mathewhe/aqua_rat huggingface dataset:
Question: At a Supermarket a certain item has increased from 72 cents per pound to 78 cents per pound. What is the % increase in the cost of item?
(A) 6.33%
(B) 7.22%
(C) 8.33%
(D) 8%
(E) 7%
Rationale: Percent change = (New Value- Old Value )/ old value x 100
=((78-72)/72)x100
= (6/72)*100
= 8.33%
There was an 8.33% increase in the cost of item
answer -C = 8.33%
Answer: (C) 8.33%
Question: How many positive 5-digit integers have the odd sum E of their digits?
(A) 9*10^2
(B) 9*10^3
(C) 10^4
(D) 45*10^3
(E) 9*10^4
Rationale: We are looking at numbers between 10000 and 99999 both inclusive.
There are 90000 numbers.
Now for
10000 : sum of digits is odd;
10001 :sum of digits is even;
10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.
(Exception for the above statement :
When it is 10009 the E sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd
and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)
This means exactly half of the numbers will have odd sum of their digits. i.e 45000
Answer :D
Answer: (D) 45*10^3
Question: There are different 15 circles. What is the number of the greatest possible points with which the circles intersect?
(A) 390
(B) 100
(C) 110
(D) 180
(E) 210
Rationale: Maximum points of intersection between n different circles = n*(n - 1) = 15*14 = 210
Answer: E
Answer: (E) 210
Question: B completes a work in 9 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) 4.73 days
(C) 5.75 days
(D) 6.75 days
(E) 7.73 days
Rationale: 1/9 + 1/10 = 19/90
90/19 = 4.73 days
ANSWER: B
Answer: (B) 4.73 days
Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
(A) 1/3
(B) 1/4
(C) 1/5
(D) 1/7
(E) 1/8
Rationale: Explanation:
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture =(3-3x/8+x)litres
Quantity of syrup in new mixture =(5-5x/8)litres
(3 -	3x/8 +x)=(5 -	5x/8)
=>5x + 24 = 40 - 5x
=>10x = 16
=>x =	8/5
So, part of the mixture replaced =(8/5 x	1/8)=1/5.
ANSWER IS C
Answer: (C) 1/5
Question: A car is running at a speed of 96kmph. What distance will it cover in 14sec?
(A) 378m
(B) 350m
(C) 380m
(D) 200m
(E) 250m
Rationale: Speed = 96kmph = 96*5/18 = 27 m/s
Distance covered in 14sec = 27*14 = 378m
Answer is A
Answer: (A) 378m
Question: The average of 6 observations is 11. A new observation is included and the new average is decreased by 1. The seventh observation is?
(A) 4
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: Let seventh observation = X.
Then, according to the question we have
=> (66 + X) / 7 = 10
=> X = 4.
Hence, the seventh observation is 4.
ANSWER:A
Answer: (A) 4
Question: The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is :
(A) 4.37%
(B) 5%
(C) 6%
(D) 8.75%
(E) None of these
Rationale: Solution
Increase in 10 year= (262500 - 175000) = 87500.
Increase% =( f87500/175000x 100 )% = 50%
∴ Required average = ( 50/10 )% = 5%
Answer B
Answer: (B) 5%
Question: If a + b = y and a - b = z , then 3ab =
can someone explain!
(A) (3y^2 - 3z^2)/4
(B) (3z^2 - 3y^2)/4
(C) 3y+3z/2
(D) 3y - 3z/2
(E) 3y^2 - 3z^2/2
Rationale: plugging numbers is quite fast in this case:
Let
a=1
b=2
Then; y= 1+2=> 3 and z= 1-2=> -1
Question asks 3ab=.........
As our number 3ab= 3*1*2=6
now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need.
Hence: Ans is A.
Answer: (A) (3y^2 - 3z^2)/4
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) 12
(B) 18
(C) 20
(D) 24
(E) 26
Rationale: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
C
Answer: (C) 20
Question: A batsman in his 12th innings makes a score of 65 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?
(A) 42
(B) 43
(C) 44
(D) 45
(E) 46
Rationale: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 2) + 65
∴ x = 43
Answer B
Answer: (B) 43
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 7 to the thrice of the remainder. The dividend is
(A) 74
(B) 78
(C) 86
(D) 92
(E) 106
Rationale: Divisor = (6 * 3) + 7 = 25
5 * Quotient = 25
Quotient = 5.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 5) + 6 = 106.
E)
Answer: (E) 106
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg. What might be the weight of the new person?
(A) 70kg
(B) 75kg
(C) 80kg
(D) 85kg
(E) 90kg
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (55 + 20) kg = 75 kg.
B)
Answer: (B) 75kg
Question: Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
(A) 10
(B) 8
(C) 6
(D) 4
(E) 2
Rationale: Explanation:
Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise she has four different routes.
Total routes = 8
Answer: B
Answer: (B) 8
Question: Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 25 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?
(A) 80 lakh
(B) 50 lakh
(C) 40 lakh
(D) 60 lakh
(E) None of these
Rationale: Let the incomes of two companies A and B be 5x and 8x respectively.
From the question,
5x+25/8x=5/4 ⇒ 20x + 100 = 40x
∴ x = 5
∴ Income of company B = 8x = 40 lakh
Answer C
Answer: (C) 40 lakh
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.
(A) 0 sq m
(B) 2 sq m
(C) 9 sq m
(D) 20 sq m
(E) 5 sq m
Rationale: S = (1 + 2 + 3)/2 = 3
=> No triangle exists
Answer: A
Answer: (A) 0 sq m
Question: P and Q started a business investing Rs. 85,000 and Rs. 30,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 17:6
(B) 17:0
(C) 17:4
(D) 17:2
(E) 17:3
Rationale: P:Q = 85000 : 30000
= 17:6.
Answer: A
Answer: (A) 17:6
Question: A and B are playing mathematical puzzles. A asks B "which whole numbers, greater than one, can divide all the nine three digit numbers 111,222,333,444,555,666, 777,888 and 999?"
B immediately gave the desired answer. It was :-
(A) 3, 37 and 119
(B) 3, 37 and 111
(C) 9, 37 and 111
(D) 3, 9 and 37
(E) None
Rationale: Explanation :
Each of the number can be written as a multiple of 111. And,
The factors of 111 are 3 and 37.
Thus, the desired answer is 3, 37 and 111.
Answer : B
Answer: (B) 3, 37 and 111
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 277 Sec
(B) 190 Sec
(C) 187 Sec
(D) 286 Sec
(E) 215 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Answer: (B) 190 Sec
Question: In how many different ways can the letters of the word ‘ARMOUM’ be arranged?
(A) 200
(B) 210
(C) 230
(D) 250
(E) 360
Rationale: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360
E
Answer: (E) 360
Question: Which digits should come in place of @ and # if the number 62684@# is divisible by both 8 and 5?
(A) 4,0
(B) 0,4
(C) 4,4
(D) 0,0
(E) None
Rationale: Explanation :
Since the given number is divisible by 5, so 0 or 5 must come in place of #.
But, a number ending with 5 is never divisible by 8.
So, 0 will replace #.
Now, the number formed by the last three digits is 4@0, which becomes divisible by 8, if @ is replaced by 4.
Hence, digits in place of @ and # are 4 and 0 respectively.
Answer : A
Answer: (A) 4,0
Question: A train 125 m long passes a man, running at 1 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 65 km/hr
(B) 17 km/hr
(C) 76 km/hr
(D) 50 km/hr
(E) 46 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 1) km/hr.
x - 1 = 45 => x = 46 km/hr.
Answer: E
Answer: (E) 46 km/hr
Question: A work which could be finished in 8 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
(A) 22
(B) 30
(C) 88
(D) 71
(E) 11
Rationale: x ------- 8
(x + 10) ---- 6
x * 8 = (x + 10)6
x = 30
\Answer: B
Answer: (B) 30
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H
(A) 153
(B) 159
(C) 137
(D) 121
(E) 89
Rationale: let the number be x, now x is halved => x/2..the question asks what is x?
x(number) + x/2 (half of that number) = something
=> 3x/2 = something
=> x = 2 (something) / 3
so the answer choice must be divisible by 3
eliminate C, E right away
check the rest
B satisfies
3x/ 2 = 159
=> x = 106
Verify. 106 + 53 = 159
Answer is B
Answer: (B) 159
Question: The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
(A) 9
(B) 2
(C) 7
(D) 8
(E) 1
Rationale: Let the numbers 13a and 13b.
Then, 13a x 13b = 2028
=>ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).
Clearly, there are 2 such pairs.
Answer: B
Answer: (B) 2
Question: Renu can do a piece of work in 8 days, but with the help of her friend Suma , she can do it in 4 days. In what time Suma can do it alone?
(A) 8
(B) 12
(C) 14
(D) 15
(E) 17
Rationale: Renuâ€™s one dayâ€™s work = 1/8
Sumaâ€™s one dayâ€™s work = 1/4 - 1/8 = 1/8
Suma can do it alone in 8 days.
ANSWER:A
Answer: (A) 8
Question: There are 4 people who has to cross a stretch of 300 km. They normally run at a speed of 10 kmph. One
of them has a bike that travels at 50 kmph. The bike first takes one person alone and crosses the
stretch while the other two keep running. Then he comes back without wasting time and picks up
another person from the way, drives him across the stretch, and does the same for the last person. How
long does this whole process take?
(A) 24 hrs
(B) 16 hrs
(C) 56/3 hrs
(D) 58/3 hrs
(E) 18 hrs
Rationale: Expl : Time taken to carry 2nd person = 300/50 = 6 hrs.
Time taken to meet 3rd person =(300-6*10)/(50+10) = 4 hrs
Time taken to carry 3rd person = 4 hours
Time taken to meet 4th person = (300 –140)/60 = 8/3
Total time = 6+4+4+8/3+8/3 = 58/3 hours
Answer :D
Answer: (D) 58/3 hrs
Question: The security gate at a storage facility requires a Six-digit lock code. If the lock code must consist only of digits from 1 through 9, inclusive, with no repeated digits, and the first and last digits of the code must be odd, how many lock codes are possible?
(A) 120
(B) 240
(C) 360
(D) 720
(E) 16800
Rationale: X-X-X-X-X --> there are 5 odd digits from 1 to 9, inclusive thus options for the first and the last X's are: 5-X-X-X-X-4. Other X's can take following values: 5-7-6-5-4-4 -> 5*7*6*5*4*4=16800.
Answer: E.
Answer: (E) 16800
Question: If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?
(A) 5%
(B) 10%
(C) 20%
(D) 30%
(E) 45%
Rationale: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%
B
Answer: (B) 10%
Question: If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour?
(A) 451 times
(B) 638 times
(C) 838 times
(D) 436 times
(E) 435 times
Rationale: There are 60 minutes in an hour.
In ¾ of an hour there are (60 * ¾) minutes = 45 minutes.
In ¾ of an hour there are (60 * 45) seconds = 2700 seconds.
Light flashed for every 6 seconds.
In 2700 seconds 2700/6 = 450 times.
The count start after the first flash, the light will flashes 451 times in ¾ of an hour.
Answer:A
Answer: (A) 451 times
Question: Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $40,000 higher than Store B's revenues. In the second month, Store A's revenues were $6,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $2,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue?
(A)  $14,000
(B)  $40,000
(C)  $42,000
(D)  $46,000
(E)  $50,000
Rationale: Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +40 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +6 in favor of A. The average was +2 in favor of A. With these numbers, use the average formula to find the third month (T):
(40 + 6 + T)/3 = 2
46 + T = 6
T = -40
Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -40 represents a $40,000 advantage in favor of Store B. Choice (B) is correct.
Answer: (B)  $40,000
Question: some digits were given like 0 2 2 3 3 4 4 then how many no will be there which is greater than 1 lac ,all numbers are distinct
(A) 530
(B) 540
(C) 550
(D) 560
(E) 570
Rationale: ( 6*6*5*4*3*2)/(2! *2!*2!)= 540 ways
ANSWER:B
Answer: (B) 540
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) 600
(B) 698
(C) 675
(D) 688
(E) 900
Rationale: 1 year = Rs. (854 - 815) = Rs. 39.
3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698
ANSWER B
Answer: (B) 698
Question: Each of the following equations has at least one solution EXCEPT D. Is it true?
(A) -2*-a = 2a
(B) 2*a = (–2)*-a
(C) -4*a = -3-a
(D) -3*a = -3-a
(E) (–2)-a = –2-a
Rationale: If we put a= 1 then
A. 2
B. 2
C. -4
E. -3
D. -3=-4 Not true
Answer: (D) -3*a = -3-a
Question: 10 people went to a hotel for combine dinner party 5 of them spent Rs. 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10. What was the total money spent by them.
(A) 1628.4
(B) 1534
(C) 1492
(D) 240
(E) None of these
Rationale: Solution: Let average expenditure of 10 people be x.
then,
10x = 20*5+5*(x+4);
Or, 10x = 20*5+5x+20;
Or, x = 24;
So, total money spent = 24*10 = Rs. 240.
Answer: Option D
Answer: (D) 240
Question: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
(A) 30
(B) 34
(C) 36
(D) 37
(E) 39
Rationale: It basically asks for the number of 5s in 150!
150/5 + 150/25 + 150/125 = 30 + 6 + 1. Hence 37
Answer: D.
Answer: (D) 37
Question: Product M is produced by mixing chemical X and chemical Y in the ratio of 5 : 4. Chemical X is prepared by mixing two raw materials, A and B, in the ratio of 1 : 3. Chemical Y is prepared by mixing raw materials, B and C, in the ratio of 2 : 1. Then the final mixture is prepared by mixing 864 units of product M with water. If the concentration of the raw material B in the final mixture is 50%, how much water had been added to product M?
(A) 328 units
(B) 368 units
(C) 392 units
(D) 616 units
(E) None of the above
Rationale: The final product is obtained by mixing 864 units of product M with water.
In 864 units of Product M, amount of B = 864×77/108 = 616
In the final mixture, concentration of B is 50%.
Therefore, the total quantity of final mixture = 616 × 2 = 1232
Water added = 1232 – 864 = 368
The correct answer is Choice B.
Answer: (B) 368 units
Question: In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many Z different victory circles are possible?
(A) 24
(B) 52
(C) 96
(D) 144
(E) 648
Rationale: Possible scenarios are:
1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;
2. Gold/Gold/Silver/No medal - 4!/2!=12;
3. Gold/Silver/Silver/No medal - 4!/2!=12;
4. Gold/Gold/Gold/No medal - 4!/3!=4.
Total Z: 24+12+12+4=52
Answer: B.
Answer: (B) 52
Question: X completes a work in 20 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) 10 days.
(B) 12 days.
(C) 14 days.
(D) 8 days.
(E) 20 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 = 20Ã— 30/ 50 = 12 days.
B)
Answer: (B) 12 days.
Question: A chair is bought for Rs.300/- and sold at Rs.420/- find gain or loss percentage
(A) 15% loss
(B) 40% gain
(C) 25% gain
(D) 30% gain
(E) 35% gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (450- 300)/300= 40% gain
B
Answer: (B) 40% gain
Question: What is the least number to be subtracted from 696 to make it a perfect square?
(A) 1
(B) 16
(C) 20
(D) 71
(E) 60
Rationale: The numbers less than 696 and are squares of certain numbers are 676, 625.
The least number that should be subtracted from 696 to make it perfect square = 696 - 676 = 20.
ANSWER:C
Answer: (C) 20
Question: There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. How many possible selections of 3 books from this shelf include at least one paperback?
(A) a) 40
(B) b) 45
(C) c) 36
(D) d) 55
(E) e) 60
Rationale: approach 1
at-least 1 paper back = total - no paper back
8c3-6c3 = 36
approach 2
at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back
= 2c1*6c2+2c2*6c1 = 36
Answer is C
Answer: (C) c) 36
Question: If a sum of money doubles itself in 20 years at simple interest, the ratepercent per annum is
(A) 12
(B) 12.5
(C) 13
(D) 5
(E) 14
Rationale: Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 20) = 5
Option D
Answer: (D) 5
Question: In a fuel station the service costs $1.15 per car, every liter of fuel costs 0.4$. Assuming that you own 2 sports cars and 2 executive cars and all fuel tanks are empty. How much will it cost to fuel all cars together if a sports car tank is 32 liters and an executive car tank is 75% bigger?
(A) 37.5$
(B) 75$
(C) 87.5$
(D) 94.5$
(E) 98.4$
Rationale: Total cars=4
1.15*4=4.6->Service Cost
Fuel Cost in Sports Car = 2*32*0.4=25.6
Fuel Cost in Executive Car=25.6*7/4=44.8
Total Fuel Cost = 25.6+44.8=70.4
Cost to fuel car = 70.4+4.6=75
Answer: B
Answer: (B) 75$
Question: Choose the missing terms out of the given alternatives.
AZ, BY, CX, DW ?
(A) EF
(B) GH
(C) EV
(D) DW
(E) KN
Rationale: C
EV
The first letter moves one step forward. The second letter moves one step backward.
Answer is C
Answer: (C) EV
Question: Company Z spent 1/4 of its revenues last year on marketing and 1/7 of the remainder on maintenance of its facilities. What fraction of last year’s original revenues did company Z have left after its marketing and maintenance expenditures?
(A) 5/14
(B) 1/2
(C) 17/28
(D) 9/14
(E) 9/11
Rationale: Total revenues = x
Spent on marketing = x/4
Remaining amount = x-x/4 = 3x/4
1/7 of the remainder on maintenance of its facilities = 3x/4*1/7 = 3x/28
Amount left = 3x/4-3x/28 = 9x/14
Answer D
Answer: (D) 9/14
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 42 sec
(C) 45 sec
(D) 48 sec
(E) 58 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
ANSWER:A
Answer: (A) 40 sec
Question: What is the scope including 1/21+1/22+1/23+......+1/30?
(A) 1/6~1/5
(B) 1/5~1/4
(C) 1/4~1/3
(D) 1/3~1/2
(E) 1/2~1
Rationale: For Maximum value : It should be less than 1/21 + 1/21 +1/21... 10 times = 10/21 ~ 1/2
For Minimum Value : It should be greater than 1/30+ 1/30+ 1/30 .. 10 times = 10/30 = 1/3
Thus, the answer should lie between 1/3 and 1/2. Correct ans : D.
Answer: (D) 1/3~1/2
Question: Company A has 13 employees, 9 of whom belong to the union. If 5 people work any one shift, and the union contract specifies that at least 4 union members work each shift, then how many different combinations of employees might work any given shift?
(A) 56
(B) 231
(C) 336
(D) 350
(E) 756
Rationale: Looks easy: -- 9C4*5C1 + 9C5= 756 (E).
Answer: (E) 756
Question: A bag contains 5 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?
(A) 1/7
(B) 2/9
(C) 3/11
(D) 4/17
(E) 2/3
Rationale: Total number of balls = 5+2 = 7
n(S) = 7C3 = 7*6*5 / 3*2 = 35
n(E) = 2C2* 5C1 = 5
Probability = 5/35 = 1/7
Answer is A
Answer: (A) 1/7
Question: A woman complete a journey in 20 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
(A) 334 km.
(B) 216 km.
(C) 314 km.
(D) 448 km.
(E) 544 km.
Rationale: 0.5x/21 + 0.5x/24 = 20
--> x/21 + x/24 = 40
--> x =448 km.
D
Answer: (D) 448 km.
Question: The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people?
(A) 179 cm and 172 cm
(B) 181 cm and 169 cm
(C) 173 cm and 178 cm
(D) 176 cm and 176 cm
(E) 174 cm and 177 cm
Rationale: Denote X as the sum of the heights of the two new people. From the stem it follows that (700+X)6>175. This reduces to X>350. Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm.
Answer: B
Answer: (B) 181 cm and 169 cm
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
(A) 70
(B) 55
(C) 60
(D) 65
(E) 80
Rationale: A+B=60 A=2B
2B+B=60===>B=20
A=40
5 yrs ages 45 and 25
Sum of their ages = 70
ANSWER A
Answer: (A) 70
Question: Find the number which when multiplied by 15 is increased by 196.
(A) 14
(B) 20
(C) 26
(D) 28
(E) 30
Rationale: Let the number be x. Then, 15x - x = 196
<=> 14x = 196 <=> x = 14.
Answer :A
Answer: (A) 14
Question: A number X equals 80% of the average of 5, 7, 14 and a number Y. If the average of X and Y is 26, the value of Y is?
(A) 13
(B) 26
(C) 39
(D) 36
(E) None of these
Rationale: Average of 5, 7, 14 and Y = ( 5 + 7 + 14 + Y )/ 4
Therefore, X = 80% of ( 5 + 7 + 14 + y )/ 4
= (80/100) x (26 + Y)/4
=> X = (26 + Y)/5
5X - Y = 26----- (i)
Also, (X + Y)/2 = 26 ----- (ii)
From (i)and (ii)
X = 13
Y = 39.
ANSWER:C
Answer: (C) 39
Question: A man covers a distance on scooter. Had he moved 3kmph faster he would have taken 40 min less. If he had moved 2kmph slower, he would have taken 40min more. The distance is.
(A) 30 km
(B) 40 km
(C) 45 km
(D) 50 km
(E) 55 km
Rationale: Let distance = x m
Usual rate = y kmph
x/y – x/y+3 = 40/60 hr
2y(y+3) = 9x ---------------------------------(1)
x/y-2 – x/y = 40/60 hr y(y-2) = 3x -----------(2)
divide 1 & 2 equations
by solving we get x = 40 km
Answer : B
Answer: (B) 40 km