divelab/Sys2Bench huggingface dataset:
Question: $4,000 is deposited in a savings account that pays 8% annual interest compounded semiannually. To the nearest dollar, how much is in the account at the end of the year?
Options:
A)$4326.40
B)$4116.20
C)$4256.21
D)$4316.54
E)$4312.45
Rationale: this is the case of semi-annual compoundingso, multiply time period by 2 and divide rate by 2
So,
new time=2periods and new rate=8/2=4%
Now,
CA=4000(1+4/100)^2=$4326.40
Hence answer is A
Answer: A
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1100 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
Options:
A)14000
B)12000
C)12019
D)12197
E)12012
Rationale: [1100 + (X-4000) * (2.5/100)] - X * (5/100)
= 600
X = 14000
Answer: A
Answer: A
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
Options:
A)17:12
B)12:17
C)21:32
D)32:21
E)17:32
Rationale: Here capital is not the same.
Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio
=(20000×6+15000×6)
Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio
=(30000×4+50000×4)
Suresh : Kiran
=(20000×6+15000×6) :(30000×4+50000×4)
=(20×6+15×6):(30×4+50×4)=(20×3+15×3):(30×2:50×2)
=105:160=21:32
Answer is C.
Answer: C
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
Options:
A)1000
B)2991
C)8216
D)2991
E)2881
Rationale: 2 * 22/7 * 1.75 * x
= 11000
x = 1000
Answer: A
Answer: A
Question: Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/3 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?
Options:
A)1/2
B)2/3
C)3/4
D)4/5
E)5/6
Rationale: Because we see H willbring 1/3 of his booksto the new home --> try to pick a number that isdivisible by 3.
Before:
Assume H = 30 books
H = 1/2 M --> M = 60 books
After:
H' = 1/3H = 10 books
M' = 1/3M = 20 books
Total = 30 books
M' = 30 = 1/2*60
Ratio: 1/2
Ans: A
Answer: A
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options:
A)11
B)12
C)13
D)15
E)14
Rationale: First codition=total hours to complete the work=39 persons * 12 days * 5 hr
Second codition=total hours to complete the work=30 persons * x days * 6 hr
since the work is still the same so
39*12*5=30*x*6
x=13
answer :C
Answer: C
Question: Find the area of a cuboid of length 15cm , breadth 10 cm . and height 16cm.
Options:
A)2400 cm cube
B)2410 cm cube
C)2420 cm cube
D)2430 cm cube
E)2480 cm cube
Rationale: Area of a cuboid = lxbxh =15cm x 10cm x 16cm = 2400 cm cube
answer :A
Answer: A
Question: By purchasing an article at 20 % discount on the original price and then selling it at a price of 25% above the original price, a trader earns Rs. 200 as the profit. What was the original price of the article?
Options:
A)444.44
B)444.409
C)444.42
D)444.429
E)444.428
Rationale: Explanation:
Let the original price of the article be Rs. 100. Hence the purchase price for the trader would be Rs. 80 and his selling price would be Rs. 125. Thus, he would earn a profit of Rs. 45 (125 – 80). Therefore,
Profit is Rs. 45 if the original price is Rs. 100
Hence, if profit is Rs. 200, then original price will be..
= 100x 200/45
= Rs. 444.44
ANSWER: A
Answer: A
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 15% per annum then the gain of B in a period of 3 years is?
Options:
A)525
B)500
C)510
D)530
E)550
Rationale: (3500*5*3)/100 => 525
Answer: A
Answer: A
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
Options:
A)87 km/hr
B)88 km/hr
C)87.5 km/hr
D)67 km/hr
E)77 km/hr
Rationale: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x =(400/4)= 100
x =100/8= 12.5
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
ANSWER C
Answer: C
Question: If d and t are integers and d^2 – t^2 is an odd integer, which of the following must be an even integer?
I. d + t + 2
II. d^2 + 2dt + t^2
III. d^2 + t^2
Options:
A)None
B)I only
C)II only
D)III only
E)I, II, and III
Rationale: d^2–t^2 is an odd integer means that either d is even and t is odd or d is odd and t is even.
Check all options:
I. d + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;
II. d^2 + 2dt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;
III. d^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.
Answer: A.
Answer: A
Question: The difference between a two-digit number and the number after interchanging the position of the two digits is 72. What is the difference between the two digits of the number?
Options:
A)4
B)6
C)3
D)Cannot be determined
E)None of these
Rationale: Let the two-digit no. be l0x + y.
Then, (10x + y) â€“ (10y + x) = 72
or, 9(x â€“ y) = 72
Answer E
Answer: E
Question: There are three different hoses used to fill a pool: hose U, hose y, and hose z. Hose U can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3
Options:
A)I
B)II
C)III
D)II &III
E)I &II
Rationale: Name T = full pool
U fills a pool in a days ==> 1 day U fills: T/a
Y fills a pool in b days ==> 1 day Y fills: T/b
Z fills a pool in c days ==> 1 day Z fills: T/c
1 day (U+Y+Z) together fill: T(1/a + 1/b + 1/c)
d days (U+Y+Z) together fill: T
==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)
==>d = abc/(ab+bc+ca)
d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3
B
Answer: B
Question: Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read?
Options:
A)251 pages
B)151 pages
C)751 pages
D)451 pages
E)351 pages
Rationale: Pages read in the first book in one week which is 7 days with 25 pages everyday.
25 ? 7 = 175 pages
Pages read in the second book in 12 days with 23 pages everyday.
23 ? 12 = 276 pages
Total number of pages read
175 + 276 = 451 pages
correct answer D
Answer: D
Question: If 2 men can color 50 m long cloth in 2 days, then 4 men can color 100 m long cloth in?
Options:
A)3 days
B)4 days
C)5 days
D)2 days
E)6 days
Rationale: The length of cloth painted by one man in one day = 50/ 2× 2 = 12.5 m
No. of days required to paint 100 m cloth by 4 men = 100/ 4 × 12.5 = 2 days
Answer : D
Answer: D
Question: Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 28 laps around the track per hour and Nick completes 13 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick?
Options:
A)5
B)8
C)12
D)16
E)20
Rationale: Maria's rate - 28 laps per hour --> 28/60 laps/min
Nick's rate - 13 laps per hour --> 13/60 laps/min
lets set equations:
28/60*t=4 (since Maria had to run 4 laps before Nick would start)
13/60*t=0 (Hick has just started and hasn't run any lap yet)
(28/60-13/60)*t=4-0 (since Nick was chasing Maria)
t=16 min needed Maria to run 4 laps
Answer : D
Answer: D
Question: By selling 32 carrots in a dollar, a man loses 40%. How many carrots must he sell in a dollar to gain 20% profit?
Options:
A)16
B)18
C)20
D)25
E)28
Rationale: This is a question that is much easier than it first appears. If you work with the percents directly, you can solve it very quickly. If the man sells 32 carrots for a dollar, he loses 40%. That means he is at 60% of his cost (100% - 40% = 60%). We are trying to figure out how many carrots he has to sell in order to make a 20% profit, or be at 120% (100% + 20% = 120%). 120% is double 60%, meaning that we simply cut the number of carrots in half to double our returns (from 60% to 120%), yielding 32/2 = 16 carrots, or answer choice A.
Answer: A
Question: A farmer spent $38 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
Options:
A)$37.80
B)$38.50
C)$39.20
D)$39.50
E)$41.80
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$38=$15.2 on chicken feed, thus he spent the remaining 38-15.2=$22.8 on goat feed.
Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$15.2 --> x=$19.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 19+22.8=$41.8.
Answer: E.
Answer: E
Question: A train 260 m long passed a pole in 40 sec. How long will it take to pass a platform 940 m long?
Options:
A)180
B)184
C)178
D)167
E)156
Rationale: Speed = 260/40= 6.5 m/sec.
Required time = (260 + 940)/6.5 = 184 sec.
Answer: Option B
Answer: B
Question: The ratio of the two natural numbers is 6 : 5. If a certain number is subtracted to both the numbers, the ratio becomes 5 : 4. If the larger number exceeds the smaller number by 5, find the number subtracted?
Options:
A)8
B)5
C)15
D)22
E)6
Rationale: Let the two numbers be 6x and 5x.
Let the numbers subtracted to both so that their ratio becomes 5 : 4 be k.
(6x - k) / (5x - k) = 5/4
=> 24x - 4k = 25x - 5k => k = x.
6x - 5x = 5 => x = 5
k = x = 5.
Answer:B
Answer: B
Question: On a playground, there is a number of children, out of which 1/4 wear red t-shirts, 1/20 wear blue t-shirts, and the remaining 14 children wear white t-shirts. How many children wear blue t-shirts?
Options:
A)6
B)20
C)1
D)3
E)5
Rationale: Let x be the number of children on the playground.
x/4+x/20=6x/20=3x/10 is the number of children who wear red and blue t-shirts
The number of the children who wear white t-shirts is x-3x/10=7x/10. Thus,
7x/10=14 implies x=20.
1/20*20=1. Hence, only 1 child wears a white t-shirt.
Answer C 1
Answer: C
Question: At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using five colors?
Options:
A)21
B)35
C)105
D)135
E)10
Rationale: The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.
As an example, a chemical with the colors A/B/C means that the following combinations CANNOT be used by any other chemical:
ABC
ACB
BAC
BCA
CAB
CBA
By extension, the first part of your calculation would be the number of possible substances that could be identified with 5 colors: 5c3 = 10 possible substances
E
Answer: E
Question: The number of cars present at a particular time was measured at 3,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday?
Options:
A)1,159
B)1,333
C)1,817
D)2,460
E)2,829
Rationale: The question states that all these 3,999 locations were measured twice, once on each day.
It also breaks the 3,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W.
Therefore, we can write two equations:
For each of the first and second day count of locations, T + W = 3999
But, for the second day count, W = 1.20 T
i.e. for Second day count, T + 1.20T = 3999
i.e. 2.20 T = 3999
i.e. T = 1817
C
Answer: C
Question: The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 6. What is the value of y in terms of x ?
Options:
A)x/6 - 6
B)x/6 - 5
C)x/7 - 5
D)x/5 - 7
E)x/5 - 6
Rationale: (A1 + A2 + .. + Ay)/y = x
(A1 + A2 + .. + Ay + 30)/(y+1) = x - 6
=> (xy + 30)/(y+1) = x - 6
=> xy + 30 = yx -6y + x - 6
=> 36 = x - 6y
=> 6y = x - 36
=> y = x/6 - 6
Answer - A
Answer: A
Question: 1: 3 = 1 2/3: x. The value of x is?
Options:
A)1
B)3
C)4 1/6
D)5
E)6
Rationale: Explanation:
x * 1 = 3 * 5/3
x = 5
ANSWER IS D
Answer: D
Question: Two trains are traveling in the same direction at speeds of 50 kmph and 20 kmph respectively If the faster train passes the driver in the slower train in 20 seconds, What is the length of the faster train?
Options:
A)ANSWER: 169 m
B)ANSWER: 162 m
C)ANSWER: 136 m
D)ANSWER: 166 m
E)ANSWER: 366 m
Rationale: Explanation:
Given :
Speed of fast train = 50 kmph.
Speed of slow train = 20 kmph.
The driver in the slower train is moving with the speed of the slower train which is 20 kmph.
The faster train will pass the driver when it has gained a distance. Distance gained by faster train
in 1 hour = (50 – 20) = 30 km
= 8.33 m/sec
Distance gained by faster train in 20 sec = 20 * 8.33 = 166.6 m.
Therefore, Length of faster train = 166.6 m.
ANSWER:D
Answer: D
Question: For a particular American football game, the probability of a team's quarterback throwing an intercepted pass on each throw is 1/10. What is the least number of times that the quarterback will throw the ball that will increase the probability of throwing an intercepted pass at least once to more than 50%.
Options:
A)10
B)3
C)9
D)7
E)5
Rationale: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
Probability quarterback throws an intercepted pass at least once in 2 throws is 1- (9/10)^2 = 1 - 81/100 = 11/100 < 50%
Probability quarterback throws an intercepted pass at least once in 3 throws is 1- (9/10)^3 = 1 - 729/1,000 = 271/1,000 < 50%
Probability quarterback throws an intercepted pass at least once in 4 throws is 1- (9/10)^4 = 1 - 6,561/10,000 = 4,439/10,000 < 50%
Probability quarterback throws an intercepted pass at least once in 5 throws is 1- (9/10)^5 = 40,951/100,000 < 50%
Probability quarterback throws an intercepted pass at least once in 5 throws is 1- (9/10)^6 = 468,559/1,000,000 < 50%
Probability quarterback throws an intercepted pass at least once in 5 throws is 1- (9/10)^7 = 5,217,031/10,000,000 > 50%
Answer: D
Answer: D
Question: An investor purchased 100 shares of stock X at 8 1/8 dollars per share and sold them all a year later at 32 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?
Options:
A)92%
B)240%
C)380%
D)300%
E)290%
Rationale: If the purchase price was 8$ per share then the investor would have made a profit of 300%.
Since the purchase price is slightly more than 8$ the profit would be slightly less than 300%.
Also a 2% brokerage is negligible and it brings down the profit percentage only by a small value. Approximation is very useful to solve these kind of problems as the answer choices are far apart.
Answer: E
Answer: E
Question: A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the invest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest?
Options:
A)28
B)65
C)89
D)12
E)14
Rationale: If the interest earned is 25% more than the earlier interest then the rate of interest also should be 25% higher than the earlier rate.
Let the earlier rate of interest be x%.
Now it will be (x + 3)%
% increase = (x + 3) - x/x * 100 = 25
=> x = 12.Answer: D
Answer: D
Question: In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 14 feet between each tree. How many trees can be planted if the road is 151 feet long?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Let T be the number of trees. Then the length required for trees on the sidewalk will be 1*T= T
To maximize the number of trees, the number of 14 feet spaces between trees should be 1 less than total number of trees.
For example, If there are 3 trees, then there should be 2 spaces between them.
So the number of 14 feet spaces will be T-1. Then, the length of sidewalk required for 14 feet spaces will be 14*(T-1)
It is given that total lenght of sidewalk is 166 feet.
or 14(T-1)+T = 151
or 14T-14+T = 151
or 15T = 165
or T=11
Answer:- D
Answer: D
Question: Month	Average Price
per Dozen
April $1.0
May $1.20
June $1.5
The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
Options:
A)1.1
B)1.29
C)1.32
D)1.42
E)1.5
Rationale: Say x dozen eggs were sold in May.
Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.
Total x+2x/3+4x/3=3x dozen eggs were sold in three months.
Total sales: 2x/3*1.+x*1.2+4x/3*1.5= $3.86x. The average price per dozen 3.86x/3x=$1.29.
B
Answer: B
Question: Walking at 5/6th of its usual speed a cab is 12mnts late. Find its usual time to cover the journey?
Options:
A)25m
B)45m
C)32m
D)50m
E)60m
Rationale: New speed = 5/6th of usual speed
New time = 6/5th of usual time
6/5 UT - UT = 12m
UT/5 = 12m
UT = 60m
Answer is E
Answer: E
Question: What is the area of a right angle triangle with base = 12 and height = 14 ?
Options:
A)80
B)81
C)82
D)83
E)84
Rationale: Since the area of a right angle triangle is 1/2 * base * height
Area = 1/2 * 12 * 14
= 84
Ans: E
Answer: E
Question: Of the three-digit integers greater than 600, how many have distinct digits ?
Options:
A) 90
B) 82
C) 80
D) 45
E)288
Rationale: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.
We need to calculate B. B=Total - A - C
Total numbers from 600 to 999 = 299 (3-digit numbers greater than 600);
A. all digits are distinct = 4*9*8=288
Answer: E
Answer: E
Question: a/(b/c)
In the expression above, a, b, and c are different numbers and each is one of the numbers 2, 3, or 6. What is the largest possible value of the expression?
Options:
A)2/18
B)6/3
C)30/2
D)18/2
E)6/18
Rationale: a/(b/c)
= (a*c)/b
The expression will have the largest value when numerator (a*c) is the largest.
=(6*3)/2
=18/2
Answer D
Answer: D
Question: A certain quantity of 45% concentration solution is replaced with 15% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
Options:
A)1:3
B)1:2
C)2:3
D)2:1
E)3:1
Rationale: 15% - - - - - - - - - 35% - - - - - - 45%
From 15 to 35 =20
From 35 to 45 = 10
So the ratio is 20/10 = 2 to 1
B it is
Answer: B
Question: How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?
Options:
A)5
B)7
C)4
D)8
E)6
Rationale: Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 x 4 = 20)
so there will be 6 significant digits to the right of the decimal point.
Answer is E.
Answer: E
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 8:3. The sum of numbers is:
Options:
A)22
B)30
C)40
D)50
E)60
Rationale: Let the numbers be 8x and 3x.
Then, their L.C.M = 24x. So, 24x = 48 or x = 2.
The numbers are 16 and 6.
Hence, required sum = (16 + 6) = 22.
ANSWER:A
Answer: A
Question: Triangle STV has sides ST = TV = 25, and SV = 14. What is the area?
Options:
A)144
B)168
C)176
D)190
E)206
Rationale: Let the base B of the triangle be SV = 14. Then we need to find the height H.
H^2 = 25^2 - 7^2 = 576 and then H = 24.
The area is (1/2)*B*H = 7*24 = 168
The answer is B.
Answer: B
Question: Christine selects an item at a 25% off ticket price sale. The item is ticket priced at $25. How much should Christine expect to pay at the register?
Options:
A)22.5
B)20.0
C)18.75
D)12.5
E)10.0
Rationale: R.P.=$25.00
Sale%=25
S.P.=R.P.*(1-(Sale%/100))=25*(1-(25/100))=18.75
ANSWER:C
Answer: C
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
Options:
A)529 sq m
B)240 sq m
C)260 sq m
D)480 sq m
E)580 sq m
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480
ANSWER:D
Answer: D
Question: A person has to cover a distance of 10km in 1hour. If he covers one half of the distance in half of the total time; to cover the remaining distance in the remaining time, his speed must be?
Options:
A)5km/hr
B)8km/hr
C)10km/hr
D)12km/hr
E)15km/hr
Rationale: Remaining distance = 5km
Remaining time = 1/2 * 60 = 30min = 1/2 hour
Required speed = 5*2 = 10km/hr
Answer is C
Answer: C
Question: If integer k is equal to the sum of all even multiples of 25 between 295 and 615, what is the greatest prime factor of k?
Options:
A)5
B)7
C)11
D)13
E)17
Rationale: if we break down what the stem is asking what is the sum of all mult of 50 between 300 and 600.
using arithmetic progression to find n : 600 = 300 + (n - 1) 50
300+ 50 = 50n
350 = 50n => n = 7
the sum would be: 11* mean
mean = [600 + 300] / 2 = 450
7*450 = 4950
B
Answer: B
Question: A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.
Options:
A)4360
B)4460
C)4560
D)4660
E)4760
Rationale: Let the sum be Rs.P.then
P(1+R/100)3=6690 …(i) P(1+R/100)6=10035…(ii)
On dividing,we get (1+R/100)3=10025/6690=3/2.
Substituting this value in (i),we get:
P*(3/2)=6690 or P=(6690*2/3)=4460
Hence,the sum is Rs.4460. answer : B
Answer: B
Question: In the Land of Oz only one or two-letter words are used. The local language has 69 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?
Options:
A)65
B)66
C)67
D)131
E)138
Rationale: The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...
The number of 1 letter words (X) that can be made from 69 letters is 69;
The number of 2 letter words (XX) that can be made from 69 letters is 69*69, since each X can take 69 values.
Total: 69+69*69.
Similarly:
The number of 1 letter words (X) that can be made from 68 letters is 68;
The number of 2 letter words (XX) that can be made from 68 letters is 68*68, since each X can take 68 values.
Total: 68+68*68.
The difference is (69+69*69)-(68+68*68)=138.
Answer: E.
Answer: E
Question: Two pipes A and B can fill a tank in 30 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Options:
A)18 hours
B)15 hours
C)10 hours
D)12 hours
E)8 hours
Rationale: Part filled by A in 1 hour = 1/30
Part filled by B in 1 hour = 1/45
Part filled by (A+B) in 1 hour = 1/30 + 1/45 = 5/90 = 1/18
Both the pipes together fill the tank in 18 hours
Answer is A
Answer: A
Question: There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?
Options:
A)r / (r + b + w)
B)(r + b + w)
C)r * (r + b + w)
D)(r + b + w)/r
E)None
Rationale: The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
A
Answer: A