mathewhe/aqua_rat huggingface dataset:
Question: Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and Q. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of Q if J is negative?
(A) -2
(B) Q=0
(C) 1
(D) 2
(E) 5
Rationale: since j is negative, therefore median of the set will be 3. which is an odd number. also, we know that odd^n will always be odd. now since 34 is even, therefore 3^w will have only one factor with 34 for w=0.
mode of the set is a number which occurs maximum number of time in the set. now, since Q is the mode of the set. therefore Q=0. hence answer is B
Answer: (B) Q=0
Question: To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 14 hours a day?
(A) 24
(B) 23
(C) 24
(D) 20.57
(E) 22
Rationale: Man-hours required to asphalt 1 km road=30*12*8=2880
Man-hours required to asphalt 2 km road=2880*2=5760
Man-hours available per day=20*14=280
Therefore number of days=5760/280=20.57 days
Ans=D
Answer: (D) 20.57
Question: The average age of a committee of 10 members is 25 years. A member aged 55 years retired and his place was taken by another member aged 35 years . The average age of
present committee is;
(A) 23 years
(B) 38 years
(C) 36 years
(D) 35 years
(E) 37 years
Rationale: Total age of the committee = 25*10 = 250,
Total age when a member is retired
and a new one was joined = 250-55 +35, =230
Average age of present committee = 230/10 = 23.
ANSWER:A
Answer: (A) 23 years
Question: A board 6ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
(A) 5ft. 7 inches
(B) 3ft. 7 inches
(C) 2ft. 3 inches
(D) 2ft. 7 inches
(E) 1ft. 7 inches
Rationale: Length of board=6ft. 9 inches=(6*12+9)inches=81 inches.
Therefore, Length of each part = (81/3) inches = 27 inches = 2ft. 3 inches
Answer is C.
Answer: (C) 2ft. 3 inches
Question: A company pays 18.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?
(A) 25
(B) 66
(C) 18
(D) 37
(E) 01
Rationale: Explanation:
Dividend on 1 share = (18.5 * 50)/100 = Rs.9.25
Rs.25 is income on an investment of Rs.100
Rs.9.25 is income on an investment of Rs. (9.25 * 100)/25 = Rs.37
ANSWER: D
Answer: (D) 37
Question: A man saves 30% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 30%, he is only able to save Rs. 300 per month. What is his monthly salary?
(A) Rs. 4000
(B) Rs. 3750
(C) Rs. 5000
(D) Rs. 5500
(E) Rs. 6500
Rationale: Income = Rs. 100
Expenditure = Rs. 70
Savings = Rs. 30
Present Expenditure 70+70*(30/100) = Rs. 91
Present Savings = 100 – 91 =Rs. 8
If savings is Rs. 8, salary = Rs. 100
If savings is Rs.300, salary = 100/8*300 = 3750
Answer : B
Answer: (B) Rs. 3750
Question: What least number should be subtracted from 3,381 so that the remainder when divided by 9, 11, and 17 will leave in each case the same remainder 8 ?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 15
Rationale: The LCM of 9, 11 and 17 is 1,683. The next multiple is 2*1,683 = 3,366.
3,366 + {remainder} = 3,366 + 8 = 3,374, which is 7 less than 3,381.
Answer: B.
Answer: (B) 7
Question: Company X provides bottled water to its employees in 10 liter bottles, $2 each. At least how many 10L bottles must Company X buy monthly, so that new contract with $50 fixed monthly rate and $1 for 50L bottle each paid off? (Assume that no other costs apply)
(A)  28
(B)  29
(C)  30
(D)  31
(E)  32
Rationale: let the no. of 10 liter bottles be x, so the no. of 50l bottles will be x/5 (to equate the vol.) since the total cost will be equal , 2x= 50+x/5 so x= 27.77 or 28. Answer is (A).
Answer: (A)  28
Question: X completes a work in 120 days and Y complete the same work in 30 days. If both of them work together, then the number of days required to complete the work will be?
(A) 24 days.
(B) 22days.
(C) 34 days.
(D) 40 days.
(E) 45 days.
Rationale: If X can complete a work in x days and Y can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 120Ã— 30/ 150 = 24 days.
A)
Answer: (A) 24 days.
Question: There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
(A) 120
(B) 720
(C) 1,060
(D) 1,520
(E) 1,980
Rationale: these are two independent events. meaning picking men from a group of men has no effect on picking women from group of women. so you have to multiply here.
11c2*9c2 =1980
Answer is E.
Answer: (E) 1,980
Question: The LCM of two numbers is 2310 and HCF is 30. If one of the numbers is 210. Then what is the other number ?
(A) 715
(B) 825
(C) 330
(D) 582
(E) 465
Rationale: First number * Second Number = LCM * HCF
Other number = 2310 * 30 / 210 = 11*30 = 330
ANSWER :C
Answer: (C) 330
Question: Between 100 and 200, how many numbers are there in which one digit is the average of the other two?
(A) 11
(B) 12
(C) 10
(D) 8
(E) 9
Rationale: Answer is 11 :A
Let's list the numbers between 100 and 200 that have digits in which one of them is average of the other 2.
(One rule before listing, it should always start with 1XX)
{102, 111, 123, 135, 147, 159 } in these five, except 111, the others has 2 ways of rearranging, i.e., 123 can also be written as 132, and so is for 135 as 153.
Therefore 1 + 2 * 5 numbers = 11
Answer: (A) 11
Question: mixture contains alcohol and water in the ratio 4 : 3. If 8 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
(A) 10
(B) 99
(C) 27
(D) 4
(E) 29
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
32x = 4(3x+5)
20x = 20
x = 1
Quantity of alcohol = (4 x 1) litres = 4 litres.
Answer: D
Answer: (D) 4
Question: A is 20 percent more efficient than B. If the two person can complete a piece of work in 60 days.in how many days. A working alone can complete the work
(A) 110
(B) 277
(C) 287
(D) 279
(E) 2781
Rationale: As A is 20% more efficient than B, If B's per day work is 100 units then A's 120.
Both persons together completes (100 + 120) units = 220 units a day.
They took 60 days to complete the work. So total work = 60 x 220
If A alone set to complete the work, he takes = 60×220120=11060×220120=110 days
Answer:A
Answer: (A) 110
Question: Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $6 more than 1/4 of the fine and Peter paid $6 less than 1/3 of the fine, leaving pay $10 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?
(A) $50
(B) $40
(C) $35
(D) $44
(E) $45
Rationale: Call the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F – 4, leaving (1/2)F – 5 left. If we add those three up, they should add up to F.
F = [(1/4)F + 6] + [(1/3)F – 6] + [(1/2)F – 10]
F = (1/4)F + (1/3)F + (1/2)F – 10
Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 120
12F = 13 F – 120
–F = – 120
F = 120
Well, if the fine cost $120, then Sam paid the part not covered by Joe or Peter. Half the fine is $60, and Sam paid $10 less than this: $50.
Answer = A
Answer: (A) $50
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 32 : 48
(B) 32 : 42
(C) 32 : 45
(D) 32 : 41
(E) 42 : 45
Rationale: Explanation:
A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
Answer:C
Answer: (C) 32 : 45
Question: 65 + 5 * 12 / (180/3) = ?
(A) 22
(B) 77
(C) 29
(D) 66
(E) 21
Rationale: 65 + 5 * 12 / (180/3) = 65 + 5 * 12 / (60)
= 65 + (5 * 12)/60 = 65 + 1 = 66.Answer:D
Answer: (D) 66
Question: Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
(4x + 8) = 5 (x + 8)
2
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2.
B
Answer: (B) 2
Question: What approximate value should come in place of the question mark (?) in the following equation ?
2⁄7 of 1596 + 3015 = ? – 2150
(A) 7200
(B) 48000
(C) 5610
(D) 58000
(E) 6300
Rationale: ? ≈ 2 × 230 + 3000 + 2150
= 460 + 3000 + 2150 = 5610
Answer C
Answer: (C) 5610
Question: If (1 – 1.25)N = 3, then N =
(A)  −400
(B)  −140
(C)  −4
(D)  4
(E)  -12
Rationale: (1 – 1.25)N = 3
Simplify to get: -0.25N = 3
Rewrite as (-1/4)N = 3
Multiply both sides by -4 to get: N = -12
Answer: E
Answer: (E)  -12
Question: If a and b are positive integers, which of the following cannot be odd?
(A) (2+4a)/(4+4b)
(B) (4a)/(b)
(C) a/b
(D) (4+a)/(2+4b)
(E) (4+a)/(1+4b)
Rationale: A. (2+4a)/(4+4b) - Under any condition this can't be odd. Answer
B. (4a)/(b) = 4.1/4 = 1 = Odd
C. a/b = 4/4 = Odd
D.(4+a)/(2+4b) = (4+2)/(2+4.1) = 1 = Odd
E.(4+a)/(1+4b) = (4+1)/(1+4.1) = 1 = Odd
ANSWER:A
Answer: (A) (2+4a)/(4+4b)
Question: The telephone bill of a certain establishment is party fixed and partly varies as the number of calls consumed. When in a certain month 540 calls made the bill is Rs.1800. In another month 620 calls are consumed then the bill becomes Rs.2040. In another month 500 units are consumed due to more holidays. The bill for that month would be :
(A) Rs.1560
(B) Rs.1680
(C) Rs.1840
(D) Rs.1950
(E) Rs.1850
Rationale: Let the fixed amount be Rs. X and the cost of each unit be Rs. Y.
Then, 540y + x = 1800 …. And 620y + x = 2040
On subtracting (i) from (ii), we get 80y = 240 -> y = 3
Putting y = 3 in (i) we get :
540 * 3 + x = 1800 x = (1800-1620) = 180
. : Fixed charges = Rs.180, Charge per unit = Rs.3.
Total charges for consuming 500 units = 180 +(500*3) = Rs.1680
ANSWER:B
Answer: (B) Rs.1680
Question: Three people each took 4 tests. If the ranges of their scores in the 4 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?
(A) a 17
(B) b) 28
(C) c) 35
(D) d) 45
(E) e) 80
Rationale: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:
A- 0 and 17
B- 0 and 28
therefore the minimum range is 28, it cant be any lower however you play with the numbers.
B
Answer: (B) b) 28
Question: Mary rolls a die 5 times. What is the probability that she gets a one on the last one of the five rolls?
(A) 100/1000
(B) 7775/7776
(C) none
(D) 1
(E) 888/881
Rationale: the die has 6 sides and it was rolle 5 times, then 6*6*6*6*6=7776
the number of ways to get 1 is 1
then 1/7776
the probability would be
1-1/7776=7775/7776
Answer B
Answer: (B) 7775/7776
Question: Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?
(A) 15
(B) 16
(C) 18
(D) 25
(E) 20
Rationale: Explanation:
Ratio of times taken by Sakshi and Tanys = 125:100 = 5:4
Suppose Tanya takes x days to do the work.
5:4 :: 20:x => x= 16 days.
Hence, Tanya takes 16 days to complete the work.
ANSWER IS B
Answer: (B) 16
Question: Three grades of milk are 1 percent,4 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
(A) y + 3z
(B) (y +z) / 4
(C) 2y + 3z
(D) 3y + z
(E) 4y + 3z
Rationale: Soln:
The resulting equation is
=> (.01x + .04y + .03z)/(x+y+z) = 1.5/100
=> x + 4y + 3z = 1.5x + 1.5y + 1.5z
taking x to one side and y and z to other side we get
=> x = 4y + 3z
Ans is E
Answer: (E) 4y + 3z
Question: Peter bought an item at 20% discount on its original price. He sold it with 40% increase on the price he bought it. The sale price is by what percent more than the original price?
(A) 7.2
(B) 7.5
(C) 10
(D) 12
(E) None
Rationale: Sol.
Let the original price be Rs. 100. Then, C.P. = Rs. 80.
S.P. = 140% of Rs. 80 = Rs. [112-100%] = 12%.
Answer D
Answer: (D) 12
Question: The area of a rectangular plot is 24 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?
(A) 14 metres
(B) 5 metres
(C) 7.5 metres
(D) Data inadequate
(E) None of these
Rationale: L × B = 24 × B
∴ L = 24 m
and L – B = 10
∴ B = 24 – 10 = 14 m
Answer A
Answer: (A) 14 metres
Question: If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 5)?
(A) 3
(B) P + 2
(C) p – 2
(D) 2p – 1
(E) 5p - 1
Rationale: The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.
Thus, the number of integers between pq and p(q+5)=pq+5p is (pq+5p-pq)-1=5p-1.
Answer: E.
Answer: (E) 5p - 1
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
(A) 50
(B) 49
(C) 87
(D) 76
(E) 66
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer:A
Answer: (A) 50
Question: A man sells a horse for Rs.200 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 227
(B) 299
(C) 277
(D) 860
(E) 460
Rationale: CP = SP + 1CP = SP - g
200 + x = 980 - 2x
3x = 780 => x = 260
CP = 200 + 260= 460
Answer: E
Answer: (E) 460
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 388
(B) 378
(C) 240
(D) 388
(E) 771
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: C
Answer: (C) 240
Question: The average age of applicants for a new job is 32, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants?
(A) 8
(B) 77
(C) 7
(D) 18
(E) 34
Rationale: Minimum age = Average - 1 Standard deviation = 32 - 8 = 24
Maximum age = average + 1 Standard deviation = 32+ 8 = 40
Maximum number of different ages of the applicants = 30 - 24 + 1 = 7
Answer C
Answer: (C) 7
Question: Peter has $642,986 in his savings account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among his nine children?
(A) $642,986
(B) $642,987
(C) $642,988
(D) $642,989
(E) $642,990
Rationale: To find the least amount the man should add to his saving account to split the money evenly among his 9 children, he needs to make the total divisible by 9
Simply add the individual digits of the total = 6+4+2+9+8+6= 35
If you add 1 , the number is divisible by 9 (35+ 1)
Correct Option : B
Answer: (B) $642,987
Question: Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches?
(A) 24
(B) 26
(C) 28
(D) 30
(E) 32
Rationale: Area of first rectangle is 12*15=180 hence area of second would be 6x=180x
x=30
answer is D
Answer: (D) 30
Question: The ratio of two natural numbers is 5:6. If a certain number is added to both the numbers, the ratio becomes 7:8. If the larger number exceeds the smaller number by 10, find the number added?
(A) 27
(B) 298
(C) 20
(D) 28
(E) 12
Rationale: Let the two numbers be 5x and 6x.
Let the number added to both so that their ratio becomes 7:8 be k.
(5x + k)/(6x + k) = 7/8
42x = 7k => k = 2x.
6x - 5x = 10 => x = 10
k = 2x = 20.
Answer: C
Answer: (C) 20
Question: What is the area of square field whose side of length 15 m?
(A) 225
(B) 2878
(C) 277
(D) 266
(E) 279
Rationale: 15 * 15
= 225 sq m
Answer: A
Answer: (A) 225
Question: The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
(A) 40 years
(B) 42 years
(C) 50 years
(D) 52 years
(E) None
Rationale: Solution
Age of the mother	= (12 x 7 - 7 x 6)
= 42 years.
Answer B
Answer: (B) 42 years
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
(A) 300km/hour
(B) 360 km/hour
(C) 600km/hour
(D) 720km/hour
(E) None of these
Rationale: Distance=(240*5)km=1200km.
Required speed=(1200*3/5)km/hr=720kilometer/hour.
Correct Option: D
Answer: (D) 720km/hour
Question: Carina has 85 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Lets say 5 and 10 ounce packages be x and y respectively.
Given that, 5x+10y=85 and x=y+2. What is the value of y.
Substituting the x in first equation, 5y+10+10y=85 ->y=75/15.=5
A
Answer: (A) 5
Question: Sundar invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income
(A) 600
(B) 648
(C) 500
(D) 700
(E) 750
Rationale: no of shares = 4455/8.25 = 540
face value = 540*10 = 5400
income = 12/100 * 5400 = 648
ANSWER B
Answer: (B) 648
Question: We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value W of the ratio A/B?
(A) 1/2
(B) 1/3
(C) 2/3
(D) 1/4
(E) 1/5
Rationale: W-> A/B=20*21*……*39/21*22*….*39*40=20/40=1/2.
Therefore, the answer is A.
Answer: (A) 1/2
Question: In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Explanation:
Let d and s represent the number of daughters and sons respectively.
Then, we have :
d - 1 = s and 2 (s - 1) = d.
Solving these two equations, we get: d = 4, s = 3.
Answer: B
Answer: (B) 3
Question: If x and y are perfect squares, then which four of the following is not necessarily a perfect square?
(A) x^2
(B) xy
(C) 4x
(D) x+y
(E) x^5
Rationale: If x=y=1^2=1, then each option but E is a perfect square, therefore E is NOT necessarily a perfect square.
Answer: E.
Answer: (E) x^5
Question: There are 70 doors marked with numbers 1 to 70. And there are 70 individuals marked 1 to 70.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with.
Now one at a time one randomly picked individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For e.g. individual marked with number 5 operates the doors marked with the following numbers: 5, 10, 15 ...70.
If every individual in the group get one turn then how many doors are open at the end?
(A) 0
(B) 1
(C) 2
(D) 7
(E) 8
Rationale: Let us start with 1.
When 1 goes, all the doors are open since every number is a multiple of 1.
Also 1 will remain opened since 1 is not a multiple of any number.
Prime numbers can only be operated by people with prime numbers.
So 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59, 61,67 will be closed when people with respective numbers perform operations on them.
From the other numbers, only those numbers will remain opened on which even number of operations are performed including the operation performed by number 1.
This is possible only for perfect squares which are 4,9 ...64.
So our numbers are 1,4,9, 16,25,36,49 and 64.
Answer:-E
Answer: (E) 8
Question: [(11/2 ÷ 1/2 × 11/2)]/[(11/2 × 1/2 ÷ 11/2)] = ?
(A) 111
(B) 101
(C) 91
(D) 81
(E) 121
Rationale: Explanation:
[(11/2 ÷ 1/2 × 11/2)]/[(11/2 × 1/2 ÷ 11/2)]
= [11/2 × 2/1 × 11/2]/[11/2 × 1/2 × 2/11]
= 121/2 / 1/2 = 121/2 x 2/1 = 121
Answer: Option E
Answer: (E) 121
Question: A and B together have $ 1210. If of A's amount is equal to of B's amount, how much amount does B have?
(A) 400
(B) 489
(C) 484
(D) 365
(E) 342
Rationale: 4	A	=	2	B
15 5
A = 2	x	15 B
5 4
A =	3	B
2
A	=	3
B 2
A : B = 3 : 2.
B's share = Rs. 1210 x	2 = $ 484.
ANSWER C
Answer: (C) 484
Question: The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above condition is
(A) 4
(B) 6
(C) 8
(D) 12
(E) 14
Rationale: Explanation:
Let the required numbers be 33a and 33b.
Then 33a +33b= 528 inline fn_jvn Rightarrow a+b = 16.
Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).
inline fn_jvn therefore Required numbers are ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)
The number of such pairs is 4. Answer: A
Answer: (A) 4
Question: A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 25 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?
(A) 40
(B) 45
(C) 108
(D) 55
(E) 60
Rationale: A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 25 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
25 = 180/4t
t = 108
B-C = 108mph
Answer C
Answer: (C) 108
Question: B completes a work in 8 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?
(A) 3.75 days
(B) 4.44 days
(C) 5 days
(D) 6.44 days
(E) 7 days
Rationale: 1/8 + 1/10 = 9/40
40/9 = 4.44 days
ANSWER:B
Answer: (B) 4.44 days
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
(A) monday
(B) Tuesday
(C) sunday
(D) friday
(E) wednesday
Rationale: The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday.
Answer:B) Tuesday
Answer: (B) Tuesday
Question: The height of a triangle is decreased by 5% and its base increased by 10%. Its area will
(A) decrease by 12.5%
(B) increase by 12.5%
(C) increase by 4.5%
(D) Increase by 25%
(E) None of these
Rationale: Explanation :
Let the initial height be 100 and the base be 200 units.
âˆ´ Area = 1/2 x 100 x 200 = 10000sq units
Now, height = 95 units and base = 220 units
âˆ´ New area = 1/2 x 95 x 220= 10450
âˆ´ Area is increased by (10450 - 10000)/10000 x 10
= 4.5%
Answer : Option C
Answer: (C) increase by 4.5%
Question: The sum of ages of 4 children born 2 years different each is 40 yrs. What is the age of the Elder child?
(A) 13
(B) 9
(C) 16
(D) 17
(E) 18
Rationale: Let the ages of children be x, (x + 2), (x + 4), (x + 6) years.
Then, x + (x + 2) + (x + 4) + (x + 6) = 40
4x+12 = 40 => 4x= 28
x = 7
x+6= 7+6= 13
Answer : A
Answer: (A) 13
Question: A city in the US has a basketball league with three basketball teams, the Aziecs, the Braves and the Celtics. A sports writer notices that the tallest player of the Aziecs is shorter than the shortest player of the Braves. The shortest of the Celtics is shorter than the shortest of the Aziecs, while the tallest of the Braves is shorter than the tallest of the Celtics. The tallest of the Braves is taller than the tallest of the Aziecs.
Which of the following can be judged with certainty ?
(A) X,U only
(B) X only
(C) Y only
(D) 8 onlY
(E) T only
Rationale: Ans: B
Sol: We solve this problem by taking numbers. Let the shortest of Braves is 4 feet. Then tallest of Aziecs is less than 4. So let it be 3 feet.
A -> 2 - 3
B -> 4 - 6
C -> 1 - 7
From the above we can safely conclude X is correct. but Y cannot be determined.
Answer:C
Answer: (C) Y only