divelab/Sys2Bench huggingface dataset:
Question: On a certain Monday, john drove to work at an average speed of 50 miles per hour and home from work along exactly the same route at an average speed of 70 miles per hour. Which of the following is closest to his average speed for both trips combined?
Options:
A)54
B)55
C)58.33
D)56
E)57
Rationale: To solve the average speed questions, we need to know the total distance and the total time.
Let us assume that the distance from work = D
This will also be the distance from work to home
Hence total distance travelled = 2D
Time in going to work = D/50,
Time in coming back from work = D/70
Hence average speed of both the trips = 2D/ (D/50 + D/70)
= 2*350/12 = 58.33
C
Answer: C
Question: By selling a watch for Rs.640/-, a man loses 20% what is that watch cost price
Options:
A)Rs. 700/-
B)Rs. 800/-
C)Rs. 900/-
D)Rs. 1000/-
E)Rs. 1100/-
Rationale: 80 % ------> 640 (80 * 8 = 640)
100 % ------>800 (100 * 8 = 800)
Cost price = Rs. 800/-
B
Answer: B
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
Options:
A)1/2
B)1/3
C)1/5
D)1/7
E)None
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
B)
Answer: B
Question: X, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 4. What is the value of Z?
Options:
A)6
B)5
C)4
D)3
E)2
Rationale: If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.
X + 3Y + 3Z = 5Y + 4
Z+2+3Z+3+3Z = 5Z+5+4
2Z = 4
Z = 2
The answer is E.
Answer: E
Question: a, b, c and d are four consecutive numbers. If the sum of a and dis 113, what is the product of b and c?
Options:
A)2652
B)2578
C)2534
D)3192
E)4234
Rationale: Here d = a + 3
a + a + 3 = 113
2a = 110
a = 55
So, numbers are 55, 56, 57 and 58
∴ b × c= 56 × 57 = 3192
D
Answer: D
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 750 resolutions?
Options:
A)277 m
B)704 m
C)278 m
D)288 m
E)1056 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 750 resolutions.
= 750 * 2 * 22/7 * 22.4 = 105600 cm
= 1056 m
Answer: E
Answer: E
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 50 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?
Options:
A)40
B)45
C)50
D)54
E)60
Rationale: A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 50 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
50 = 180/4t
t = 54
B-C = 54mph
Answer D
Answer: D
Question: A single discount equivalent to a series of 30%, 20%, and 10% is
Options:
A)50%
B)49.6%
C)49.4%
D)51%
E)52%
Rationale: Let the marked price be Rs. 100
Then S.P = 90% of 80% of 70% of 100
= ( 90/100*80/100*70/100*100 ) =50.4
Single discount = ( 100- 50.4 )% = 49.6%
ANSWER:B
Answer: B
Question: Cost of 16 mirror and 8 comb is Rs.344 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?
Options:
A)19
B)12
C)20
D)21
E)22
Rationale: Let the cost of each pen and pencil be 'p' and 'q' respectively.
16m + 8c = 344 --- (1)
4m + 4c = 96
8m + 8c = 192 --- (2)
(1) - (2) => 8p = 152
=> m = 19
A
Answer: A
Question: How many ways can 9 friends be arranged around a circular dinner table?
Options:
A)5!
B)6!
C)7!
D)8!
E)9!
Rationale: The number of ways to order 9 people is 9!
However, around a circular table, each pattern would be repeated 9 times.
So the number of ways to seat 9 friends around a circular table is 8!
The answer is D.
Answer: D
Question: Angelina walked 250 meters from her home to the grocery at a constant speed. She then walked 360 meters to the gym at double the speed. She spent 70 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
Options:
A)2
B)3
C)4
D)6
E)12
Rationale: let the speed be X...
so time taken from home to grocery= 250/x..
the speed to gym = 2x..
so time taken = 360/2x=180/x..
its given 250/x-180/x=70..
70/x=70..
x=1m/secs..
so grocery to gym=2*1=2m/s...
Answer : A
Answer: A
Question: In a group of 7 boys and 8 girls , 5 members are to be selected. In how many different ways can they be selected such that at least 3 boys should be there ?
Options:
A)1200
B)1500
C)1281
D)1339
E)1296
Rationale: No of boys = 7
No of girls = 8
Therefore,
No of ways at least 3 boy can be selected = 7C5 * 8C0 + 7C4* 8C1 + 7C3*8C2
= 1281
Ans - C
Answer: C
Question: If the product of two positive integers is 40, which of the following could be the LCM and HCF of the two numbers? a. LCM 20 : HCF 2 b. LCM 40 : HCF 5 c. LCM 20 : HCF 4
Options:
A)b only
B)c only
C)a only
D)a, c only
E)a, b only
Rationale: a is the correct answer.
Answer : C
Answer: C
Question: A metal bar weighs 8.15 ounces. 93% of the bar is silver. How many ounces of silver are in the bar? (round to the nearest thousandth)
Options:
A)5.580 ounces
B)7.580 ounces
C)8.560 ounces
D)4.480 ounces
E)9.880 ounces
Rationale: 93/100=x/8.15
Multiply the opposites:
93 x 8.15 = 757.95
Divide by the remaining number:
100)7.5795/757.9500
7.580 ounces
correct answer B
Answer: B
Question: Tom travels first 5 kilometers in 80km/hr and another 5 kilometers in 20km/hr. What is his average speed?
Options:
A)32km/hr
B)42km/hr
C)40km/hr
D)30km/hr
E)36km/hr
Rationale: Since the distance traveled is same, we can apply direct formula= 2XS1XS2/(S1+S2)
2X80X20/100= 32. 'A' is the answer.
Answer: A
Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $94 per day. What was his wage on the 8th day?
Options:
A)$83
B)$90
C)$92
D)$97
E)$104
Rationale: Average daily wage of a worker for 15 consecutive working days = 90$
During the first 7 days , the daily average daily wage = 87$
During the last 7 days , the daily average daily wage = 94$
Wage on 8th day = 90*15 -( 87*7 + 94 *7)
= 1350 - (609 + 658)
=1350 - 1267
= 83
Answer A
Answer: A
Question: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 13th, 13th, and 15th terms in the sequence?
Options:
A)2^18
B)3(2^17)
C)7(2^16)
D)3(2^16)
E)7(2^12)
Rationale: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
so 13th term will be 2^12
14th term 2^13
15th term 2^14
adding all three
we get
2^12+(2^12)*2+(2^12)*4
so answer is 2^15(1+2+4)=>7(2^12)
answer E
Answer: E
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
Options:
A)20%
B)90%
C)80%
D)10%
E)50%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer:A
Answer: A
Question: A man can row a boat at 21 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 70 km downstream?
Options:
A)11/9
B)5/7
C)3/2
D)5/3
E)5/2
Rationale: Speed downstream = 21 + 7 = 28 kmph.
Time required to cover 60 km downstream = d/s = 70/28
= 5/2 hours.
Answer: E
Answer: E
Question: 10% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
Options:
A)25
B)30
C)50
D)55
E)60
Rationale: I came up with (A) 25
Think of 100 people total:
From the first fact, 10 of these are women with fair hair.
From the second fact, these 10 women make up 40% of the total fair haired population.
We can then make a ratio of 60:40 fair haired men to fair haired women.
This means that (60/40)*10 equals the number of fair haired men, which is 15 men with fair hair.
Add this 15 to the 10 women and get 25 fair haired men and women out of 100 total men and women.
25%
A
Answer: A
Question: up to 20,how many no. are odd and prime both?
Options:
A)9
B)5
C)6
D)7
E)8
Rationale: we have to calculate it manually.
odd 1,3,5,7,9,11,13,15,17,19
prime 2,3,5,7,11,13,17,19
common 3,5,7,11,13,17,19
total no. 7
answer D
Answer: D
Question: Selling an kite for Rs. 30, a shop keeper gains 30%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
Options:
A)8%
B)10%
C)11%
D)17%
E)20%
Rationale: Explanation:
Marked price = Rs. 30
C.P. = 100/130 * 30 = Rs. 23.07
Sale price = 90% of Rs. 30 = Rs. 27
Required gain % = 3.92/23.07 * 100 = 17%.
Answer: D
Answer: D
Question: The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 6. What is the radius of circle O?
Options:
A)–2/pi
B)2
C)3
D)4
E)5
Rationale: pi*r^2 + 2r -2*pi*r =6
Simplifying the equation: pi*r(r-2)+2r=6
Without much algebraic: We can Test the answers quickly, then 3 is the only possible answer that will eliminate pi from equation.
Answer is C
Answer: C
Question: Machine X can complete a job in half the time it takes Machine Y to complete the same job, and Machine Z takes 50% longer than Machine X to complete the job. If all three machines always work at their respective, constant rates, what is the ratio L of the amount of time it will take Machines X and Z to complete the job to the ratio of the amount of time it will take Machines Y and Z to complete the job?
Options:
A)5 to 1
B)10 to 7
C)1 to 5
D)7 to 10
E)9 to 10
Rationale: Solutioning this exercise can be facilitated by using a R T W (rate time work) table:
We translate the exercise into the table:
R T W
X t/2 1
Y t 1
Z (t/2*3/2 =3t/4) 1
From this table we find the rates
Rx = 2/t
Ry = 1/t
Rz = 4/3t
The Q is what is the ratio of (Tx + Ty) / (Ty + Tz)
Rx + Ry = 2/t + 4/3t = 6/3t+4/3t = 10/3t
Ry+Rz = 1/t + 4/3t = 3/3t + 4/3t = 7/3t
The (10/3t)/(7/3t) = 10/7 then the work ratios is 10 to 7
Since Time Ratio L is the inverse of work, the the answer is 7 to 10
CORRECT ANSWER D
Answer: D
Question: The digit in unit's place of the product 81 ×82×.....×89 is
Options:
A)0
B)2
C)6
D)8
E)4
Rationale: Solution
Required digit	= Unit digit
=(1×2×3×4×5×6×7×8×9)	=0.
Answer A
Answer: A
Question: There are 5 red shoes, 4 green shoes. If one drasw randomly a shoe what is the probability of
getting redshoe
Options:
A)1/9
B)2/9
C)3/9
D)4/9
E)5/9
Rationale: total shoes=9
probability of getting only red shoe=5/9
ANSWER:E
Answer: E
Question: There are 17 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Options:
A)288
B)267
C)261
D)211
E)342
Rationale: The total number of stations = 19
From 19 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 19P₂ ways.
19P₂ = 19* 18 = 342.
Answer: E
Answer: E
Question: A man sells two articles for Rs.2250 each and he gains 24% on the first and loses 45% on the next. Find his total gain or loss?
Options:
A)9%loss
B)2%loss
C)7%loss
D)8%loss
E)11%loss
Rationale: Explanation:
(24*45)/100
= 11%loss
Answer:E
Answer: E
Question: If each data point in a certain set Q is increased by a factor of 20, what happens with the set's standard deviation?
Options:
A)Doesn't Change
B)Decreases by Factor 20
C)Can't be determined
D)Increases by 20
E)Increases by Factor 20
Rationale: Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 20, the standard deviation will increase proportionately, giving us answer choice E
Answer: E
Question: In the xy plane line m has the equation 4x + y = q. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
Options:
A)-4/3
B)1/4
C)-4
D)3/4
E)4/3
Rationale: The equation of line m is y=-4x+q. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A.
Answer: A
Question: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Options:
A)360
B)480
C)720
D)5040
E)None of these
Rationale: Explanation:
The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
ANSWER IS C
Answer: C
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 4 ounces of corn syrup, how many ounces of water does it contain?
Options:
A)15
B)30
C)45
D)60
E)90
Rationale: Standard:
Fl: Corn S: Water = 1:12:30
Sport:
Fl: Corn S: Water = 3:12:180
This simplifies to 1:4:60
If the large bottle has a capacity of x ounces, then
4x / 65 = 4.
So, x = 65 ounces.
Water = (60 / 65) * (65) = 60 ounces.
Ans D
Answer: D
Question: Find the number of digits that are to be used in numbering a book of 400 pages.
Options:
A)1094
B)1093
C)1092
D)1099
E)None of above
Rationale: Explanation:
One digit numbers from 1 to 9 = 9
Two digit numbers from 10 to 99 = 90
Three digit numbers from 100 to 400 = 301
.:Total numbers of digits that are to be used
=(9 x 1) + (90 x 2) + (301 x 3) = (9 + 180 + 903) = 1092
Answer: Option C
Answer: C
Question: An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 3/2M + 10, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold?
Options:
A)a.	A - 10
B)b.	B - 15
C)c.	C – 22.5
D)d.	D – 20
E)e.	E – 67.5
Rationale: A --- 30/2 + 10 = 25 --- wrong
B --- 45/2 + 10 = not an integer --- wrong
C --- 22.5(3/2) + 10 = not an integer --- wrong
D --- 60/2+10 = 40 --- CORRECT
This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method.
D
Answer: D
Question: The cost of an article (which is composed of raw materials and wages) was 3 times the value of raw materials used. The cost of raw materials increased in the ratio 3 : 7 and wages increased in the ratio 4 : 9. Find the present cost of the article if its original cost was Rs. 18.
Options:
A)Rs. 41
B)Rs. 30
C)Rs. 40
D)Rs. 46
E)Rs. 56
Rationale: Assume the raw materials’ cost as Rs.150, then the total cost will be Rs. 450, (Thus, wages cost is Rs. 300)
Since, the cost of raw materials goes up in the ratio of 3 : 7, the new raw material cost would become Rs. 350
The new wages cost would be in the ratio 4 : 9 as Rs. 675.
The new total cost would become, Rs. 1025.
Since Rs 450 become Rs. 1025 (change in total cost),
Unitary method calculation would give us that Rs. 18 would become Rs. 41.
ANSWER:A
Answer: A
Question: If YWVSQ is 25 - 21 - 21 - 19 - 17, Then MKIGS
Options:
A)13 - 11 - 9 - 7 - 9
B)13 - 11 - 6 - 7 - 6
C)13 - 11 - 9 - 7 - 7
D)13 - 11 - 9 - 7 - 3
E)13 - 11 - 9 - 7 - 1
Rationale: MKIGS = 13 - 11 - 6 - 7 - 6
Note: this is a dummy question. Dont answer these questions
Answer:B
Answer: B
Question: Consider a square of diagonal length d. Let Another square be formed with d as its side. Find the ratio of the area of the bigger square to that of the smaller square.
Options:
A)2
B)3
C)4
D)16
E)41
Rationale: d^2/(1/2)*d^2= 2
ANSWER:A
Answer: A
Question: The length of the bridge, which a train 100 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)10 m
B)16 m
C)275 m
D)19 m
E)27 m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (100 + x)/30
= 25/2 => 2(100 + x) = 750 => x
= 275 m.
Answer: C
Answer: C
Question: If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability T that this product will be a multiple of 45?
Options:
A)1/32
B)1/28
C)1/24
D)1/16
E)1/14
Rationale: There are 3 single digit multiple of 3, that is, 3,6,9.
There are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19
Total outcome - 8*3 = 24
Favourable outcome = 1 (9*5)
Hence required probability T= 1/24. Answer C.
Answer: C
Question: 1,3,5,7,9,..50 find term of sequnce for this?
Options:
A)1368
B)1457
C)1567
D)1478
E)2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500.
E
Answer: E
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
Options:
A)12.9 kmph
B)18.9 kmph
C)28.9 kmph
D)12.5 kmph
E)27.8 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b)
= 4 and 45/(a + b) + 40/(a - b)
= 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D
Answer: D
Question: The manager of a theater noted that for every 10 admissions tickets sold, the theater sells 3 bags of popcorn at 2.75 $ each, 4 sodas at 1.50 $ each and 2 candy bars at 1.00$ each. To the nearest cent, what is the average (arithmetic mean) amount of these snacks sales per ticket sold?
Options:
A)1.48$
B)1.58$
C)1.60$
D)1.63$
E)1.70$
Rationale: For every 10 tickets amount of snacks sold is 3*2.75+4*1.5+2*1=$16.25, hence amount of the snacks sales per ticket is $16.25/10=~$1.63.
Answer: D.
Answer: D
Question: Find the one which does not belong to that group ?
Options:
A)3
B)4
C)5
D)8
E)6
Rationale: Explanation:
3, 5, 9 and 7 are odd numbers, but not 4.
Answer: B
Answer: B
Question: A cistern which could be filled in 6 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
Options:
A)76 hrs
B)99 hrs
C)15 hrs
D)90 hrs
E)11 hrs
Rationale: 1/6 - 1/x = 1/10
=> 15 hrs
Answer: C
Answer: C
Question: A 1400 m long train crosses a tree in 100 sec, how much time will It take to pass a platform 700 m long?
Options:
A)288
B)190
C)150
D)188
E)12
Rationale: L = S*T
S= 1400/100
S= 14 m/Sec.
Total length (D)= 2100 m
T = D/S
T = 2100/14
T = 150 Sec
Answer:C
Answer: C
Question: A university cafeteria offers 6 flavors of pizza - pork,gobi-manjurian,pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?
Options:
A)4
B)8
C)12
D)36
E)32
Rationale: 6 flavours * 6 choices = 6C1*6C1 = 6*6=36=D
Answer: D
Question: You are renting an apartment and you need √625 for each side, how many feet are you looking to measure?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 625.
Answer E
Answer: E
Question: Find the HCF of 54, 288, 360
Options:
A)18
B)36
C)54
D)108
E)None of these
Rationale: Explanation:
Lets solve this question by factorization method.
18=2×32,288=25×32,360=23×32×5
So HCF will be minimum term present in all three, i.e.
2×32=18
Answer: Option A
Answer: A
Question: Find the odd man out. 187, 264, 386, 473, 682, 781
Options:
A)187
B)386
C)781
D)682
E)473
Rationale: In all numbers except 386, the middle digit is the sum of other two digits.
Answer is B
Answer: B
Question: 3 numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
Options:
A)3/40
B)28/243
C)3/25
D)33/100
E)64/125
Rationale: Solution:
Total possible ways = 10*10*10 = 1000
Case1: w=0.
if x = 1, then y can have 8 ways.
if x =2 , then y can have 7 ways and so on.
So, no. of ways = 8+7+..+1
Case2 : w=1.
if x = 2, then y can have 7 ways.
if x =3 , then y can have 6 ways and so on.
So, no. of ways = 7+6 +..+1
There will be 8 cases in this way and they will follow a pattern which looks like this:
No. of ways for Case1 : 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8
No. of ways for Case2 : 1 + 2 + 3 + 4 + 5 + 6 + 7
No. of ways for Case3 : 1 + 2 + 3 + 4 + 5 + 6
No. of ways for Case4 : 1 + 2 + 3 + 4 + 5
No. of ways for Case5 : 1 + 2 + 3 + 4
No. of ways for Case6 : 1 + 2 + 3
No. of ways for Case7 : 1 + 2
No. of ways for Case8 : 1
____________________________________________________________
Total number of ways : 8(1) + 7(2) + 6(3) + 5(4) + 4(5) + 3(6) + 2(7) + 1(8) = 2(4(5) + 3(6) + 2(7) + 1(8)) = 2(60) = 120
Therefore, ans is 120/1000 = 3/25.
Option c.
Answer: C
Question: Which of the following is(are) true for a@b=b@a?
I. a@b=ab+a
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)
Options:
A)only Ⅰ
B)only Ⅱ
C)only Ⅲ
D)only ⅠⅢ
E)only ⅡⅢ
Rationale: -> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (X).
Thus, ⅠⅢ are the answers. Therefore, E is the answer.
Answer: E
Question: In the new budget the price of milk rose by 10%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
Options:
A)7.5%
B)9.1%
C)10.9%
D)12.6%
E)15%
Rationale: Reduce in consumption = R/(100+R) *100% = 10/110 *100 = 9.1%
Answer is C
Answer: C
Question: xy+yx=46xy+yx=46 Find x & y values ?
Options:
A)45
B)878
C)66
D)88
E)01
Rationale: l: 145+451=46145+451=46
Hence x = 1, y = 45
AnswerA
Answer: A