mathewhe/aqua_rat huggingface dataset:
Question: The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 36. Find their present ages.
(A) 20,35,45
(B) 8,20,28
(C) 16,28,36
(D) 12,21,27
(E) None of these
Rationale: Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 36
20K = 60
K = 3
Therefore, then present ages are 12,21,27.
ANSWER:D
Answer: (D) 12,21,27
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently ten spaces behind player B, what is the probability that player B will be frozen after player A rolls?
(A) 1/12
(B) 5/36
(C) 1/6
(D) 1/3
(E) 17/36
Rationale: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 10 (as A is 10 spaces behind B) = 3 ( (4,6), (5,5), (6,4) )
So, the probability = 3/36 =1/12(Option A)
Answer: (A) 1/12
Question: The average mark of the students of a class in a particular exam is 70. If 5 students whose average mark in that exam is 50 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam?
(A) 20
(B) 15
(C) 10
(D) 12
(E) 25
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 70 x.
Total marks of (x - 5) students = 90(x - 5)
70x - (5 * 50) = 90(x - 5)
200 = 20x => x = 10
Answer: C
Answer: (C) 10
Question: A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge?
(A) Rs. 105 and Rs. 6
(B) Rs. 216 and Rs. 12
(C) Rs. 210 and Rs. 12
(D) Rs. 210 and Rs. 6
(E) None
Rationale: Explanatory Answers
Let half of the full basic fare be Rs. X.
Therefore, full basic fare is Rs. 2X.
Let the reservation charge be Rs. Y per ticket.
Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge)
2X + Y = 216 --- (1)
The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y.
Hence, 3X + 2Y = 327 --- (2)
Solving (1) and (2) we get,
X = 105 and Y = 6
Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6
Answer D
Answer: (D) Rs. 210 and Rs. 6
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
(A) 280
(B) 579
(C) 500
(D) 400
(E) 100
Rationale: C
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500
Answer: (C) 500
Question: Find the fourth proportional to 2.9, 4.6 and 7.6?
(A) 12.05
(B) 13.5
(C) 15.23
(D) 15.34
(E) 16
Rationale: Formula = Fourth propotional = (b Ã— c)/a
A = 2.9, B = 4.6 and C = 7.6
(4.6 Ã— 7.6)/2.9 = 12.05
A
Answer: (A) 12.05
Question: Given the equation e = f/4 + g/4^2 + h/4^3, where f, g, and h are each equal to 1 or 0, then e could be any of the values below EXCEPT:
(A) 1/16
(B) 10/32
(C) 1/8
(D) 17/64
(E) 1/64
Rationale: e =f/4 + g/4^2 + h/4^3,
= f/4 + g/16 + h/64,
= (16f + 4g + h ) /64
Depending on whether f, g and h take 0 or 1:
substitute 0 or 1 for the different values of f, g and h.
Answer C
Answer: (C) 1/8
Question: A & B THROW A DICE ALTERNATIVELY TILL ONE OF THEM GETS A '6' AND WINS THE GAME. WHAT WILL BE A PROBABILITY?
(A) 4/11
(B) 5/11
(C) 6/11
(D) 7/11
(E) 8/11
Rationale: Whoever starts first will have a probability of 6/11 and the other has a probability of 5/11. So, if A starts, as has to be logically inferred from the question, pbbl that A wins = 6/11 and that B wins = 5/11.
Pbbl that the starting person wins = (1/6) + (5/6)*(5/6)*(1/6) + (5/6)*(5/6)*(5/6)*(5/6)*(1/6) + ... = G.P. with first term (1/6) and common ratio (5/6)*(5/6) = (1/6)/[1-(5/6)*(5/6)] = 6/11
ANSWER:C
Answer: (C) 6/11
Question: 60% of the registered candidates in an election are from congress and 40% of the registered candidates are from BJP. If 3/4th of the registered Congress candidates and 1/5 of the registered BJP candidates fight election. What is the percentage of people fighting elections?
(A) 34%
(B) 43%
(C) 53%
(D) 54%
(E) 56%
Rationale: Let total people be x
Congress =60/100*x=3x/5
3/4 of 3x/5=9x/20
Bjp=40/100*x=2x/5
1/5 of 2x/5=2x/25
Adding both
9x/20+2x/25=53x/100
Ans=53%
ANSWER:C
Answer: (C) 53%
Question: If 20 men can build a water fountain 56 metres long in 42 days, what length of a similar water fountain can be built by 35 men in 3 days?
(A) 3 m
(B) 4 m
(C) 7 m
(D) 9 m
(E) 10 m
Rationale: Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 42: 3 : : 56 : x
Therefore (20 x 42 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/840=7
Hence, the required length is 7 m.
Answer : C
Answer: (C) 7 m
Question: In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 10 and 400, then the least and greatest integer on the card would be
(A) 3 and 15
(B) 3 and 20
(C) 4 and 13
(D) 4 and 14
(E) 5 and 14
Rationale: Given: 10<x(x+1)<400.
Now, it's better to test the answer choices here rather than to solve:
If x=3 then x(x+1)=12>10 --> so, the least value is 3. Test for the largest value: if x=20 then
x(x+1)=20*21=420>400
Answer: B.
Answer: (B) 3 and 20
Question: If you have 6 black socks, 4 blue socks, 8 brown socks, and 2 red socks in your sock drawer, what is the minimum number of socks that you need to pull out in the dark to be sure you had a matching pair?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 2
Rationale: A
5
At least 5, so that at least one color has two socks!
Answer: (A) 5
Question: The difference between a number and its two-fifth is 510. What is 10% of that number ?
(A) 33
(B) 85
(C) 37
(D) 27
(E) 28
Rationale: Explanation:
Let the number be x. Then, .
10 % 0f 850 = 85.
Answer: B) 85
Answer: (B) 85
Question: 40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 25 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
(A) 1/4
(B) 9/14
(C) 1/2
(D) 7/8
(E) 8/7
Rationale: Say total male = 40
Total female =60
Required ratio =( .25/40)/ (.75/60) = 1/2 C is the answer
Answer: (C) 1/2
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 9 days. In how many days Peter complete the work separately.
(A) 26 days
(B) 27.5 days
(C) 22.5 days
(D) 25.35 days
(E) 24 days
Rationale: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.
Peter completes the remaining (8/20) of the job in 9 days which means that the whole job(1) can be completed in X days.
<=> 8/20->9 <=> X=9/(8/20)=22.5Thus the answer is C.
Answer: (C) 22.5 days
Question: N be a number,the 2,3 and 5 base notations u get last digit is 1.and two out of three the leading digit is 1. N is equal to
(A) 31
(B) 63
(C) 74
(D) 91
(E) 98
Rationale: number shuld be in format of 2k+1,3k+1,5k+1
so take lcm of 2 3 5 we get 30k+1
so it may be 31 or 91
but in case of 31 leading digit of all 3 case is one
31 base2 = 11111
31 base3 = 1011
31 base5 = 111
so ans is 91
ANSWER:D
Answer: (D) 91
Question: Vid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Vid have meant to type?
(A) 10
(B) 16
(C) 21
(D) 24
(E) 27
Rationale: Vid intended to type a seven-digit number Should be 21.
there are two possibilities for placing 2 3s .
case 1: two 3s were missed consecutively. i.e. he typed 33 and it came blank on screen.
-5-2-1-1-5- in this arrangement we can fit 33 in 6 ways . (Six dashes, each dash represent one possible place for placing 33)
case 2: two 3s are not together, i.e. they have one or more digits between them .
-5-2-1-1-5- , in this arrangement
if we place first 3 at first dash i.e. 35-2-1-1-5- then the other 3 can fit into 5 places.
if we place first 3 at second dash i.e. -532-1-1-5- then the other 3 can fit into 4 places.
if we place first 3 at third dash i.e. -5-231-1-5- then the other 3 can fit into 3 places.
if we place first 3 at fourth dash i.e. -5-2-131-5- then the other 3 can fit into 2 places.
if we place first 3 at Fifth dash i.e. -5-2-1-135- then the other 3 can fit into 1 place.
so total 15 ways.
case 2 + case 1 = 6+ 15 = 21 ways
Answer C
Answer: (C) 21
Question: A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 12% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
(A) 70 lbs
(B) 40 lbs
(C) 30 lbs
(D) 50 lbs
(E) 60 lbs
Rationale: These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:
A = # of pounds sold at 7% profit
B = # of pounds sold at 12% profit
A+B = 100 pounds
(.07A + .12B)/(A+B) = .10
.07A + .12B = .1A + .1B
.02B = .03A
2B = 3A
2/3 = A/B
So, for every 6 pounds of A, we have 4 pounds of B.
With 100 pounds total, we have 40 pounds of A and 60 pounds of B.
Option B
Answer: (B) 40 lbs
Question: Express 22 mps in kmph?
(A) 79.2 kmph
(B) 89.2 kmph
(C) 79.6 kmph
(D) 99.2 kmph
(E) 69.2 kmph
Rationale: 22 * 18/5 = 79.2 kmph
ANSWER:A
Answer: (A) 79.2 kmph
Question: A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum V of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?
(A)  5
(B)  7
(C)  9
(D)  10
(E)  14
Rationale: Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum V of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D
Answer: (D)  10
Question: What percent of 9.6 kg is 28 gms ?
(A) 25
(B) 66
(C) 288
(D) 29
(E) 17
Rationale: Explanation:
Required percentage = (28/9600 * 100)% = 29/100% = 0.29%
Answer: D) .29%
Answer: (D) 29
Question: the cost of manufacturing a popular model car is made up of three items:cost of raw material,labour and overheads- in a year the cost of three items were in the ration of 4:3:2.next year the cost of the raw material rose by 10% ,labour cost increased by 8% but overhead reduced by 5%.then %increase int the price of the car ?
(A) 7.67%
(B) 6%
(C) 0.54%
(D) 9.54%
(E) 8.54%
Rationale: before increase total cost = 4+3+2=9,
after increasing the cost = 9.54
so increase of .54 over 9 , equal to 6%
ANSWER:B
Answer: (B) 6%
Question: Average expenditure of a person for the first 3 days of a week is Rs. 350 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
(A) 350
(B) 370
(C) 390
(D) 430
(E) None
Rationale: Explanation:
Assumed mean = Rs. 350
Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280
Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40
Therefore, Average expenditure for 7 days = Rs. 350 + Rs. 40 = Rs. 390
Correct Option: C
Answer: (C) 390
Question: If a rectangular billboard has an area of 130 square feet and a perimeter of 46 feet, what is the length of each of the longer sides?
(A) 4
(B) 7
(C) 8
(D) 13
(E) 26
Rationale: This question can be solved algebraically or by TESTing THE ANSWERS.
We're told that a rectangle has an area of 130 and a perimeter of 46. We're asked for the length of one of the LONGER sides of the rectangle.
Since the answers are all INTEGERS, and the area is 130, the shorter side will almost certainly be closer to 10 (since 10x10 = 100, but we're NOT dealing with a square). Answer B (7) does NOT divide evenly into 130,
IF...
The shorter side = 10...
The area = 130/10 = 13 = the longer side
Perimeter = 10+10+13+13 = 46
D
Answer: (D) 13
Question: A standard Veggiematik machine can chop 35 carrots in 5 minutes. How many carrots can 3 standard Veggiematik machines chop in 3 minutes?
(A) 63
(B) 87
(C) 90
(D) 98
(E) 112
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 35 Carrots - 5 minutes,
1 standard Veggiematik machine - 7 Carrots - 1 minute,
Now
3 standard Veggiematik machine - ? Carrots - 3 minutes,
Hence = 7X3X3 =63 Carrots
Answer A
Answer: (A) 63
Question: The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $12.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?
(A) 14
(B) 15
(C) 16
(D) 28
(E) 29
Rationale: Option #1: $0.75/crossing....Cross twice a day = $1.5/day
Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.
If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: A
Answer: (A) 14
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 296 m
(B) 267 m
(C) 297 m
(D) 150 m
(E) 255 m
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9
= 150 m
Answer:D
Answer: (D) 150 m
Question: In how many ways can 4 men & 3 women can be made from a gang of 7 men & 8 women ?
(A) 91
(B) 94
(C) 89
(D) 10
(E) 19
Rationale: Explanation:
7C4 * 8C3 = 91
A
Answer: (A) 91
Question: Patrick has three daughters named Avery, Bridget, & Catherine. He decides he wants to make a 3-letter password using the a combination of the each of their first initials (e.g. ABC, CBA, etc.). How many different permutations can he come up with?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 11
Rationale: Permutation calc is: n P r = n! / (n-r)! 3 P 3 = 3!/(3-3)! = 3x2x1/0!=6/1=6 Correct answer is C (6) ANSWER:C
Answer: (C) 6
Question: At exactly what time past 8:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
(A) 20 13/21 minutes past 8:00
(B) 20 13/17 minutes past 7:00
(C) 21 3/23 minutes past 7:00
(D) 21 9/11 minutes past 7:00
(E) 22 4/9 minutes past 7:00
Rationale: A1 = hour angle
A2 = minute angle
A1-A2 = 90
Assume the minutes = M
A1 = (8*60+M)/12*60 )*360
A2 = M*360/60
Solving all three equation , results in the answer A
Answer: (A) 20 13/21 minutes past 8:00
Question: What is the 26th digit to the right of the decimal point in the decimal form of 6/11?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 6/11 = 0.54545454...
The even numbered positions in the decimal expansion are all 4.
The answer is B.
Answer: (B) 4
Question: The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 3 type B widgets, and the weight of 5 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?
(A) 1:2
(B) 2:3
(C) 3:4
(D) 4:5
(E) 5:6
Rationale: 5B = 7C and so B = 7C/5
7A = 3B and so A = 3B/7 = 3C/5
A+B = 3C/5 + 7C/5 = 10C/5
B+C = 7C/5 + C = 12C/5
The ratio of A+B:B+C = 10:12 = 5:6
The answer is E.
Answer: (E) 5:6
Question: If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x?
(A) 308
(B) 154
(C) 70
(D) 44
(E) 21
Rationale: If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that.
LCM of 2,7,11= 154
Hence x must be divisible by 154
Hence B
Answer: (B) 154
Question: A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs , then the weight of the pipe is
(A) 3.496 kg
(B) 3.696 kg
(C) 3.690 kg
(D) 9.696 kg
(E) 3.296 kg
Rationale: Explanation:
External radius = 4 cm,
Internal radius = 3 cm.
Volume of iron = =
Weight of iron = (462 x 8)gm = 3696 gm = 3.696 kg
Answer: B) 3.696 kg
Answer: (B) 3.696 kg
Question: In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a
shelf so that two books on Hindi may not be together?
(A) 1240
(B) 1280
(C) 1340
(D) 1440
(E) 1540
Rationale: In order that two books on Hindi are never together, we must place all these books as under:
X E X E X E X .... X E X
where E - denotes the position of an English book and X that of a Hindi book.
Since there are 21 books on English, the number of places marked X are therefore, 22. Now, 19 places out of 22 can be chosen in
22C19 = 22C3 = 22 x 21 x 20 = 1540 ways.
3 x 2 x 1
Hence, the required number of ways = 1540.
ANSWER:E
Answer: (E) 1540
Question: A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job?
(A) 98 days
(B) 21 days
(C) 17 days
(D) 18 days
(E) 19 days
Rationale: WC = 1:2
2x + x = 1/14 => x = 1/42
2x = 1/21 => 21 days
Answer:B
Answer: (B) 21 days
Question: Jack invested $2000 in fund A and $2000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after Jack made these investments. Jack's investment in fund B was worth how much more than his investment in fund A?
(A) 1. $1000
(B) 2. $1500
(C) 3. $900
(D) 4. $1140
(E) 5. $700
Rationale: interest on fund A will be 240. rate of interest will be 6% per annum simple interest as 12% is for 2 year. this will make investment A 2240 at the end of 2nd year.
interest on fund B will be 1380 on 30% interest compounded annually. This will make investment B 3380 at the end of 2nd year.
Difference in investment B and investment A=3380-1690=1140
answer is D.
Answer: (D) 4. $1140
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team.
(A) 23 years
(B) 20 years
(C) 24 years
(D) 21 years
(E) 25 years
Rationale: Explanation:
Number of members in the team = 11
Let the average age of of the team = xx
=> Sum of the ages of all 11 members = 11x11x
Age of the captain = 26
Age of the wicket keeper = 26 + 3 = 29
Sum of the ages of 9 members of the team excluding captain and wicket keeper
=11x−26−29=11x−55=11x−26−29=11x−55
Average age of 9 members of the team excluding captain and wicket keeper
=11x−559=11x−559
Given that 11x−559=(x−1)11x−559=(x−1)
⇒11x−55=9(x−1)
⇒11x−55=9x−9⇒2x=46
⇒x=462=23 years
ANSWER IS A
Answer: (A) 23 years
Question: A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
(A) 8
(B) 9
(C) 4
(D) 18
(E) None
Rationale: Ratio of rates of working of A and B = 2 : 1
So, ratio of times taken = 1 : 2
B's 1 day's work = 1/12
Therefore A's 1 day's work = 1/6
(A + B)'s 1 day's work =	(1/6	+ 1/12)= 1/4
So, A and B together can finish the work in 4 days.
Answer: C
Answer: (C) 4
Question: The edge of a cube is 2a cm. Find its surface?
(A) 24a8
(B) 24a4
(C) 24a1
(D) 24a2
(E) 24a7
Rationale: 6a2 = 6 * 2a * 2a = 24a2
Answer:D
Answer: (D) 24a2
Question: If 20% of a number is equal to one-third of another number, what is the ratio of first number to the second number?
(A) 2:5
(B) 1:4
(C) 5:3
(D) 6:11
(E) 2:3
Rationale: Let 20% of A = 1/3 B
then 20A/100 = 1B/3
A/5 = B/3
A/B = 5/3
A:B = 5:3
Answer is C
Answer: (C) 5:3
Question: if (HE)^H=SHE,where the alphabets takes the values from (0-9) & all the alphabets are single digit then find the value of (S+H+E)
(A) 10
(B) 13
(C) 5
(D) 19
(E) data in sufficient
Rationale: 25^2=625
6+2+5=13
ANSWER:B
Answer: (B) 13
Question: Find the simple interest on Rs.580 for 11 months at 9 paisa per month?
(A) 574
(B) 270
(C) 566
(D) 266
(E) 121
Rationale: I = (580*11*9)/100 = 574
Answer: A
Answer: (A) 574
Question: In how many ways can a cricket eleven be chosen out of a batch of 15 players.
(A) 1254
(B) 1365
(C) 1204
(D) 5421
(E) 1234
Rationale: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
Ans: B
Answer: (B) 1365
Question: x^2 + bx + 72 = 0 has two distinct integer roots; how many values are possible for b?
(A) 3
(B) 6
(C) 8
(D) 12
(E) 24
Rationale: As 72 is positive either both roots are + or -
but as 'b' is +ve, both the roots carry same sign, i.e. +ve, and the factors are as below
72, 1
2, 36
4, 18
8, 9
24, 3
6, 12
ANSWER:D
Answer: (D) 12
Question: A car covers a distance of 624 km in 6 ½ hours. Find its speed?
(A) 104 kmph
(B) 194 kmph
(C) 109 kmph
(D) 174 kmph
(E) 101 kmph
Rationale: 624/6
=104 kmph
Answer:A
Answer: (A) 104 kmph
Question: Two varieties of steel, A and B, have a ratio of iron to chromium as 5:1 and 7:2, respectively. Steel C is produced by mixing alloys A and B at a ratio of 3:2. What is the ratio of iron to chromium in C?
(A) 17 : 73
(B) 78 : 14
(C) 45 : 30
(D) 73 : 17
(E) 4 : 9
Rationale: In 6 parts of alloy A, 5 parts are iron, and 1 part is chromium.
In 9 parts of alloy B, 7 parts are iron and 2 parts are chromium.
First, to compare the two alloys, get the same number of parts in total - we can use 18. So we have:
In 18 parts of alloy A, 15 parts are iron and 3 are chromium.
In 18 parts of alloy B, 14 parts are iron and 4 are chromium.
So combining 3 of A with 2 of B, we'd be combining 45 and 28 parts of iron, or 73 parts of iron, with 9 and 8 of chromium, or 17 of chromium, so 73 to 17 is the answer.
ANSWER:D
Answer: (D) 73 : 17