

Solution: Just check the answers and reverse the numbers until you get 18.   42 - 24= 
42 - 24 = 18
18   Answer 42
Answer: E
By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Choose the most appropriate option:	A) 8	B) 9	C) 7	D) 6	E) 4

Solution: 80% --- 12   120% --- ?     80/120 * 12= 
  80/120 * 12 = 8
8   8nswer: 8
Answer: A
Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?  Choose the correct choice from the following answers:	A) Rs.460	B) Rs.5640	C) Rs.5460	D) Rs.5604	E) Rs.5704

Solution: 5000 * 104/100 * 105/100= 
5000 * 104/100 * 105/100 = 5_460
> 5460   ANSWER:Rs.5460
Answer: C
Let each different arrangement of all the letters of DELETED be called a word. In how many of these words will the D's be separated? Pick
A) 150
B) 200
C) 300
D) 350
E) 400

Solution: here are 7 letters in the word "DELETED", out of which: D=2, E=3, L=1, T=1.   Total # of permutations is 7!/2!3!=420   # of permutations with D's together is 6!3!=120. Consider 2 D's as one unit: {DD}{E}{E}{E}{L}{T} - total 6 units, out of which {DD}=1, {E}=3, {L}=1, {T}=1.   # of permutations with D's not come together is: 7/2!3!−6!3!=300   ANSWER:300
Answer: C
In a two-digit number, if unit digit exceeds its ten's digit by 2 and the product of the given number and the sum of its digits is equal to 144, then what is the number?  Answers.
A) 21  B) 22  C) 23  D) 24  E) 25

Solution: Let the 10's digit be x.Then the units digit will be x+2.   the number is 11x+2.   The sum of the digits will be 2x+2   (11x+2)(2x+2)=144   Solving the quadratic eqn we get x=2;so the number is 24.   ANSWER:24
Answer: D
A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
Choose the correct choice from the following:
A) 65 cm2
B) 30 cm2
C) 16 cm2
D) 17 cm2
E) 15 cm2

Solution: The circumference of the circle is equal to the permeter of the rectangle.   Let l = 6x and b = 5x 2(6x + 5x)   = 2 * 22/7 * 3.5   => x = 1   Therefore l = 6 cm and b = 5 cm Area of the rectangle   = 6 * 5= 
6 * 5 = 30
30 cm2   Answer: 30 cm2
Answer: B
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Choose the correct choice from the following options: A) 10.2 B) 10.5 C) 10.9 D) 10.8 E) 10.1

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 160= 
140 + 160 = 300
300 m.   Required time= 300 * 9/250 = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.Answer: 10.8
Answer: D