mathewhe/aqua_rat huggingface dataset:
Question: A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped three times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 6?
(A) 3/8
(B) 1/16
(C) 1/8
(D) 1/2
(E) 0
Rationale: One approach to solve the problem is to list the different possibilities for a toss of coin three times. Because there are two outcomes and the coin is tossed three times, the table will have 2*2*2 or 8 rows.
Next add the resulting rows together to find the sum (the fourth column in the table below).
Toss 1 | Toss 2 | Toss 3 | Sum
1 ---------- 1 -------- 1 ------ 3
1 ---------- 1 -------- 2 ------ 4
1 ---------- 2 -------- 1 ------ 4
1 ---------- 2 -------- 2 ------ 5
2 ---------- 1 -------- 1 ------ 4
2 ---------- 1 -------- 2 ------ 5
2 ---------- 2 -------- 1 ------ 5
2 ---------- 2 -------- 2 ------ 6
From the table we see that there are 0 situations where the sum of the tosses will be greater than 6. And there are 8 possible combinations resulting in a probability of
0/8 or a probability of 0.
SO the correct answer is E.
Answer: (E) 0
Question: Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 480. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
(A) 2:1
(B) 5:6
(C) 5:2
(D) 5:8
(E) 5:2
Rationale: Let the amount lent at 7% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 7/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 480 => x = 5000
Amount lent at 10% = 2000
Required ratio = 2000 : 1000 = 2:1
Answer:A
Answer: (A) 2:1
Question: If 4 and 8 are factors of 60n, what is the minimum value of n?
(A)  2
(B)  3
(C)  8
(D)  14
(E)  56
Rationale: 60n/4*8 should be integer => 2*2*3*5*n/2*2*2*2*2 = 3*5*n/8must be an integer
for this to be true n must multiple of 8, thus min of n = 8
hence C
Answer: (C)  8
Question: In how many ways can be 3 boys and 3 girls sit around circular table so that no two boys sit next to each other?
(A) (5!)^2
(B) (6!)^2
(C) 3!2!
(D) 11!
(E) (5!)^2*6!
Rationale: first fix one boy and place other 2 in alt seats so total ways is 3!
now place each girl between a pair of boys... total ways of seating arrangement of girls 3!
total is 2!*3!
ANS C
Answer: (C) 3!2!
Question: A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result?
(A) 125
(B) 113
(C) 189
(D) 153
(E) 142
Rationale: A
125
96 passes out of 125 give an average of 76.8% .
Answer: (A) 125
Question: If (x + yi) / i = ( 7 + 9i ) , where x and y are real, what is the value of (x + yi)(x - yi)?
(A) 120
(B) 130
(C) 150
(D) 170
(E) 200
Rationale: (x + yi) / i = ( 7 + 9i )
(x + yi) = i(7 + 9i) = -9 + 7i
(x + yi)(x - yi) = (-9 + 7i)(-9 - 7i) = 81 + 49 = 130
CORRECT ANSWER IS B) 130
Answer: (B) 130
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
(A) 4 min
(B) 6 min
(C) 8 min
(D) 2 min
(E) 9 min
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Answer: A
Answer: (A) 4 min
Question: The difference of the cubes of two consecutive even integers is divisible by which of the following integers?
(A) 3
(B) 6
(C) 4
(D) 5
(E) 2
Rationale: Solution: let take 2 consecutive even numbers 2 and 4.
=> (4*4*4)-(2*2*2)=64-8=56 which is divisible by 4.
Answer C
Answer: (C) 4
Question: From a total of 5 boys and 5 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?
(A) 16
(B) 24
(C) 60
(D) 100
(E) 240
Rationale: Answer=D=100
No of 4 person committees that can be formed=5C2*5C2=100
Answer D
Answer: (D) 100
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 54. By how much do the two digits differ?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  7
Rationale: Given that (10a + b) - (10b + a) = 54 --> 9a - 9b =54 --> a - b = 6.
Answer: D.
Answer: (D)  6
Question: If x+y=280, x-y=200, for integers of x and y, y=?
(A) 200
(B) 240
(C) 50
(D) 115
(E) 150
Rationale: x+y = 280
x-y = 200
2x = 80
x = 40
y = 240
Answer is B
Answer: (B) 240
Question: How many multiples of 7 are there between 14 and 343, exclusive ?
(A) 48
(B) 47
(C) 46
(D) 45
(E) 44
Rationale: 7 * 2 = 14
7 * 49 = 343
Total multiples = (49-2) + 1 = 48
Exclude 7 343 = 48-2 = 46
Answer is (C)
Answer: (C) 46
Question: The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.7. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
(A) 0.8321
(B) 0.7
(C) 0.8108
(D) 0.7531
(E) 0.8213
Rationale: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.75*80 = 60.
Out of 20 matches Matt does not play in, team wins 0.7*20 = 14.
So, out of 100 matches 60 + 14 = 74 are won.
It is known that the team has won the last match. Out of 74 matches won, Matt is in 60: 60/74 = 0.8108...
Answer: C.
Answer: (C) 0.8108
Question: A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and captain) to a nearby port. Altogether, these passengers have 15 heads and 42 legs. How many cats does the ship host?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: sa's +co +ca +cats = 15. sa's + 1 +1 +cats =15 or sa's +cats =13.
sa's(2) +2 +2 +cats*4 =42 sa's*2 +cats*4 = 38 or sa's +cats*2 =19 or 13-cats +cat*2 =19
then cats =6
B
Answer: (B) 6
Question: What will come in place of the x in the following Number series? 6, 12, 21, x , 48
(A) 33
(B) 35
(C) 39
(D) 41
(E) 42
Rationale: (A)
The pattern is + 6, + 9, + 12, +15 ………..
So the missing term is = 21 + 12 = 33
Answer: (A) 33
Question: Sunil invested $ 1800 fir 2 years and $ 1400 for 3 years at the same rate of Simple Interest. If the total interest from these investments is $ 810, what is the rate of interest?
(A) 12 3/4%
(B) 25 1/3%
(C) 10 1/4%
(D) 8%
(E) 13 2/4%
Rationale: (1800x2xR)/100+(1400x3xR)/100=810
78R=810
R= 10 1/4%
Answer is C
Answer: (C) 10 1/4%
Question: A shepherd has 1million sheep at the beginning of Year 2010. The no's grow by xx during the yr. A famine hits his village in the next year & many of his sheep die. The sheep population decreases by yy during 2001 and at the beginning of 2011 the shepherd finds that he is left with 1million sheep. Which of the following is correct?
(A) x<y
(B) x>y
(C) x=y
(D) x<=y
(E) x>=y
Rationale: Let us assume the value of xx to be 10%10%.
Therefore, the number of sheep in the herd at the beginning of year 2001 (end of 2000) will be 1 million + 10%10% of 1 million = 1.1 million
In 2001, the numbers decrease by y%y% and at the end of the year the number sheep in the herd = 1 million.
i.e., 0.1 million sheep have died in 2001.
In terms of the percentage of the number of sheep alive at the beginning of 2001,
it will be (0.1/1.1)×100%=9.09%(0.1/1.1)×100%=9.09%.
From the above illustration it is clear that x>y
B
Answer: (B) x>y
Question: To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse?
(A) 6
(B) 8
(C) 10
(D) 15
(E) 30
Rationale: Total number of ways to choose 2 chairs from 5= 5C2=10
Total number of combination=150
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C2=15..... 15*10=150
Answer is 6... A
Answer: (A) 6
Question: Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 10% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
(A) 10%
(B) 20%
(C) 21%
(D) 23%
(E) Cannot be determined
Rationale: Answer: A.
Answer: (A) 10%
Question: Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $3500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?
(A) $3,750
(B) $5,600
(C) $8,100
(D) $15,000
(E) $31,500
Rationale: x=8%
112/x years=112/8=14 years
Now, money triples every 14 years
Therefore, in 14 yrs , if $3500 triples to $10500, in 28 years, it will again triple to $10500*3=$31,500
Answer E
Answer: (E) $31,500
Question: If a man lost 5% by selling apples at the rate of 15 a rupee at how many a rupee must he sell them to gain 25%?
(A) 9.4
(B) 10.4
(C) 11.4
(D) 12.4
(E) 13.4
Rationale: 95% ---- 15
125% ---- ?
95/125 * 15 = 11.4
Answer: C
Answer: (C) 11.4
Question: A cistern is two-third full of water. Pipe A can fill the remaining part in 12 minutes and pipe B in 8 minutes. Once the cistern is emptied, how much time will they take to fill it together completely?
(A) 12 minutes
(B) 12.5 min
(C) 14.4 min
(D) 10.2 min
(E) 14.66 min
Rationale: As pipe A takes 12min. to fill remaining one-third it takes 36min. to fill completely. similarly pipe B takes 24min. to fill completely
so, total time taken by both together is reciprocal of:
(1/36)+(1/24)=5/72
ans:14.4 min.
ANSWER:C
Answer: (C) 14.4 min
Question: An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 1 year: 100/3 = 33.33 approx $34: Total: 134
2nd year: 134/3 = 45: Total: 134+45 = 179
3rd year: 179/3 = 60: Total: 179+60 = 239
4th year: 239/3 = 80: Total: 239+80 = 319 > 3(100)
;4 years;
ANSWER:A
Answer: (A) 4
Question: In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ?
(A) 2/3
(B) 5/8
(C) 3/5
(D) 4/7
(E) 4/9
Rationale: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
B
Answer: (B) 5/8
Question: The function f is defined by subtracting 25 from the square of a number and the function a is defined as the square root of one-half of a number. If a(f(x))=10, then which of the following is a possible value of x?
(A) -15
(B) -5
(C) 0
(D) 5
(E) 25
Rationale: f(x) = x^2-25
a(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).
a(f(x)) = 10
a(x^2-25) =10
sqrt((x^2-25)/2) = 10
=> (x^2-25)/2 = 100
=>x^2 = 225
=> x = 15 or -15
Answer is A.
Answer: (A) -15
Question: The triplicate ratio of 1:2 is?
(A) 1:64
(B) 1:8
(C) 1:10
(D) 3:8
(E) 5:64
Rationale: 1^3: 2^3 = 1:8
ANSWER:B
Answer: (B) 1:8
Question: John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 170% of John's weight. Which of these 5 people weighs the least?
(A) John
(B) Susan
(C) Sam
(D) Mark
(E) Lynn
Rationale: John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;
Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;
Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;
Lynn weighs 170% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);
As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.7*J)=0.85*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight ismore than 50%of that of John.
Answer: B.
Answer: (B) Susan
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
(A) 210
(B) 7200
(C) 1890
(D) 31970
(E) 10984
Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
= (7C3 x 4C2)
= 210.
ANSWER A 210
Answer: (A) 210
Question: In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?
(A) 8
(B) 9
(C) 7
(D) 6
(E) 5
Rationale: Since A beats B by 200 m or 25 seconds, i
t implies that B covers 200 m in 25 seconds.
Hence speed of B = 200/25 = 8 m/s.
Answer:A
Answer: (A) 8
Question: If each digit in the set of A = {0,1,2,3,4,5,6,7,8,9} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?
(A) 10! / 2!
(B) 10! - 9!
(C) 9!
(D) 10!
(E) 8*9!
Rationale: The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent).
The number of ways to arrange 10 units is 10!
If we think of 2 and 5 as one single unit, the number of arrangements is 9!
Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*9!
The total number of valid arrangements is 10! - 2*9! = 10*9! - 2*9! = 8*9!
The answer is E.
Answer: (E) 8*9!
Question: Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?
(A) 7
(B) 8
(C) 10
(D) 5
(E) 2
Rationale: (A + B)'s 1 hour work = (1/12 + 1/15) = 3/20
(A + C)'s 1 hour work = (1/12 + 1/20) = 2/15
Part filled in 2 hrs = (3/20 + 2/15) = 17/60
Part filled in 6 hrs = 3 * 17/60 = 17/20
Remaining part = 1 - 17/20 = 3/20
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
Total time taken to fill the tank = (6 + 1) = 7 hrs
ANSWER A
Answer: (A) 7
Question: If Re.1 amounts to Rs.9 over a period of 10 years. What is the rate of simple interest?
(A) 90%
(B) 30%
(C) 50%
(D) 80%
(E) 70%
Rationale: 8 = (1*10*R)/100
R = 80%
ANSWER:D
Answer: (D) 80%
Question: If a and b are the roots of the equation x2 - 7x + 7 = 0, then the value of a2 + b2 is:
(A) 35
(B) 24
(C) 17
(D) 6
(E) 5
Rationale: Sol.(b) The sum of roots = a+ b = 7
Product of roots = ab = 8
Now, a2 + b2 = (a + b)2 - 2ab = 49 - 14 = 35
Answer A
Answer: (A) 35
Question: If the simple interest on a certain sum of money for 4 years is one–fifth of the sum, then the rate of interest per annum is
(A) 4%
(B) 7%
(C) 6%
(D) 5%
(E) 3%
Rationale: Explanation:
Let the Principal(P) be x
Then, Simple Interest(SI) = x/5
Time(T) = 4 years
Rate of interest per annum(R) = (100×SI)/PT
= (100 × (x/5)/(x × 4) = 20/4 = 5%
Answer: Option D
Answer: (D) 5%
Question: A train 180 m long passed a pole in 10 sec. How long will it take to pass a platform 800 m long?
(A) 80
(B) 89
(C) 54
(D) 67
(E) 56
Rationale: Speed = 180/10= 18 m/sec.
Required time = (180+ 800)/18 = 54 sec.
Answer: Option C
Answer: (C) 54
Question: A basketball coach will select the members of a five-player team from among 10 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter?
(A) 1/9
(B) 1/6
(C) 2/9
(D) 5/18
(E) 1/3
Rationale: straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 8c3
total number of ways of selecting 5 players out of 10 = 10c5
probability = 8c3/10c5 =2/9
C
Answer: (C) 2/9
Question: If two numbers are in the ratio 2:3. If 17 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) A)10
(B) B)20
(C) C)34
(D) D)30
(E) E)35
Rationale: 2:3
2x + 17 : 3x + 17 = 3 : 4
4[2x + 17] = 3[3x + 17]
8x + 68 = 9x + 51
9x - 8x = 68 - 51
x = 17
Then smallest number is = 2
2x = 34
Correct Option C
Answer: (C) C)34
Question: The area of a square field is 900 km2. How long will it take for a horse to run around at the speed of 12 km/h ?
(A) 12 h
(B) 10 h
(C) 8 h
(D) 6 h
(E) None of these
Rationale: Explanation Area of field = 900 km2. Then, each side of field = √900=30km Distance covered by the horse = Perimeter of square field = 30 × 4 = 120 km ∴ Time taken by horse = distances/peed=120/12=10h Answer B
Answer: (B) 10 h
Question: If a and b are two different prime numbers, which of the following cannot be true?
(A) ab is odd.
(B) a/b is an integer
(C) a +b is odd.
(D) ab is even.
(E) a + b is even
Rationale: A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option C not possible (a/b=integer means that a is a multiple ofb).
Answer: C.
All other options are possible:
A. ab is odd --> a=3 and b=5;
B. a + b is even --> a=3 and b=5;
C. a + b is odd --> a=2 and b=3;
D. ab is even --> a=2 and b=3;
C
Answer: (C) a +b is odd.
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 80 years. What is the age of the youngest child?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) 10 years
Rationale: Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 80
5x = 50 => x = 10.
Age of youngest child = x = 10 years.
ANSWER:E
Answer: (E) 10 years
Question: The ratio between the number of sheep and the number of horses at the Stewart farm is 4 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?
(A) 18
(B) 28
(C) 32
(D) 56
(E) 60
Rationale: Actual number of horses = 12,880/230 (hold it since it is a harder calculation)
Ratio multiplier = 1288/(23*7)
Actual number of sheep = 1288/(23*7) * 4.
First divide 1288 by 7 to get: 184*4/23
Use the last digit to figure out that 23 will go 8 times into 184. Confirm. 8*4 = 32
Answer (C)
Answer: (C) 32
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time cistern will get filled ?
(A) 7 hours
(B) 7.1 hours
(C) 7.2 hours
(D) 7.3 hours
(E) 7.4 hours
Rationale: Explanation:
When we have question like one is filling the tank and other is empting it, then we subtraction as,
Filled in 1 hour = 1/4
Empties in 1 hour = 1/9
Net filled in 1 hour = 1/4 - 1/9
= 5/36
So cistern will be filled in 36/5 hours i.e. 7.2 hours
ANSWER IS C
Answer: (C) 7.2 hours
Question: At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.60. What is the price of 2 doughnuts?
(A) $ 0.55
(B) $ 1.00
(C) $ 1.10
(D) $ 1.30
(E) $ 1.80
Rationale: 3D + C = 2.25......(1)
2D + C = 1.6........(2)
(1) - (2) --> D = 0.65 --> 2D = 1.3
Answer: D
Answer: (D) $ 1.30
Question: An aeroplane covers a certain distance of 480 Kmph in 4 hours. to cover the same distance in 4 1/3 hours, it Must travel at a speed of
(A) 440
(B) 540
(C) 443
(D) 740
(E) 250
Rationale: Speed of aeroplane = 480 Kmph
Distance travelled in 4 hours
= 480 * 4 = 1920 Km
Speed of aeroplane to acver 1920 Km in 13/3
= 1920*3/13 = 443 Km
Answer C.
Answer: (C) 443
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 6%
(B) 3%
(C) 8%
(D) 1%
(E) 4%
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: E
Answer: (E) 4%
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
(A) 5/18
(B) 5/12
(C) 5/19
(D) 5/15
(E) 5/11
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
Answer: B
Answer: (B) 5/12
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
(A) 27 7/5
(B) 27 7/09
(C) 27 7/2
(D) 27 7/9
(E) 24 7/2
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer: D
Answer: (D) 27 7/9
Question: Both Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 50 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?
(A) 1 p.m.
(B) 3 p.m.
(C) 4 p.m.
(D) 7 p.m.
(E) 9 p.m.
Rationale: 7:00 am so 6 hours later is 1:00 pm
In six hours, Robert will have driven 6*30 = 180 miles
In six hours, Alive will have driven 6*50 = 300 miles
So Robert needs 300-180 = 120 miles do catch Alice up.
So at 30 mph, he will need 2 hours
1:00 pm + 6 hours = 7:00 pm
ANS : D
Answer: (D) 7 p.m.
Question: If the diameter of circle R is 40% of the diameter of circle S, the area of circle R is what percent of the area of circle S?
(A) 16%
(B) 18%
(C) 20%
(D) 22%
(E) 24%
Rationale: Let diameter of circle R , dr = 40
and diameter of circle S , ds = 100
Radius of circle R , Rr = 20
Radius of circle S , Rs = 50
Area of circle R/ Area of circle S = (pi * Rr ^2 ) /( pi * Rs^2 )
= (20/50)^2 = (4/10)^2
=16%
Answer :A
Answer: (A) 16%
Question: What is the area of square field whose side of length 13 m?
(A) 225
(B) 662
(C) 169
(D) 882
(E) 21
Rationale: 13 * 13
= 169 sq m
Answer:C
Answer: (C) 169
Question: Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?
(A) 14
(B) 15
(C) 17
(D) 19
(E) 11
Rationale: A
14
In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
Answer: (A) 14
Question: Each student is given a five-character identification code. The first two characters are selected from the numbers 0 to 9 inclusive, and the last three characters are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?
(A) 1,491,000
(B) 1,527,200
(C) 1,638,400
(D) 1,757,600
(E) 1,841,800
Rationale: The number of possible codes is 10*10*26*26*26=1,757,600.
The answer is D.
Answer: (D) 1,757,600
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
(A) 1/127
(B) 1/129
(C) 1/128
(D) 1/198
(E) 1/126
Rationale: Out of nine, five are good and four are defective. Required probability
= ⁴C₄/⁹C₄
= 1/126
Answer: E
Answer: (E) 1/126
Question: find S.P when CP=Rs 80.40,loss=5%
(A) Rs 66.34
(B) Rs 69.34
(C) Rs 58.34
(D) Rs 68.34
(E) Rs 60.34
Rationale: CP=Rs 80.40,loss=5%
sol: sp=85% of Rs 80.40
=Rs {(85/100)*80.40}=Rs 68.34.
Answer is D.
Answer: (D) Rs 68.34
Question: How many words can be formed by using all letters of the word â€˜DAUGHTERâ€™ so that the vowels always come together?
(A) 42
(B) 420
(C) 470
(D) 5400
(E) 4320
Rationale: Sol. Given word contains 8 different letters. When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter.
Then, the letters to be arranged are DGNTR (AUE).
Then 6 letters to be arranged in 6p6 = 6! = 720 ways.
The vowels in the group (AUE) may be arranged in 3! = 6 ways.
Required number of words = (720x6) = 4320.
ANSWER E
Answer: (E) 4320
Question: A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
(A) Rs.500
(B) Rs.250
(C) Rs.5012.50
(D) Rs.5062.50
(E) None of these.
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.500
(P)(8)(5)/100 = 500
P = 1250
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}
= 2500/400(441 - 400)
= 25/4(41) = 1025/4 = Rs.256.25
ANSWER:E
Answer: (E) None of these.
Question: Jacob is 18years old. He is 2 times as old as his brother. How old will Jacob be when he is twice as old?
(A) 36
(B) 38
(C) 33
(D) 32
(E) 38
Rationale: j=18;
j=2b;
b=18/2=9;
twice as old so b=9(now)+(9)=18;
jacob is 18+18=36
ANSWER:A
Answer: (A) 36