mathewhe/aqua_rat huggingface dataset:
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
(A) 238
(B) 227
(C) 720
(D) 128
(E) 191
Rationale: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Answer: C
Answer: (C) 720
Question: On dividing 23 by a number, the quotient is 4 and the remainder is 3. Find the divisor.
(A) 1
(B) 2
(C) 4
(D) 5
(E) 7
Rationale: d = (D-R)/Q
= (23 - 3)/4
= 20/4 = 5
D
Answer: (D) 5
Question: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 4-percent solution?
(A) 35
(B) 33 1/3
(C) 21
(D) 16 2/3
(E) 15
Rationale: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 4-percent solution?
3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 4% of the solution. Set up an inequality and solve for x:
1.5/x = 1/4
x = 6
Since you need a 15L solution, you must evaporate 21 of the original 50L solution to get a 4% solution.
Answer is C.
Answer: (C) 21
Question: If CRY is coded as MRYC then how will GET be coded?
(A) MTEG
(B) MGET
(C) MEGT
(D) METG
(E) METC
Rationale: CRY=M+RYC
GET=M+ETG
METG
ANSWER:D
Answer: (D) METG
Question: A and B walk around a circular track. They start at 8 a.m from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9 a.m
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
Relative speed = (2+3) =5 rounds per hour
So, they cross each other 5 times in an hour hence, they cross 5 times before 9 a.m
Answer: Option A
Answer: (A) 5
Question: Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?
(A) 2(26)^3
(B) 26(26)^2
(C) 27(26)^2
(D) 26(26)^3
(E) 27(26)^3
Rationale: 26^2+26^3 = 26^2(1+26)=27*26^2
The answer is C.
Answer: (C) 27(26)^2
Question: The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 20%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
(A) 32.5
(B) 35
(C) 48
(D) 65
(E) 66.67
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 25% , therefore bringing down the price to $75.
3) Again it is further discounted by 20%, therefore bringing down the price to $60.
4) Now 60 has to be added byX %in order to equal the original price.
60 + ( X% ) 60 = 100.
Solving this eq for X, we get X = 66.67
Ans is E.
Answer: (E) 66.67
Question: A train is 360 meter long is running at a speed of 72 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 27 seconds
(B) 29 seconds
(C) 25 seconds
(D) 11 seconds
(E) 12 seconds
Rationale: Speed = 72 Km/hr = 72*(5/18) m/sec = 20 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/20) = 25 seconds
Answer:C
Answer: (C) 25 seconds
Question: A and B together can do a work In 3 days. A alone can do it in 12 days. What time B will take to do the work alone?
(A) 4 days
(B) 8 days
(C) 12 days
(D) 10 days
(E) 5 days
Rationale: Explanation:
A and B 1day's work = 1/3
A alone can do 1day's work = 1/12
what time B will take to do the work alone?
B = (A+B) - A = (1/3 - (1/12) = 4 Days
Answer: Option A
Answer: (A) 4 days
Question: If 10 crates have 95 apples each and how many apples more is required in order to make 100 apples in each crate?
(A) 5
(B) 10
(C) 15
(D) 50
(E) 0
Rationale: Each crate requires 5 apples and totally there are 10 crates so required apples = 10 * 5 = 50
Answer: D
Answer: (D) 50
Question: A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,160 ?
(A) $12
(B) $14
(C) $11.5
(D) $17
(E) $18
Rationale: I solved it as follows:
10+2(x) = 100 -5(x)
x= 12
Equation should be (10+$2*x)(100-5x)=1,160, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,160 --> (5+x)(20-x)=116 --> x=0.75 or x=14.25 --> price=10+$2*0.75=$11.5 or price=10+$2*14.25=$38.5.
Answer: C.
Answer: (C) $11.5
Question: The sum of ages of 5 children born 1 years different each is 30 years. What is the age of the Elder child?
(A) 8
(B) 9
(C) 10
(D) 16
(E) 17
Rationale: Let the ages of children be x, (x + 1), (x + 2), (x + 3) and (x + 4) years.
Then, x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 30
5x = 20
x = 4.
x+4= 4+4= 8
Answer : A
Answer: (A) 8
Question: The ratio between the present ages of P and Q is 6:8. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
(A) A)8:9
(B) B)3:5
(C) C)4:3
(D) inadequate
(E) of these
Rationale: Let P's age and Q's age be 6x and 8x years respectively.
Then, 8x - 6x = 4 => x =2
Required ratio = (6x + 4) : (7x + 4)
16 : 18 = 8:9
ANSWER:A
Answer: (A) A)8:9
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 1/2
(B) 10/21
(C) 9/11
(D) 7/11
(E) 5/2
Rationale: Total number of balls = 2 + 3 + 2 = 7
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 7 = 7C2
Let E = Event of drawing 2 balls , none of them is blue.
n(E) = Number of ways of drawing 2 balls , none of them is blue
= Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2
(∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)
P(E) = n(E)/n(S)=5C2/7C2=(5×42×1)/(7×62×1)=5×4/7×6=10/21
Answer is B
Answer: (B) 10/21
Question: The probability that a convenience store has no iced tea is 40%. If Karl is stopping by 2 convenience stores on his way to work, what is the probability that at least one of the stores will not have a can of iced tea?
(A) 1/8
(B) 1/4
(C) 1/2
(D) 3/4
(E) 21/25
Rationale: p=1-2/5^2(all stores have iced tea)=21/25
E
Answer: (E) 21/25
Question: Running at the same constant rate, 6 identical machines can produce a total of 240 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
(A)  648
(B)  1,800
(C)  1,600
(D)  10,800
(E)  64,800
Rationale: 6 machines produce 240 bottles per minute;
1 machine produces 240/6=40 bottles per minute;
10 machines produce 40*10=400 bottles per minute;
In 4 minutes 10 machines produce 400*4=1,600 bottles.
Answer: C.
Answer: (C)  1,600
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 2996 sq m
(B) 2897 sq m
(C) 4312 sq m
(D) 2768 sq m
(E) 2786 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7)
= 4312 sq m
Answer:C
Answer: (C) 4312 sq m
Question: Two-fifth of one-third of three-seventh of a number is 15. What is 40% of that number?
(A) 182
(B) 108
(C) 162
(D) 721
(E) 105
Rationale: Let the number be x. Then,
2/5 of 1/3 of 3/7 of
x = 15 => x = (15 * 5/3 * 3 * 5/2)
= 525/2
40% of 525/2 = (40/100 * 525/2)
=105
Answer:E
Answer: (E) 105
Question: A city with a population of 218,000 is to be divided into 10 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
(A) 19,920
(B) 19,940
(C) 19,960
(D) 19,980
(E) 20,000
Rationale: The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district.
Let p be the population of the least populated district.
Then 218,000 = p + 9(1.1)p
10.9p=218,000
p = 20,000
The answer is E.
Answer: (E) 20,000
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
(A) 3 1/5 Km
(B) 2 1/5 Km
(C) 3 Km
(D) 4 Km
(E) 4 1/3 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
A)
Answer: (A) 3 1/5 Km
Question: If p is a natural number and p! ends with q trailing zeros, then the number of zeros that (5p)! ends with will be
(A) a) (p+q) trailing zeros
(B) b) (5p+y) trailing zeros
(C) c) (5p+5y) trailing zeros
(D) d) (p+5y) trailing zeros
(E) e) none of them above
Rationale: Let p = 1. p! = 1! = 1, which means q= 0
(5p)! = 5! = 120, trailing zeros = 1
1 = 1 + 0 = p + q
Answer (A).
Answer: (A) a) (p+q) trailing zeros
Question: If a is an odd integer, which of the following must be an even integer?
(A) a^4−a+1
(B) (a^4−a)(a+1/a)
(C) a^4−a^3+a^2+2a
(D) (a^3+a^2+a)^2
(E) None of the above
Rationale: Let assume a be 1..
A. 1-1+1..odd
B.(1-1)(2) = 0.. even
C.1-1+1+2..odd
D.1+1+1..odd
E.None
Ans: option B.
Answer: (B) (a^4−a)(a+1/a)
Question: How many seconds will a 800 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 23 sec
(B) 30 sec
(C) 27 sec
(D) 48 sec
(E) 49 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 800 * 3/50
= 48 sec.
Answer:D
Answer: (D) 48 sec
Question: Let the function R(n) represent the product of the first n prime numbers, where n > 0. If x = R(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
(A) ii only
(B) iii only
(C) i and ii only
(D) i and iii only
(E) ii and iii only
Rationale: R(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of R(n). Thus, R(n) + 1 = even + 1 = odd. So, (i) is always true.
Now, use logic:
If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since onlyi and iii onlyis among the options, then it must be true.
Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.
Answer: D.
Answer: (D) i and iii only
Question: Two sets of 3 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
(A) 4
(B) 7
(C) 6
(D) 12
(E) it cannot be determined from the information given.
Rationale: A=(2,3,4), sum of this=9
B=(4,5,6), sum of this=15,
The differenct between 15-9=6
Hence,6 is the answer i.e.C
Answer: (C) 6
Question: Find the least number must be subtracted from 568219 so that remaining no.is divisible by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: On dividing 568219 by 5 we get the remainder 4, so 4 should be subtracted
E
Answer: (E) 4
Question: In how much time will a train of length 110 m, moving at 36 kmph cross an electric pole?
(A) sec
(B) sec
(C) sec
(D) sec
(E) sec
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 110/10 = 11 sec.
Answer:D
Answer: (D) sec
Question: A motorboat, whose speed in 15 km/hr in sƟll water goes 30 km downstream and comes back in a
total of 4 hours 30 minutes. The speed of the stream (in km/hr) is
(A) 2 km/hr
(B) 3 km/hr
(C) 4 km/hr
(D) 5 km/hr
(E) None of these
Rationale: Explanation:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr
So we know from quesƟon that it took 4(1/2)hrs to travel back to same point.
So,
3015+x−3015−x=412=>900225−x2=92=>9x2=225=>x=5km/hr
Answer: D
Answer: (D) 5 km/hr
Question: If 7 spiders make 7 webs in 7 days, then how many days are needed for 1 spider to make 1 web?
(A) 1
(B) 7
(C) 3
(D) 14
(E) 16
Rationale: Explanation:
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)7:1
(webs) 1:7}::x:7
⇒7×1×7=1×7 × x
⇒x=7
Answer: Option B
Answer: (B) 7
Question: Ram professes to sell his goods at the cost price but he made use of 950 grms instead of a kg, what is the gain percent?
(A) 5 15/19%
(B) 3 15/19%
(C) 4 15/19%
(D) 6 15/19%
(E) 9 15/19%
Rationale: 950 --- 50
50 --- ? =>
=50/950 *100
= 5 15/19%
Answer: A
Answer: (A) 5 15/19%
Question: If x^3 = y^2 > z, which of the statements could be true?
I. x < y < z
II. x < z < y
III. y < x < z
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Given : x^3 = y^2 > z
x^3 = y^2 is possible only when 9^3=27^2=729
I. x < y < z is true for x=9, y=27, z=30 i.e. Answers can only be Options A, C or E
II. x < z < y is true for x=9, y=27, z=10 i.e. Answers can only be Options C or E
III. y < x < z is not true for x=9, y=27
Answer: option C
Answer: (C) I and II only
Question: If f(x) = x^3/(x^5 - 1), what is f(1/x) in terms of f(x)?
(A) -f(x)
(B) 1/f(x)
(C) 2/f(x)
(D) 3/f(x)
(E) f(x)
Rationale: If x = 2 then f(x) = 8/31 and f(1/x) = -8/31 which is equal to -f(x)
answer A
Answer: (A) -f(x)
Question: If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is?
(A) 1/2
(B) 1
(C) -1/2
(D) -1
(E) 0
Rationale: When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero.
Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p
=> x = (p + q - r + p - q + r + q + r - p) / (r + q + p)
=> x = (r + q + p) / (r + q + p) = 1
p + q + r is non-zero.
ANSWER:B
Answer: (B) 1
Question: If 2 cards are selected (with replacement) at random from the deck of 52 cards then what is the probability that both of the selected cards will be a king, a queen, or a jack? A deck of cards has a total of 52 cards, consisting of 4 suits: spades (black), hearts (red), diamonds (red), and clubs (black). In each suit, there are 13 cards including 1 king, 1 queen, and 1 jack.
(A) 1/16
(B) 2/25
(C) 3/64
(D) 5/128
(E) 9/169
Rationale: P(both cards are king, queen, or jack) = 12/52*12/52 = 9/169
The answer is E.
Answer: (E) 9/169
Question: Income of A is 25% more than the income of B. What is the income of B in terms of income of A?
(A) 80%
(B) 75%
(C) 78.66%
(D) 71.25%
(E) None of these
Rationale: Explanation:
One of the most basic questions.
Let income of B be 100. Income of A is 25% more than income of B which means Income of A becomes 125
Now income of B in terms of A = 100/125 *100 = 80%
ANSWER A
Answer: (A) 80%
Question: A sum of money at simple interest amounts to Rs. 1717 in 1 year and to Rs. 1734 in 2 years. The sum is:
(A) Rs. 1200
(B) Rs. 1690
(C) Rs. 1600
(D) Rs. 1700
(E) Rs. 1500
Rationale: S.I. for 1 year = Rs. (1734 - 1717) = Rs. 17.
Principal = Rs. (1717 - 17) = Rs. 1700.
Answer: Option D
Answer: (D) Rs. 1700
Question: Two pipes A and B can fill a cistern in 12 and 24 minutes respectively, and a third pipe C can empty it in 36 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 10 2/7 min
(B) 10 1/8 min
(C) 11 1/7 min
(D) 12 8/7 min
(E) 11 3/7 min
Rationale: 1/12 + 1/24 - 1/36
= 7/72
72/7 = 10 2/7
Answer:A
Answer: (A) 10 2/7 min
Question: The Guests at a football banquet consumed a total of 323 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?
(A) 160
(B) 161
(C) 162
(D) 163
(E) 164
Rationale: To minimize one quantity maximize other.
161*2 (max possible amount of food a guest could consume) = 322 pounds, so there must be more than 161 guests, next integer is 162.
Answer: C.
Answer: (C) 162
Question: If 20 % of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together.
(A) 11 1/9
(B) 10 1/9
(C) 12
(D) 15
(E) Source: TIME material.
Rationale: Use algebra :
0.2/A + 0.8/B = 20
1/A + 4/B = 100
0.8/A + 0.2/B = 30
4/A+ 1/B = 150
15/B = 250
B = 3/50 work per day
A = 3/100 work per day
Combined rate = 3/40 + 3/100 = 9/100
Time taken when working together = 100/9 = 11(1/9) days
Answer (A)
Answer: (A) 11 1/9
Question: Three friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share twice, no apples were left.How many apples were there?
(A) 62
(B) 63
(C) 64
(D) 65
(E) 66
Rationale: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 6 times. So answer is (2^6)-1=63.
ANSWER:B
Answer: (B) 63
Question: The percentage profit earned by selling an article for Rs. 1520 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
(A) 3000
(B) 1230
(C) 1750
(D) 5600
(E) 3400
Rationale: C.P. be Rs. x.
Then, (1520 - x)/x * 100 = (x - 1280)/x * 100
1520 - x = x - 1280
2x = 2800 => x = 1400
Required S.P. = 125 % of Rs. 1400 = 125/100 * 1400 = Rs. 1750.
ANSWER C
Answer: (C) 1750
Question: Jeremy bought 2Q steaks for P dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?
(A) 50RP/Q.
(B) 50QR/P.
(C) 25RQ/P.
(D) 25RP/Q.
(E) RP/(4Q).
Rationale: Jeremy bought 2Q steaks for P dollars, so 1 steak = P/2Q
Jerome buys R steaks for a 50% discount: r* (P/4Q)
in cents the answer will be : r* (100 P/4Q)= 25 RP/ Q=D
Answer: (D) 25RP/Q.
Question: There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?
(A) 80
(B) 140
(C) 120
(D) 100
(E) 150
Rationale: Let the number of persons in building P = p
and the number of persons in building Q = q
If 15 persons are sent from P to Q,
then the number of persons in each building is the same
=> p-15 = q+15
=> p - q = 30 ----(Equation 1)
If 20 persons are sent from Q to P,
then the number of persons in P is double the number of persons in Q
=> 2(q - 20) = (p + 20)
=> 2q - 40 = p + 20
=> 2q - p = 60 ----(Equation 2)
(Equation 1) + (Equation 2)=> q = 90
From Equation 1, p = 30 + q = 30 + 90 = 120
i.e., Building P has 120 persons
Answer : Option C
Answer: (C) 120
Question: There are 12 cans in the refrigerator. 7 of them are red and 5 of them are blue. In how many ways we can remove 9 cans so that at least one red and at least one blue cans to remain the refrigerator.
(A) 460
(B) 175
(C) 493
(D) 455
(E) 445
Rationale: Ways to pick 3 cans so that at least one red and at least one blue cans to remain the refrigerator =
total ways to pick 3 can out of 12 - ways to pick 3 red out of 7 red - ways to pick 3 blue out of 5 blue
12C3âˆ’7C3âˆ’5C3=220âˆ’35âˆ’10=175
ANSWER:B
Answer: (B) 175
Question: In Country S, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
(A)  50% decrease
(B)  30% decrease
(C)  15% decrease
(D)  30% increase
(E)  55% increase
Rationale: In Country S 1992 1996
No of construction workers 100 120
Unemployment Rate 16% 9%
Unemployed workers 16 11
% change in unemployed workers=(16-11)=5/16=~33% decrease
Closest ans=30% decrease
Ans=B
Answer: (B)  30% decrease
Question: What will be the compound interest on a sum of Rs. 26,000 after 3 years at the rate of 12% p.a.?
(A) s.10123.77
(B) s.10123.21
(C) s.10123.20
(D) s.10123.28
(E) s.10528.12
Rationale: Amount = [26000 * (1 + 12/100)3]
= 26000 * 28/25 * 28/25 * 28/25
= Rs. 36528.12
C.I. = (36528.12 - 26000)
= Rs. 10528.12
Answer:E
Answer: (E) s.10528.12
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 36 hours respectively. The ratio of their speeds is?
(A) 4:9
(B) 4:3
(C) 4:5
(D) 3:1
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √36 : √4
= 6:2 = 3:1
Answer:D
Answer: (D) 3:1
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
(A) A
(B) B
(C) C
(D) all alike
(E) None of these
Rationale: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
ANSWER:C
Answer: (C) C
Question: If three numbers are randomly selected from a set, what is the probability that sum will be greater than 18 if he given set is
{5,6,7,8,9,10}
(A) 7/18
(B) 5/13
(C) 5/16
(D) 5/19
(E) 5/9
Rationale: First problem is 6C3 = 18 .. Not 20..
Point 2, your sum should be greater than 18, so these are the following possibilities you have
({5,7,8},{5,9,10},{6,7,8},{6,9,10},{8,9,10}) which leads to 5 combinations
So the probability is 5 on 18 or 5/18..
ANSWER:D
Answer: (D) 5/19
Question: . Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
(A) 5/0
(B) 5/9
(C) 5/1
(D) 5/3
(E) 5/6
Rationale: Explanation:
No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer:B
Answer: (B) 5/9
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
(A) Sunday
(B) Friday
(C) Saturday
(D) Monday
(E) NONE OF THESE
Rationale: Explanation :
Given that 8th Feb, 2005 was Tuesday
Number of days from 8th Feb, 2004 to 7th Feb, 2005 = 366 (Since Feb 2004 has 29 days as it is a leap year)
366 days = 2 odd days
Hence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday. Answer : Option A
Answer: (A) Sunday
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:3
(B) 3:4
(C) 3:8
(D) 3:1
(E) 3:2
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4.Answer: B
Answer: (B) 3:4
Question: A customer purchased a package of ground beef at a cost of $1.76 per pound. For the same amount of money, the customer could have purchased a piece of steak that weighed 36 percent less than the package of ground beef. What was the cost per pound of the steak?
(A) $2.00
(B) $2.25
(C) $2.50
(D) $2.75
(E) $3.00
Rationale: For simplicity, let's assume the customer bought 1 pound of ground beef for $1.76.
Let x be the price per pound for the steak.
Then 0.64x = 176
x = 176/0.64 = $2.75
The answer is D.
Answer: (D) $2.75