mathewhe/aqua_rat huggingface dataset:
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is
(A) 1/7
(B) 1/5
(C) 1/9
(D) 1/2
(E) 1/1
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer: B
Answer: (B) 1/5
Question: What is the sum of the digits of integer k, if k = (10^30- 36)
(A) 251
(B) 260
(C) 263
(D) 269
(E) 262
Rationale: There are 31 digits in 10^30
When we subtract 36 from it, there will be 30 digits left.
10^30 can be written as 9999999....(30 times) + 1
So,
10^30 - 36 = 9999999....(30 times) + 1 - 36 = 9999999....(30 times) -35
Consider the last 2 digits,
99-35 = 64
The last 2 digits will be 64.
And our number would be 99999......99964 with 2 less 9s after subtraction.
Number of 9s left are 28 and the last two digits are 64
The sum of the digits will be
(28*9) + 6 + 4 =262
Answer:- E
Answer: (E) 262
Question: Five men and five women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
(A) 4!*5!
(B) 6!*6!
(C) 5!*7!
(D) 6!*7!
(E) 7!*7!
Rationale: The number of arrangements of n distinct objects in a row is given by n!.
The number of arrangements of n distinct objects in a circle is given by (n-1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!
Now, 5 men in a circle can be arranged in (5-1)! ways and if we place 5 women in empty slots between them then no two women will be together. The # of arrangement of these 5 women will be 5! and not 4! because if we shift them by one position we'll get different arrangement because of the neighboring men.
So the answer is indeed 4!*5!.
A
Answer: (A) 4!*5!
Question: There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 35 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?
(A) 90.
(B) 55.
(C) 50.
(D) 40.
(E) 25.
Rationale: STREET-CAT DOMESTIC-Cat
70 130
(35gray+35other) 75gray+55other
Answer:B
Answer: (B) 55.
Question: Rs.400 at 5% p.a compound interest will amount to Rs.441 in ________ years (interest compounded yearly).
(A) 1 year
(B) 2 years
(C) 3/2 year
(D) 5 years
(E) 6 years
Rationale: 1st year compound interest is =400*5/100 = 20
2nd year compound interest is = first year CI + 5%of first year CI= 20 + 20*5/100=>20+1=>21
total CI= first year CI + second year CI= >20+21=21
so total amount to paid = 400 +41=441
so answer is 2 years
ANSWER:B
Answer: (B) 2 years
Question: A student needs 30% of the marks on a test to pass the test. If the student gets 80 marks and fails the test by 10 marks, find the maximum marks set for the test.
(A) 240
(B) 300
(C) 360
(D) 420
(E) 480
Rationale: 30% = 90 marks
1% = 3 marks
100% = 300 marks
The answer is B.
Answer: (B) 300
Question: 15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 4 hrs. each would it take for 21 women if 3 women do as much work as 2 men?
(A) 30
(B) 20
(C) 15
(D) 25
(E) 45
Rationale: Let 1Man does 1unit/hr of work
15M in 21 days of 8hrs will do (15*21*8) units
3W = 2M
1W=(2/3)units/hr
21W with 4hrs a day will take (15*21*8)/(21*4*(2/3)) days
=> 45 Days
ANSWER:E
Answer: (E) 45
Question: Hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench. If the total weight of 1 hammers and three wrenches is one-third that of 8 hammers and 5 wrenches, then the total weight of one wrench is how many times that of one hammer?
(A) 1/2
(B) 2/3
(C) 1
(D) 5/4
(E) 2
Rationale: x be the weight of a hammer and y be the weight of a wrench.
(1x+3y)=1/3*(8x+5y)
3(1x+3y)=(8x+5y)
3x+9y=8x+5y
4y=5x
y=5x/4
Ans - D
Answer: (D) 5/4
Question: If the speed of Y meters per second is equivalent to the speed of X meters per hour, what is X in terms of Y? (1 kilometer=1000 meters)
(A) 15y/18
(B) 6y/5
(C) 18y/5
(D) 3600y
(E) 3600000y
Rationale: If the speed of Y meters per second is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
We need to find an equation with y in the answer...
convert all measurements so they are alike (i.e. convert km to m, seconds to hours, etc)
Speed = y/t
y meters/second
(3600) x meters/hour
Speed = x/t
x KM/hour
Speed = x/hour
x/hour = (3600) x meters/hour
x/1hour = y(3600) / 1 hour
x = y(3600)
x = 3600y
Answer: D.
Answer: (D) 3600y
Question: If x−log48+3log2=log125/3−log3, what is the value of x?
(A) 2
(B) 1
(C) 3
(D) 5
(E) 8
Rationale: Explanation:
1/3 log 125= log (125^1/3) = log 5
3 log 2= log (2^3)= log 8
log a + log b= log (a*b)
Utilizing the same,
LHS= x -log 48 +log 8= x - log 6 - log 8 + log 8 = x - log 6
RHS= log 5 - log 3
=> x= log 5 - log 3 + log 6 = log 5 - log 3 + log 2 + log 3
=> x= log 10 = 1
Answer B
Answer: (B) 1
Question: If the product of two positive integers is 50, which of the following could be the LCM and HCF of the two numbers? a. LCM 50 : HCF 1 b. LCM 25 : HCF 2 c. LCM 10 : HCF 5
(A) c only
(B) a only
(C) b only
(D) a, b only
(E) a,b only
Rationale: The right answer is c only
Answer : A
Answer: (A) c only
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, what is the average marks of all the students?
(A) 54.68
(B) 54
(C) 45.68
(D) 45
(E) 55
Rationale: Average marks of batch1 = 50
Students in batch1 = 55
Total marks of batch1 = 55 × 50
Average marks of batch2 = 55
Students in batch2 = 60
Total marks of batch2 = 60 × 55
Average marks of batch3 = 60
Students in batch3 = 45
Total marks of batch3 = 45 × 60
Total students = 55 + 60 + 45 = 160
Average marks of all the students
=((55×50)+(60×55)+(45×60))/160
=(275+330+270)/16
=875/16
=54.68
Answer is A.
Answer: (A) 54.68
Question: Let Q be any number less than 200 which leaves remainder 2 when divisible by 5 or 7. What is the sum of all those numbers of Q?
(A) 535
(B) 545
(C) 555
(D) 565
(E) 585
Rationale: least number which gives remainder of 2 when divided by 5 or 7 is the LCM of 5 and 7 plus 2 i.e 35+2=37.
now,second number will 72 and by this way,we can say that sum all number less than 200 is
37+72+107+142+177=535
ANSWER:A
Answer: (A) 535
Question: What is the difference between the place value and the face value of 3 in the numeral 593827?
(A) None of these
(B) 5999
(C) 994
(D) 5994
(E) 5997
Rationale: Explanation:
Place value of 3 = 3000
Face value of 3 = 3
Difference = 3000 - 3 = 5997
Answer: E
Answer: (E) 5997
Question: A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance Z that he will have a matched pair?
(A) Z=2/5
(B) Z=3/5
(C) Z=1/5
(D) 1/2
(E) 7/5
Rationale: P(both doves) + P(both rabbits) = p (matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5
Hi How did you get the probability 2/4 and 1/4???
You have 3 doves and 2 rabbits i.e. a total of 5 animals.
The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)
The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)
Similarly,
The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)
The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. Also only 4 animals are left to choose from)
Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
Answer: (A) Z=2/5
Question: Find the least number which when divided by 20,25,35 and 40 leaves remainders 14,19,29 and 34 respectively.
(A) 1934
(B) 1394
(C) 1943
(D) 1493
(E) None of them
Rationale: Here,(20-14) = 6,(25 – 19)=6,(35-29)=6 and (40-34)=6.
Required number = (L.C.M. of 20,25,35,40) – 6 =1394.
Answer is B.
Answer: (B) 1394
Question: A bread merchant declares a 15% discount after 8 P.M. Ana goes before 8 P.M. with Rs.50 in her pocket to buy 3 pieces of bread and got some change. Tom goes after 8 P.M. with Rs.40. How many pieces of bread can Tom buy at the most?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: At the most, a piece of bread costs 50/3 = 16.67 before 8 P.M.
After 8 P.M., each piece of bread will now cost (1 - 15%) * 16.67 = 0.85 * 16.67 = 14.17
Since Tom has Rs.40, 40 / 14.17 = 2.82
Since you cannot buy half pieces of bread, at the most, Tom can buy 2 pieces of bread after 8 P.M.
Correct Option: B
Answer: (B) 2
Question: The “z-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^z, where z is the z-number of the result of his die roll, and plots 3^z on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?
(A)  3/8
(B)  13/36
(C)  17/36
(D)  19/36
(E)  23/36
Rationale: If you calculate 3^z for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.
About distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.
On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:
probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9
probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9
probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36
All together: 1/9 + 1/9 + 5/36 = 13/36=B
Answer: (B)  13/36
Question: How many methods are possible for arranging 5 boys and 4 girls in such a way that no 2 girls could sit together?
(A) 43200
(B) 43700
(C) 44200
(D) 53200
(E) 33200
Rationale: The arrangement can be done as below
X..B..X..B...X..B...X..B...X..B..X
where b is the position of Boys and 4 girls can be placed at any of 6 positions marked as X.
so Number of arrangements will be
5! * 6p4 = 120*360 = 43200
ANSWER:A
Answer: (A) 43200
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1290
(B) 1430
(C) 1500
(D) 2433
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: A rectangular garden is to be twice as long as it is wide. If 900 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?
(A) 40
(B) 50
(C) 60
(D) 200
(E) 300
Rationale: ALTERNATE APPROACH
Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.
Given Perimeter is 900
So, 2 ( L + B ) = 900
Or, L + B = 450
Now use the answer options ( Given Length ; Breath will be half the length)
(A) 40
L = 40 ; B = 20
L + b = 60
(B) 50
L = 50 ; B = 25
L + b = 75
(C) 60
L = 60; B = 30
L + b = 90
(D) 200
L = 200; B = 100
L + b = 300
(E) 300
L = 300; B = 150
L + b = 450
Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (E)
Answer: (E) 300
Question: A basket contains one dozen fruits.Six of the fruits are apples, Three are oranges, and three are Bananas. If two fruits are randomly selected from the basket, one after the other, what is the probability that both will be apple fruit?
(A) 8/11
(B) 5/19
(C) 14/3
(D) 12/3
(E) 5/22
Rationale: Probability of getting the first Apple fruit - 6/12
Probability of getting the second Apple fruit - 5/11
total probability = 6/12*5/11 = 5/22
correct option E
Answer: (E) 5/22
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,54,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:
(A) 0.22598
(B) 0.14544
(C) 0.25632
(D) 0.35466
(E) 0.63435
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 354000x
\therefore Required percentage = \inline \frac{800x}{354000}\times 100 = 0.22598
A
Answer: (A) 0.22598
Question: A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 46 instead of 56 then find the correct average marks up to two decimal places.
(A) 73.41
(B) 72.28
(C) 72.43
(D) 73.43
(E) Cannot be determined
Rationale: Total marks = 35 x 72 =2520
Corrected total marks = 2520 - 46 + 56 =2530
Correct Average = 2530/35 = 72.28
Answer : B
Answer: (B) 72.28
Question: Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 20% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?
(A) $15,840
(B) $17,820
(C) $18,000
(D) $19,800
(E) $21,780
Rationale: 10000 seats --> Full Price : Half Price = 8000 : 2000
Price when all seats are filled = 16000 + 2000 = 18000
100 seats are unsold --> Loss due to unfilled seats = 20 + 2*80 = 180
Revenue = 18000 - 180 = 17820
Answer: B
Answer: (B) $17,820
Question: John must arrange 3 different physics books and 2 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
(A) 6
(B) 9
(C) 36
(D) 12
(E) 720
Rationale: First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways
Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places
Second Place, Physics Book - in 2 ways
Third Place, Math Book - in 2 ways (only 2 books left)
Fourth Place, Physics - in 2 ways (only 2 Physics book left)
Rest two places can be arranged in one way only.
Total no of ways =3*2*2*1*1 = 12 ways
D
Answer: (D) 12
Question: A can do a piece of work in 4 hours ;B and C together can do it in 3 hours,while A and C together can do it 2 hours.How long will B alone take to do it ?
(A) 8 hours
(B) 10 hours
(C) 12 hours
(D) 24 hours
(E) None of these
Rationale: Solution
A’s 1 hour’s work = 1/4; (B + C)'s 1 hour’s work=1/3; (A + C)'s 1 hour’s work = 1/2
(A+B+C)’s 1 hour’s work =(1/4 +1/3) =7/12
B’s 1 hour’s work = (7/12-1/2)=1/12
∴ B alone will take 12 hours to do the work.
Answer C
Answer: (C) 12 hours
Question: The distance between Delhi and Mathura is 180 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 40.00 a.m.
(B) 10.00 a.m.
(C) 12.00 a.m.
(D) 18.00 a.m.
(E) 11.30 a.m.
Rationale: Explanation:
D = 180 â€“ 20 = 160
RS = 20 + 25 = 45
T = 160/45 = 3 hours 30 minutes
8 a.m. + 3 hours 30 minutes = 11:30 a.m.
Answer: Option E
Answer: (E) 11.30 a.m.
Question: Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 192, what is the area of the side face of the box?
(A) 13
(B) 16
(C) 18
(D) 29
(E) 32
Rationale: Lets suppose length= l, breadth= b, depth= d
Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l)
top face area= w*d
side face area= w*d = 1.5 d*l (w=1.5l)
Volume = l*w*d= 192
l*1.5l*2l= 192
l=4
Side face area= l*d= l*2l= 4*2*4
=32
E is the answer
Answer: (E) 32
Question: A $84.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased?
(A) 15%
(B) 20%
(C) 25%
(D) 29%
(E) 80%
Rationale: Listed selling price of chair = 84.95 $
Discounted selling price of chair = 59.95 $
Discount = 84.95 - 59.95 = 25 $
% decrease in price of chair = (25/84.95) * 100% = 29 % approx
Answer D
Answer: (D) 29%
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
(A) 5%
(B) 25%
(C) 45%
(D) 75%
(E) 95%
Rationale: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =80/1600 x 100% = 5%
Answer: A
Answer: (A) 5%
Question: What is the smallest number which, when increased by 9, is divisible by 7, 8, and 24?
(A) 143
(B) 150
(C) 159
(D) 168
(E) 177
Rationale: LCM(7,8,24)=24x7=168
So the least divisible number is 168, and the number we are looking for is 168-9=159.
The answer is C.
Answer: (C) 159
Question: I am an odd number; take away an alphabet and I become even. What number am I?
(A) 6
(B) 8
(C) 9
(D) 3
(E) 7
Rationale: E
7 (SEVEN-S=EVEN)
Answer: (E) 7
Question: The avg. age of a group of 12 students is 20yers.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
(A) 45yr
(B) 46yr
(C) 47yr
(D) 48yr
(E) 49yr
Rationale: total age=12*20
=240
let the sum of age of four new student=x
so the total avg become =(240+x)/16=21
x=196
then the avg age of new student is 196/4=49yr
ANSWER:E
Answer: (E) 49yr
Question: The difference between a two digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2?
(A) 4
(B) 8
(C) 12
(D) 16
(E) 18
Rationale: Sol.
Since the number is greater than the number obtained on reversing the digits, so the ten's is greater than the unit's digit.
Let the ten's and units digit be 2x and x respectively.
Then, (10× 2x + x) - (10x + 2x) = 36
⇔ 9x = 36
⇔ x = 4.
∴ Required difference = (2x+x)-(2x-x) = 2x = 8.
Answer B
Answer: (B) 8
Question: Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on Sunday. They were very happy. What day of the week would come on 14 Feb. 2010?
(A) monday
(B) tuesday
(C) saturday
(D) wednesday
(E) thursday
Rationale: feb 14 2005 - sunday
feb 14 2006 - monday
feb 14 2007 - tuesday
feb 14 2008 - wednesday
feb 14 2009 - friday[since 2008 is leap year , 2 days ll go forward]
feb 14 2010 - saturday
ANSWER:C
Answer: (C) saturday
Question: A bill for Rs. 3000 is drawn on 14th July at 5 months. It is discounted on 5th October at 10%. What is the Banker's Discount?
(A) Rs. 60
(B) Rs. 82
(C) Rs. 90
(D) Rs. 120
(E) None of these
Rationale: Explanation :
F = Rs. 3000
R = 10%
Date on which the bill is drawn = 14th July at 5 months
Nominally Due Date = 14th December
Legally Due Date = 14th December + 3 days = 17th December
Date on which the bill is discounted = 5th October
Unexpired Time
= [6th to 31st of October] + [30 Days in November] + [1st to 17th of December] = 26 + 30 + 17
= 73 Days
=73/365 year=1/5 year
BD = Simple Interest on the face value of the bill for unexpired time
=FTR/100=[3000×(1/5)×10]/100=30×1/5×10 = Rs. 60 Answer : Option A
Answer: (A) Rs. 60
Question: A train 500m long takes 10 sec to cross a man walking at 4kmph in a direction opposite to that of the train. Find the speed of the train?
(A) A)174kmph
(B) B)150kmph
(C) C)162kmph
(D) D)145kmph
(E) E)100kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+4 = (x+4)*5/18 m/sec
500/[(x+4)*5/18] = 10
10(x+4) = 1800
x = 174kmph
Answer is A
Answer: (A) A)174kmph
Question: What will be the result of 2^25 - 2^14 +(2*4 /8) ?
(A) 12
(B) 18
(C) 15
(D) 30
(E) 22
Rationale: The multiplication(e.g. 2^14) and division(e.g. 4/8) is done first and then the sum(e.g. 22+0) and
subtraction (e.g.50-28). And the answer is 22, option E.
Answer: (E) 22
Question: If a, q, and c are consecutive even integers and a < q < c, all of the following must be divisible by 4 EXCEPT
(A) a + c
(B) q + c
(C) ac
(D) (bc)/2
(E) (abc)/4
Rationale: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.
The 3 numbers can be written as
a, (a + 2)(a + 4).
If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.
A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2q. 2q will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'q' already has a prime factorization of at least a '2'. Hence '2q' has two 2s.
C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.
D - qc/2 = (a + 2)(a + 4)/2. Either q or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.
E - aqc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'q' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.
B - q + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.
As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B
Answer: (B) q + c
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 6
(C) 18
(D) Cannot be determined
(E) None of these
Rationale: let rate = R% and time = R years
Then ( 1200 x R x R /100) = 432
=> 12R2= 432
=> R2= 36
=> R= 6
Answer B
Answer: (B) 6
Question: A train passes a station platform in 30 seconds and a man standing on the platform in 12 seconds. If the speed of the train is 72 km/hr, what is the length of the platform?
(A) 320
(B) 340
(C) 360
(D) 380
(E) 400
Rationale: The speed of the train is 72 * 5/18 m/s = 20 m/s
The length of the train is 20 x 12 = 240 m
platform + 240 = 20 * 30
platform = 600 - 240 = 360
The answer is C.
Answer: (C) 360
Question: What was the day of the week on 24th Feb, 2006?
(A) Thursday
(B) Friday
(C) Saturday
(D) Sunday
(E) Monday
Rationale: 28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days
Jan. Feb.
(31 + 24 ) = 55 days
55 days = (7 weeks + 6 day) 1 odd day.
Total number of odd days = (0 + 0 + 6 + 6) = 12 0 odd day.
Given day is Friday.
Answer: Option B
Answer: (B) Friday
Question: A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 20DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
(A) 40/3 DAYS
(B) 10/3 DAYS
(C) 20/3 DAYS
(D) 3/20 DAYS
(E) 3/10 DAYS
Rationale: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2
A'S 1 DAY'S WORK = 1/10, B'S 1 DAY'S WORK = 1/20
(A+B)'S 1 DAY'S WORK = (1/10+1/20)=3/20=20/3
SO, A AND B TOGETHER CAN FINISH THE WORK IN 20/3 DAYS.
CORRECT OPTION: C
Answer: (C) 20/3 DAYS