divelab/Sys2Bench huggingface dataset:
Question: A boy has Rs 2. He wins or loses Re 1 at a time If he wins he gets Re 1 and if he loses the game he loses Re 1.He can loose only 5 times. He is out of the game if he earns Rs 5.Find the number of ways in which this is possible?
Options:
A)16
B)15
C)32
D)81
E)31
Rationale: He has 2Rs.He wins or loses Re 1 at a time.
for 1Rs.He may have different probabilities as (WW,WL,LW,LL)i.e,for one rupee he has 8chances in the same way for another one rupee he has another 8 chances .
So,total number of chances/ways are 16.
ANSWER:A
Answer: A
Question: 32.32/2000 is equal to:
Options:
A)1.012526
B)0.012625
C)0.12526
D)0.01616
E)0.12725
Rationale: 25.25/2000 = 2525/200000
= 0.01616
ANSWER:D
Answer: D
Question: A train 160 m long passed a pole in 40 sec. How long will it take to pass a platform 320 m long?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: Speed = 160/40 = 40 m/sec.
Required time = (160 + 320)/40
= 12 sec.
Answer:A
Answer: A
Question: Ms. Lovely deposits $ 300 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
Options:
A)$118.00
B)$120.00
C)$121.00
D)$122.00
E)$140.00
Rationale: Using Formula - A = P(1+r/n)^nt
Given
P=300
n=2
t=1
r=0.2
Substituting value in formula
A = 300(1+0.2/2)^2
A= 363.00$=C
Answer: C
Question: In the rectangular coordinate system, points (16, 0) and (– 16, 0) both lie on circle C. What is the maximum possible value of the radius of C ?
Options:
A)2
B)4
C)8
D)16
E)None of the above
Rationale: D
It takes 3 distinct points to define a circle. Only 2 are given here.
The two points essentially identify a single chord of the circle C. Since no other information is provided, however, the radius of the circle can essentially be anything. All this information tell us is that the radius isgreater 16 D
Answer: D
Question: What is the perimeter, in meters, of a rectangular garden 12 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide?
Options:
A)48
B)56
C)60
D)56
E)192
Rationale: Say Length of garden is L meters.
Then (L*12) = 16 * 12 [Given area is same. Area= L * B]
Therefore L works out to 16 meters.
Perimeter of Garden = 2* (16+12) = 56 meter.
Answer is D
Answer: D
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
Options:
A)1/15
B)1/17
C)1/20
D)1/21
E)3/25
Rationale: Option 'C'
(2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
Answer: C
Question: The sum and the product of the roots of the quadratic equation x2 + 20x + 3 = 0 are?
Options:
A)10, 3
B)-10, 3
C)20, -3
D)-10, -3
E)None of these
Rationale: Explanation:
Sum of the roots and the product of the roots are -20 and 3 respectively.
ANSWER IS E
Answer: E
Question: Jamie's friend Bob is having a party, but Jamie forgot and went to dinner with her friend Emily instead. Bob's party starts in half an hour. Bob lives 30 km away from Jamie, and the restaurant Jamie and Emily are at is three times as far away from Bob's house as Jamie's house is.
How fast would Jamie have to drive in order to get to Bob's party on time?
Options:
A)30 km/h
B)45 km/h
C)60 km/h
D)75 km/h
E)90 km/h
Rationale: Distance between Bob's house and Jamie's restaurant: 30 x 3 = 90 km
Rate of speed to get to Bob's house in an hour: 90 x 1 = 90 km/h
Rate of speed to get to Bob's house in half an hour: 90/2 = 45 km/h
Answer: B
Question: For an upcoming charity event, a male vocalist has agreed to sing 3 out of 5 “old songs” and 1 out of 4 “new songs.” How many ways can the singer make his selection?
Options:
A)240
B)50
C)150
D)480
E)600
Rationale: =5C3*4C1
=5*4/1*4*3/1
=5*4*4*3
=240
Ans = A
Answer: A
Question: Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)
Options:
A)2.7
B)3
C)3.6
D)4.5
E)4.7
Rationale: Option 'C'
Answer: C
Question: e.	Janet has to pay back her bank loan over 7 months following the below sequence.
$50, $55, $65, $80, $85, $95, ?
How much will she pay back on the seventh month?
Options:
A)$155
B)$145
C)$135
D)$125
E)$110
Rationale: The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 7th Month is $110
Ans E
Answer: E
Question: In expressing a length 81.472 km as nearly as possible with three significant digits, find the percentage error?
Options:
A)0.075%
B)0.156%
C)0.034%
D)0.048%
E)0.152%
Rationale: Error = 81.5-81.472 = 0.028
Required percentage = (0.028/81.472)*100 = 0.034%
Answer is C
Answer: C
Question: A candidate got 35% of the votes polled and he lost to his rival by 2370 votes. How many votes were cast?
Options:
A)7500
B)7900
C)2665
D)2888
E)2661
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2370
100%---------? => 7900
Answer: B
Answer: B
Question: The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 112 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)70, 10 kmph
B)106, 6 kmph
C)50, 60 kmph
D)45, 55 kmph
E)45, 65 kmph
Rationale: Speed of the boat in still water = (100+112)/2 = 106 kmph. Speed of the stream = (100-112)/2 = 6 kmph
ANSWER:B
Answer: B
Question: Find the average of first 30 natural numbers.
Options:
A)A)13.5
B)B)20.5
C)C)18.6
D)D)15.5
E)E)12.3
Rationale: Sum of first n natural numbers = n(n+1)/2
sum of first 30 natural numbers = 30*31/2 =465
average = 465/30 = 15.5
Answer is D
Answer: D
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Options:
A)200
B)300
C)350
D)400
E)450
Rationale: Speed = 300/18 = 50/3
length of the platform x meters
(x+300)/39 = 50/3
3x+900 = 1950 ==> x = 350 m
ANSWER C
Answer: C
Question: A charitable woman gave one penny more than half pennies in her purse to a farmer .Afterwards she came across a beggar whom she gave 2 pennies more than half of what she had in her purse. In the end she gave 3 pennies more than half of what she had in her purse and left with a penny with her to a boy. Find what she had in the beginning?
Options:
A)41
B)42
C)43
D)44
E)45
Rationale: she gave 1 penny more than the half in the purse i.e (x/2 +1)
now she is left with:: (x-(x/2+1))=(x-2)/2
now to the beggar::
she gave 2 pennies more than the half in the purse i.e(x-2)/4 +2
and she is left with :: ((x-2)/2)-((x-2)/4 +2)= (x-10)/4
now at last
sh gave 3 pennies more then the half she was left with i.e ((x-10)/8+ 3)=A
so she is left with
(x-10)/4-A=(x-34)/8
now acc. to quest
(x-34)/8=1
hence x=42
ANSWER:B
Answer: B
Question: Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes V, each draining water at the same constant rate, will be needed to drain the pool in 4 days?
Options:
A) 6
B) 9
C) 10
D) 12
E) 15
Rationale: This is an inverse proportional problem......
5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15
So, V=15-5 = 10.C
Answer: C
Question: If an object travels at five feet per second, how many feet does it travel in one hour?
Options:
A)3488
B)3778
C)12788
D)1800
E)2881
Rationale: Explanation:
If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour.
Answer = 1800
Answer: D) 1800
Answer: D
Question: A vendor sold two things at same cost of 17 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much
Options:
A)0.60 loss
B)0.75 loss
C)0.80 loss
D)0.85 loss
E)0.40 loss
Rationale: CP when profit of 25% = 13.60
CP when loss of 20% = 21.25
Total CP = 34.85
Total SP = 34.00
Total loss = 0.85
ANSWER:D
Answer: D
Question: Which of the following is equal to 3^k*7^(k-1)?
Options:
A)3*21^(k-1)
B)7*21^(k-1)
C)21^k
D)3*21^k )
E)21^(2k-1)
Rationale: 3^k*7^(k-1) = 3*3^(k-1)*7^(k-1) = 3*21^(k-1)
The answer is A.
Answer: A
Question: Set A consists of the integers from 3 to 12, inclusive, while set B consists of the integers from 6 to 20, inclusive. How many distinct integers do belong to the both sets at the same time?
Options:
A)5
B)7
C)8
D)9
E)10
Rationale: A={3,4,5,6,7,8,9,10,11,12}
B={6,7,8,9,10,11,12...}
Thus we see that there are 7 distinct integers that are common to both. B is the correct answer.
Answer: B
Question: In Sivakasi, each boy’s quota of match sticks to fill into boxes is not more than 200 per session. If he reduces the number of sticks per box by 25, he can fill 3 more boxes with the total number of sticks assigned to him. Which of the following is the possible number of sticks assigned to each boy ?
Options:
A)200
B)150
C)100
D)175
E)None
Rationale: Explanation :
Let no. of matchstick assigned to boy=n;
no. of matchsticks he put in each box=x;
And, the no. of boxes=y;
Initially we have;
=> n / x = y. -----------------------(i)
After he reduces no. of matchsticks in each box by 25, we have :-
=> n / x - 25 = y + 3. -----------------------(ii)
On solving eq (i) and (ii), we have;
=> n= 3* x * ( x - 25 ) / 25;
i.e. no. of stick must be a multiple of 25;
Let x=50, we have;
=>3 * 50 * (50-25) /25.
=> 3 * 50 = 150.
Hence, the required number of sticks is 150.
Answer : B
Answer: B
Question: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 880 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
Options:
A)880 * sqrt 2
B)880 * sqrt (2^7)
C)880 * sqrt (2^12)
D)880 * the twelfth root of (2^7)
E)880 * the seventh root of (2^12)
Rationale: Let the constant be k.
F1 = 880
F2 = 880k
F3 = 880 k * k = 880 * k^2
F13= 880 * k^12
we know F13 = 2 *F1 = 2 * 880 = 1760
1760/880 = k^12
k = twelfth root of 2
for F7...
F7 = 880 * k^6 ( as we wrote for F2 and F3)
F7 = 880 * (twelfth root of 2) ^ 6
F7 = 880 * sqrt (2)
The answer is A.
Answer: A
Question: The product of a and b is equal to 1 more than twice the sum of a and b. If b = 7, what is the value of b - a?
Options:
A)2
B)5
C)4
D)24
E)35
Rationale: ab= 1 + 2(a+b)
7a= 1+2a +14
5a= 15
a=3
b-a= 7-3=4
C is the answer
Answer: C
Question: From a seven-member dance group, four will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the seven members, what is the probability that both will be chosen to volunteer?
Options:
A)1/21
B)1/7
C)4/21
D)2/7
E)3/7
Rationale: Total number of ways to choose 4 out of 7 = 7C4 = 35.
Number of ways to choose 2 (any but Kori and Jason) out of 5 (excluding Kori and Jason) = 5C2 = 10.
P = favorable/total = 10/35 = 2/7.
Answer: D.
Answer: D
Question: If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
Options:
A)600
B)490
C)720
D)435
E)679
Rationale: Let x be the number of days in the initial plan. Therefore, the whole field is 120⋅x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
120x=85(x+2)+40
35x=210
x=6
So the farmer planned to have the work done in 6 days, and the area of the farm field is 120⋅6=720 hectareS
correct answer C
Answer: C
Question: 60 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple?
Options:
A)47
B)46
C)54
D)58
E)67
Rationale: orange+mango-apple=7
mango+apple-orange=10
apple=60
orange+mango+apple=4
60+10+4-7=67 like apple
ANSWER:E
Answer: E
Question: Narendra started a business, investing 45000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra?
Options:
A)A)Rs.7000
B)B)Rs.8000
C)C)Rs.8571
D)D)Rs.8600
E)E)Rs.8700
Rationale: The ratio of their investments = 45000 × 12 : 15000 × 6 = 6 : 1.
:. Narendra’s share on profit of Rs.10000 = 10000 × 6/7 = Rs.8571.
C)
Answer: C
Question: Calculate the simple interest on Rs 12 000 at 15% per annum for the period from 10th January 2017 to 15th March 2014.
Options:
A)Rs. 315.6
B)Rs. 325.6
C)Rs. 215.6
D)Rs. 112.6
E)Rs. 425.6
Rationale: Explanation:
One thing which is tricky in this question is to calculate the number of days.
Always remember that the day on which money is deposited is not counted while the day on which
money is withdrawn is counted.
So lets calculate the number of days now,
Time = (21+28+15) days = 64/365 years
P = 12000
R = 15%
S.I. = =12000Ã—15Ã—64/(365*100)=315.6
Answer: A
Answer: A
Question: The total number of apples and oranges in the refrigerator is 7 more than the total number of oranges and peaches in the refrigerator. How much lesser is the number of peaches in the refrigerator as compared to apples?
Options:
A)2
B)8
C)7
D)6
E)4
Rationale: (Apples + Oranges) - (Oranges + Peaches) = 7
Apples - Peaches = 7
Answer: C
Answer: C
Question: The rate of Interest on a sum of money is 11% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is
Options:
A)1,000
B)2,000
C)2,100
D)2,250
E)2,540
Rationale: Explanation:
I1 = (P x 3 x 11)/100 = P/3
I2 = (P x 4 x 4)/100 = 4P/25
I3 = (P x 1 x 5)/100 = P/20
P/3 + 4P/25 + P/20 = 540
27P/50 = 540
P = 1000
Answer: Option A
Answer: A
Question: A worker can load one truck in 5 hours. A second worker can load the same truck in 8 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill one truck?
Options:
A)2.5
B)2.7
C)2.9
D)3.1
E)3.3
Rationale: The workers fill the truck at a rate of 1/5 + 1/8 = 13/40 of the truck per hour.
Then the time to fill one truck is 40/13 which is about 3.1 hours.
The answer is D.
Answer: D
Question: If (x^2 + 1)y=5, which of the following is not a possible value for y?
Options:
A)1/2
B)2
C)4/3
D)3
E)13/2
Rationale: Its simple
equation is (x^2 +1)y = 5 ===> x^2 = (5/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.
Hence, (5/y) - 1>= 0 ===> y =< 5. Now only option E has greater value of 'y' than 5.
Thus, correct ans is E
Answer: E
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)49 Years
B)51 Years
C)53 Years
D)54 Years
E)55 Years
Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years
A
Answer: A
Question: A bag is bought for Rs.400 and sold at a gain of 25% find its selling price
Options:
A)A)Rs.460/-
B)B)Rs.470/-
C)C)Rs.480/-
D)D)Rs.500/-
E)E)Rs.520/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
125 % ------> 500 (125 * 4 = 500)
Selling price = Rs.500/
Answer : D
Answer: D
Question: If a 3-number code is formed of the integers from 1 to 18 inclusively, and each of the numbers in the code is different, how many possible codes are there?
Options:
A)4896
B)4986
C)5076
D)5166
E)5256
Rationale: 18*17*16=4896
The answer is A.
Answer: A
Question: The true discount on a bill of Rs. 2160 is Rs. 360. What is the banker's discount?
Options:
A)Rs. 432
B)Rs. 422
C)Rs. 412
D)Rs. 442
E)None of these
Rationale: Explanation :
F = Rs. 2160
TD = Rs. 360
PW = F - TD = 2160 - 360 = Rs. 1800
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 1800 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2160 for unexpired time
=360/1800 × 2160 = 15 × 2160 = Rs. 432 Answer : Option A
Answer: A
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 10% while buying and by 20% while selling. What is his percentage profit?
Options:
A)10.22%
B)20.22%
C)21.22%
D)10%
E)Can't be calculated
Rationale: The owner buys 100kg but actually gets 110kg;
The owner sells 100kg but actually gives 80kg;
Profit: (110-80)/80*100=10%
Answer: D.
Answer: D
Question: The area of a base of a cone is 30 cm2. If the height of the cone is 6cm, find its volume?
Options:
A)87
B)16
C)17
D)60
E)18
Rationale: πr2 = 30 h = 6
1/3 * 30 * 6 = 60
Answer: D
Answer: D
Question: Linda spent 4/5 of her savings on furniture and the rest on a TV. If the TV cost her $100, what were her original savings?
Options:
A)$900
B)$300
C)$500
D)$700
E)$800
Rationale: If Linda spent 4/5 of her savings on furniture, the rest
5 / 5 - 4 / 5 = 1 / 5 on a TV
But the TV cost her $100. So 1 / 5 of her savings is $100. So her original savings are 5 times $100 = $500
correct answer C
Answer: C
Question: Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 11 on the two dice?
Options:
A)7/9
B)5/9
C)11/18
D)19/36
E)23/36
Rationale: There are 36 possible outcomes for two dice.
The number of outcomes with an even number on the first die is 3*6=18.
The number of outcomes with a sum of 11 is 2.
We need to subtract the outcomes that have both an even number on the first die and a sum of 11 because we have counted those outcomes twice. This number of outcomes is 1.
The number of outcomes with either an even number on the first die or a sum of 11 is 18+2-1=19.
The probability is 19/36.
The answer is D.
Answer: D
Question: A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 54 minutes. The total distance is?
Options:
A)1 km
B)2 km
C)3 km
D)3.4 km
E)5 km
Rationale: D
3 km
Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 54/60
47x/60 = 54/60 => x = 1.14
Total distance = 3 * 1.14 = 3.4 km.
Answer: D
Question: Tough and Tricky questions: Word Problems.
It takes Sarah 25 minutes to do one oil change, and it takes Alice 20 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?
Options:
A)10:00 a.m.
B)10:12 a.m.
C)10:40 a.m.
D)1:00 p.m.
E)2:00 p.m.
Rationale: LCM of 2025
20 = 2 * 2 * 5
25 = 5 * 5
LCM = 2 * 2 * 5 * 5= 20 = 100 =1 hour 40 minutes
1040AM
C
Answer: C
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 8 years, son's age will be:
Options:
A)12 years
B)14 years
C)18 years
D)20 years
E)22 years
Rationale: Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 8 years = (x+ 8) = 22 years..
Answer: E
Answer: E
Question: Prints a page 40 pg per min .If the printed for 2 hours except 20 min.Where there
was an paper jam,how many page did it print
Options:
A)4,000
B)12,880
C)14,880
D)8,880
E)18,880
Rationale: 40 pages ------->1 min
2 hrs except 20 mints means=2*60=120-20=100 mints
i.e.,100*40=4,000 pages printed.
ANSWER:A
Answer: A
Question: A basketball coach will select the members of a five-player team from among 15 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter?
Options:
A)1/9
B)1/6
C)2/21
D)5/18
E)1/3
Rationale: straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 13c3
total number of ways of selecting 5 players out of 15 = 15c5
probability = 13c3/15c5 = 2/21
C
Answer: C
Question: From the given equation find the value of y: yÂ² + y - 20
Options:
A)5
B)4
C)3
D)2
E)1
Rationale: (y âˆ’ 4)(y + 5)
y = 4 or -5
Answer is B
Answer: B
Question: At a certain supplier, a machine of type A costs $24,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
Options:
A)$2,640
B)$11,200
C)$12,000
D)$12,800
E)$13,200
Rationale: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 48000 + (48000 - 20% of 48000) + 40% of (48000 - 20% of 48000)
= 63360
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)
= 66000
Diff = 66000 - 63360 = 2640
Hence, A.
Answer: A
Question: From the money that Ajay has, he gives as much to Bunti as much as Bunt i has
with him. Bunti then dives as much money to Chintu as much as Chintu has with
him. Finally Chintu gives as much money to Ajay as much as Ajay had before
Chintu gave home the money. How much money did each of the three friends
Ajay, Bunti, and Chintu have with them initially if between them they have totally
Rs 48 and after the transactions each of them have equal amounts?
Options:
A)Rs. 22,14,12
B)Rs. 22,14,14
C)Rs. 24,14,12
D)Rs. 22,16,12
E)Rs. 27,14,12
Rationale: As they have total Rs 48, each one will have Rs 16 after these transactions.
Finally amounts with ABC are 16,16,16
One step earlier, amounts were 8,16,24
One step before that, amounts were 8,28,12
Initially they had Rs. 22,14,12
ANSWER:A
Answer: A
Question: In the coordinate plane, points (x, 2) and (4, y) are on line k. If line k passes through the origin and has slope 1/4, then x - y =
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Line k passes through the origin and has slope 1/4 means that its equation is y=1/4*x.
Thus: (x, 2)=(8, 2) and (4, y) = (4,1) --> x-y=8-1=7.
Answer: B
Answer: B
Question: When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 3, the speed of the leak is Vâ€™, When the height of the oil remaining is 9, what was the speed of the leak, in terms of Vâ€™?
Options:
A)9Vâ€™
B)4Vâ€™
C)Vâ€™/2
D)Vâ€™/4
E)Vâ€™
Rationale: When h=3 v=V'
So V' = k.9
Hence k = V'/9
Now when h=9
v=(V'/9).9^2
v=V'.9
v=9V'
Ans : A
Answer: A
Question: What is the sum of all 3 digit nos formed by {1,3,5,7,9} with nos not repeated
Options:
A)33300
B)34500
C)38500
D)39800
E)45200
Rationale: Here 3 digit no. Can be formed in 5*4*3 = 60. Thus we hv to find the sum of 60 nos.
Now 60/5= 12 ; we hv 12 no's. starting with 1 ,12 no's. with 3,5,7,9....
So 12*100*(1+3+5+7+9)+12*10*(1+3+5+7+9)+12*1*(1+3+5+7+9)
=30000+3000+300
=33300
ANSWER:A
Answer: A
Question: Four business people wish to invest in a new company. Each person is willing to pay one fourth of the total investment. After careful calculations, they realize that each of them would pay $6,200 less if they could find two more equal investors. How much is the total investment in the new business?
Options:
A)$74,400
B)$62,200
C)$25,000
D)$ 6,200
E)$ 4,300
Rationale: Total Investment between 6: (x/6)
Total investment including 6200 less between 4 people(x-(6200*4))/4
Set both eq. equal to each other.
74,400
Answer A)
Answer: A