divelab/Sys2Bench huggingface dataset:
Question: A farmer has a field that measures 1000 ft wide by 2000 ft long. There is an untillable strip 20 ft wide on the inside edge of the field, and a 30 ft wide untillable strip bisects the field into two squares (approximate). Approximately what percentage of the field is tillable?
Options:
A)98%
B)93%
C)91%
D)90%
E)88%
Rationale: Total Area = 1000*2000
Tillable Square's side horizontally = (2000-20-30-20)/2 = 1930/2 = 965
Tillable Square's side vertically = (1000-20-20) = 960 = 960
Consider it as 960:
Why approximated to 93 and not 91 because we shortened one side from 965 to 960. Thus, in reality the squares are bigger.
Ans: "B"
Answer: B
Question: Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 6 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
Options:
A)396
B)1260
C)825
D)7920
E)15840
Rationale: As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be
(X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)
given that X1, X2 lie between 6 and 11..ie., 6 possible numbers
Possible combinations for X1,X2 would be 6C2 = 15
Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55
Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2
= 15 * 55 = 825
Ans. C
Answer: C
Question: A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
Options:
A)110
B)140
C)250
D)987
E)165
Rationale: Explanation:
Total number of persons in the committee = 5 + 6 = 11
Number of ways of selecting group of eight persons = 11C8 = 11C3= (11 * 10 * 9)/(3 * 2) = 165 ways.
Answer: E
Answer: E
Question: Two clocks were set right at noon on Sunday. One gains 2 min and the other loses 3 min in 24 hours. What will be the true time when the first clock indicates 3 pm on Wednesday?
Options:
A)2 : 38 pm
B)2 : 54 pm
C)2 : 23 pm
D)2 : 48 pm
E)None of these
Rationale: Time from noon on Sunday to 3 pm on Wednesday = 75 hours.
24 hours 2 minutes of the first clock = 24 hours of the correct one.
⇒ 1 hour of the first clock = 24 × (30/721) hours of correct one.
⇒ 75 ours of the first clock
= 24 × 30 × (75/721) hours of correct one
= 54000/721 hours = 74 hours 53.7 min.
Hence the answer is 2 : 54 pm.
Answer B
Answer: B
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 50 liters and they are all empty, how much money total will it cost to fuel all cars?
Options:
A)320$
B)380$
C)420$
D)450$
E)411$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 50) = 21 + 390 => 411
Hence answer will be (E)
Answer: E
Question: Find the value of m 72519 x 9999 = m?
Options:
A)724533811
B)353654655
C)545463251
D)725117481
E)477899932
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: D
Question: For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 25 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?
Options:
A)22%
B)24%
C)25%
D)27%
E)28%
Rationale: Total sales =800
Comission = (20/100)*500+ (25/100)*300
=100 + 75
=175
%Comission =(175/800)*100=21.8~ 22%
Answer is A
Answer: A
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Options:
A)54000
B)50400
C)40500
D)45000
E)None of them
Rationale: In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters = 7!/2! = 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
in 5!/3!= 20 ways.
Required number of ways = (2520 x 20) = 50400.
Answer is B.
Answer: B
Question: The diagonals of a rhombus are 12 cm and 20 cm. Find its area?
Options:
A)176
B)186
C)120
D)179
E)172
Rationale: 1/2 * 12 * 20
= 120
Answer:C
Answer: C
Question: 99,997^2 - 3^2 =
Options:
A)10^10 - 2
B)(10^5 – 2)^2
C)10^4(10^5 – 2)
D)10^5(10^5 – 6)
E)10^5(10^5 – 2)
Rationale: (99,997)^2 - (3)^2 = (100,000 -3)^2 - (3)^2 = (100,000)^2 - 2*3*100,000 + 3^2-3^2=(10^5)^2 - 2*3*(10^5) = 10^10 - 6*(10^5)=10^5(10^5 - 6) Answer D
Answer: D
Question: The average of first 10 prime numbers is?
Options:
A)10.11
B)12.9
C)12.11
D)13.11
E)14.11
Rationale: Sum of 10 prime no. = 129
Average = 129/10 = 12.9
Answer : B
Answer: B
Question: Set A contains four different positive odd integers and six different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?
Options:
A)3/5
B)4/5
C)17/25
D)21/25
E)43/50
Rationale: There can be an odd product only if both integers are odd.
P(odd product) = 4/10*2/5 = 4/25
P(even product) = 1 - 4/25 = 21/25
The answer is D.
Answer: D
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150 m
B)165 m
C)155 m
D)160 m
E)170 m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
ANSWER:A
Answer: A
Question: The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 216 metres, what is its area?
Options:
A)1325 sq.metres
B)1260 sq.metres
C)2835 sq.metres
D)3380 sq.metres
E)None of these
Rationale: Let the length and breadth be 7x and 5x respectively.
Then, P = 2(7x + 5x) = 216 â‡’ x = 9
Area = 7 Ã— 9 Ã— 5 Ã— 9 = 2835 sq.m.
Answer C
Answer: C
Question: A boy was asked to find 7/9 of x. But he divided the x by 7/9, Thus he got 32more thanthe answer. Find the x.
Options:
A)43
B)45
C)59
D)63
E)65
Rationale: x/7/9 = 9x/7 = 32 + y
Actualy he should do 7x/9 = y
y = (9x/7) - 32
y = (9x - 224)/7
(9x - 224)/7 = 7x/9
81x - 2016 = 49x
81x - 49x = 2016
32x = 2016
x = 63
D
Answer: D
Question: A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 20 inches. Find b.
Options:
A)8
B)16
C)4
D)32
E)48
Rationale: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.
From the second premise, we know that the LCM of 12 (2^2*3) andbis 20 (2^2*5), sob=2^2 or 2^2*5(4 or 20).
Combining 2 premises shows the answer is C(4).
Answer: C
Question: On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and the triangle has an area of 30. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?
Options:
A)(2, 25)
B)(4, -15)
C)(3, -24)
D)(-2, 16)
E)(-6, -12)
Rationale: The area of the triangle formed will be:
1/2 * base * height =
1/2 * |(X-coordinate of point C)| * |(Y-coordinate of point C)| = 30
Thus |product of coordinates of point C| = 60
The answer is B.
Answer: B
Question: A boat crossed a lake from North to East at the speed of 10 km/h, entered a river and covered twice as much distance going upstream at 9 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?
Options:
A)4
B)5
C)6
D)7
E)11
Rationale: One way of solving this is:
Speed of boat on still water (lake)=10kmph
Speed upstream = 9kmph = speed in still water - speed of river => speed of river = 1kmph
=>Speed downstream = speed in still water + speed of river = 10+1 =11kmph
Ans is E
Answer: E
Question: From the set of numbers x, y, t, z, p, q, r and w, how many different combinations can we have without the t,p,q and r in them? Ex:. (x,y), (x), (w,z,y,x), etc and (x,y)=(y,x)
Options:
A)10
B)12
C)15
D)16
E)30
Rationale: Another way: Any letter (x, y, z, w) can be included or not. So, we have 2^4 combinations - 4 empty combination = 12 combinations
B
Answer: B
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 50/r years. If Luke's parents invested $13,500 in a long term bond that pays 12 percent interest compounded annually, what will be the approximate total amount of the investment 12 years later, when Luke is ready for college?
Options:
A)62,000
B)85,500
C)95,500
D)100,500
E)100,000
Rationale: Answer equals D in 48 years. I thought by 50th year it would reach 100,500. Options should have been separated more widely for clarity.
Answer: D
Question: A man can row with a speed of 25 kmph in still water. If the stream flows at 15 kmph, then the speed in downstream is?
Options:
A)A)35
B)B)38
C)C)30
D)D)40
E)E)45
Rationale: M = 25
S = 15
DS = 25 + 15 = 40
Answer:D
Answer: D
Question: Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of an alpha raised to the seventh power and a beta raised to the seventh power?
Options:
A)alpha
B)beta
C)gamma
D)delta
E)epsilon
Rationale: Let the alpha be 5k and let the beta be 5j+1.
(5k)^7 + (5j+1)^7 which has the form 5k+1, which is a beta.
The answer is B.
Answer: B
Question: The denominator of a fraction is 3 more than the numerator. If the numerator as well as the denominator is increased by 4, the fraction becomes 4/5. What was the original fraction ?
Options:
A)8/19
B)8/11
C)8/12
D)8/99
E)8/17
Rationale: Explanation:
Let the numerator be x Then, denominator = x + 3.
Now. (x + 4)/(x + 3) +4 = 4/5 <=> 5 (x + 4) = 4(x + 7)
=> x = 8.
The fraction is 8/11.
Answer: B) 8/11
Answer: B
Question: There are four inns in a town. If 3 men check into the inns in a day, then what is the probability that each checks into a different inn?
Options:
A)1/6
B)2/8
C)3/8
D)2/3
E)4/3
Rationale: Total ways for the 3 men to check into the inns = 4³ ways.
The number of cases where 3 men are checking in different inns = 4 x 3 x 2 = 24 ways.
Therefore, the required probability = 24/4³ = 3/8.
ANSWER:C
Answer: C
Question: If Finn was 18 months old one year ago, how old was he, in months, x months ago?
Options:
A)x − 30
B)x − 12
C)18 − x
D)24 − x
E)30 − x
Rationale: Age Today = 18 months + 12 months (1year) = 30 months
X months ago- Today's Age - X = 30 - X
Ans- E
Answer: E
Question: $350 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share?
Options:
A)$200
B)$225
C)$250
D)$275
E)$300
Rationale: Let the shares for A, B, and C be x, 2x, and 4x respectively.
7x = 350
x = 50
4x = 200
The answer is C.
Answer: C
Question: A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
Options:
A)2400
B)2828
C)1208
D)1272
E)1292
Rationale: Explanation:
1200 * 12: x * 9 = 2:3
x = 2400
Answer:A
Answer: A
Question: here's an easy question of averages, but let's try to see innovative ways of solving this.
A class has 12 boys and x girls. Average score of boys and girls is 79 and 92 respectively. the average of the whole class is 86, what is the value of x?
Options:
A)a) 14
B)b) 7
C)c) 8
D)d) 10
E)e) 12
Rationale: 12(79)+92x/12+x=86
948+92x/12+x=86
948+92x=86(12+x)
948+92x=1032+86x
X's one side, numbers one side we get,
92x - 86x=1032-948
6x=84
hence, x=14
Answer A
Answer: A
Question: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 5 years would be
Options:
A)(1.5)^4
B)(1.05)^5
C)(1.05)^4
D)1 + (0.05)^4
E)1 + 4(0.05)
Rationale: In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 5% (which would 'translate' as .05) and a T of . We'd have....
Answer :B
Answer: B
Question: 4, 9, 13, 22, 35, ?
Options:
A)44
B)27
C)57
D)81
E)43
Rationale: C
57
Sum of two consecutive numbers of the series gives the next number.
Answer: C
Question: Diesel costs Rs.4 per lit and petrol costs 4.63 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol.
Options:
A)9 months
B)5 months
C)6 months
D)3 months
E)2 months
Rationale: Explanation :
=>In the First Month the price of the diesel would be 4*110/100 = 4.4
=>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84 which is higher than the
price of the petrol!
Answer : E
Answer: E
Question: Each child has 2 pencils and 13 Skittles. If there are 9 children, how many pencils are there in total?
Options:
A)16
B)12
C)18
D)22
E)08
Rationale: 2*9=18.Answer is C.
Answer: C
Question: Of 70 players on a football team, 49 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Options:
A)54
B)59
C)63
D)71
E)92
Rationale: Total = 70
Thrower = 49
Rest = 70 - 49 = 21
Left Handed = 21/3 = 7
Right handed = 14
If all Thrower are right handed then total right handed is 49 + 14 = 63
so C. 63 is the right answer
Answer: C
Question: When n is divided by 13, the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: N = 139 q + 6
N = 11 z + 6
Equating
13Q + 6= 11z+6
11z=193
11z/13 = q
since q is an integer Z must be divisible by 19.
Hence A
Answer: A
Question: A woman has 4 shirts, 5 pants and 2 belts. How many different clothing combinations can she wear?
Options:
A)11
B)20
C)40
D)60
E)4
Rationale: 4 shirts x 5 pants x 2 belts = 40
Answer: C
Answer: C
Question: if bell rang at a difference of 6,8,12,18,45 sec. respectively.if they start ranging together at 8'o clock morning.then at what time they rang together?
Options:
A)3 minute
B)6 minute
C)15/2 minute
D)1 min. 19 sec.
E)none of the above
Rationale: l.c.m {6,8,12,18,45}
=360 sec=6 min
answer B
Answer: B
Question: A certain car uses 12 gallons of gasoline in traveling 420 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?
Options:
A)2
B)4
C)6
D)7
E)10
Rationale: 420/10 = 42 The difference is 42 - 35 = 7.
Answer D
Answer: D
Question: There are 18 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?
Options:
A)21
B)24
C)27
D)45
E)54
Rationale: Note that each handshake includes two people.
The total number of handshakes is 18*3/2 = 27
The answer is C.
Answer: C
Question: We have 9 people and 6 chairs. In how many ways chairs can be occupy?
Options:
A)3258
B)3215
C)5000
D)4200
E)3024
Rationale: no. of ways they can be occupy = 9*8*7*6 = 3024
Answer is E
Answer: E
Question: Suppose a car can run on ethanol and gas and you have a 15 gallons tank to fill. You can buy fuel that is either 30 percent ethanol or 80 percent ethanol. How much of each type of fuel should you mix so that the mixture is 40 percent ethanol?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Le x represent number of gallons of gas that contain 30 percent ethanol
Let 15 - x be number of gallons of gas that contain 80 percent ethanol
Since the mixture contains 40 percent ethanol, only 40% of the 15 gallons will be ethanol
40% of 15 = (40/100) times 15 = (40/100) times 15/1 = (40 × 15) / (100 × 1) = 600 / 100 = 6
In order for x gallons of gas to contain 30% ethanol, we must take 30% of x or 30% times x
In order for 15 - x gallons of gas to contain 80% ethanol, we must take 80% of 15 - x or 80% times 15 - x
0.30 × x + 0.80 × (15 - x) = 6
0.30x + 0.80 × 15 - 0.80 × x = 6
0.30x + 12 - 0.80x = 6
0.30x - 0.80x + 12 = 6
-0.50x + 12 = 6
-0.50x = -6
x = 12
So 12 gallons of gass contain 30 percent ethanol and 15 - 12 = 3 gallons contain 80 percent ethanol
Therefore, mix 12 gallons of a 30% ethanol with 3 gallons of an 80% ethanol
Answer B
Answer: B
Question: A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord S, in feet?
Options:
A)30
B)25
C)15
D)10
E)5
Rationale: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.
The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.
S=pi*r = 30. Round pi = 3, then r = 10.
Chord is about 10 feet long.D
Answer: D
Question: A person can swim in still water at 6 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 14km?
Options:
A)3.5
B)4.5
C)5
D)9
E)6
Rationale: M = 6
S = 2
US = 6 - 2 = 4
D = 42
T = 14/4 = 3.5
Answer: A
Answer: A
Question: If positive integer k is divided by 10, the quotient is m and the remainder is 2, then which of the following must be true?
I. k + m is even
II. k cannot be a prime number
III. k is divisible by 4
Options:
A)None
B)I
C)II
D)III
E)I and II only
Rationale: k = 10m+2 = 2(5m+1)
I. k + m = 2(5m+1) + m => even if only m is even, however m can be odd => not always true
II. k can not be a prime: not always true:
m=0 => k=2 : a prime
III. not true if m is even
Ans: none of the above
Answer: A
Question: Six children â€” A, B, C, D, E, and F â€” are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?
Options:
A)60
B)180
C)240
D)360
E)720
Rationale: If we wanted, we could make this one extremely difficult, counting out all kinds of possibilities in several different cases. Instead, we are going to make this ridiculously easy.
First of all, with absolutely no restrictions, how many ways can the six children be arranged on the six chairs? Thatâ€™s a permutation of the 6 items â€”- 6P6 = 6! = 720. Thatâ€™s the total number of arrangements with no restrictions. Of course, those 720 arrangements have all kinds of symmetry to them. In particular, in all of those arrangements overall, itâ€™s just as likely for E to be to the left of F as it is for E to be to the right of F. Therefore, exactly half must have E to the right of F, and exactly half must have E to the left of F. Therefore, exactly (1/2)*720 = 360 of the arrangements have E to the left of F. Answer = D.
Answer: D
Question: 250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days?
Options:
A)700
B)666
C)600
D)400
E)800
Rationale: Number of men needed to finish the required work (variation, proportion method ) =3*16*250/20 =600 Answer : C
Answer: C
Question: The food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last?
Options:
A)22 days
B)30 days
C)76 days
D)88 days
E)82 days
Rationale: one man can consume the same food in 30*40 = 1200 days.
10 more men join, the total number of men = 40
The number of days the food will last = 1200/40 = 30 days.
Answer: B
Answer: B
Question: In an electric circuit, two resistors with resistances D and E are connected in parallel. In this case, if F is the combined resistance of these two resistors, then the reciprocal of F is equal to the sum of the reciprocals of D and E. What is F in terms of D and E?
Options:
A)DE/(D + E)
B)(D+E)/DE
C)DE
D)D-E
E)NONE OF THESE
Rationale: The wording is a bit confusing, though basically we are told that 1/F= 1/D + 1/E, from which it follows that F=DE/(D + E).
Answer: A
Answer: A
Question: If 20% of (x-y) = 14% of (x+y), then what percent of x is y?
Options:
A)50.5%
B)44.4%
C)22.2%
D)17.6%
E)25%
Rationale: 20% of (x-y) = 14% of (x+y)
20/100 (x-y) = 14/100 (x+y)
6x = 34y
Required percentage = y/x *100 = 6y/34y * 100 = 17.64%
Answer is D
Answer: D
Question: If the average marks of three batches of 47, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is
Options:
A)54.48
B)54.93
C)54.6
D)54.58
E)None of these
Rationale: Explanation:
=(47*50+60*55+45*60)/(47+60+45)=54.93
Answer: Option B
Answer: B
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.961. Find the cost of each ice-cream cup?
Options:
A)Rs.25
B)Rs.22.50
C)Rs.20
D)Rs.17.50
E)None of these
Rationale: Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 961
96 + 225 + 490 + 6x = 961
6x = 150 => x = 25.
ANSWER:A
Answer: A
Question: If m and n are whole numbers such that mn = 169, then the value of (m – 1)^(n + 1) is:
Options:
A)1
B)13
C)169
D)1728
E)1628
Rationale: Clearly, m = 13 and n = 2.
Therefore, (m – 1) n + 1 = (13 – 1)3 = 12³ = 1728.
ANSWER:D
Answer: D
Question: For any number a, a* is defined as the greatest positive even integer less than or equal to a. What is the value of 5.2 – 5.2*?
Options:
A)0.2
B)1.2
C)1.8
D)2.2
E)4.0
Rationale: Since a* is defined as the greatest positive even integer less than or equal to a, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).
Hence, 5.2 – 5.2* = 5.2 - 4 = 1.2
Answer: B.
Answer: B
Question: A two digit number is divided by the sum of its digits. What is the maximum possible remainder?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: Solution
The maximum possible remainder must be less than 18 as the sum of any two digits can not be greater than 18. So we check when the sum of digits is 18. If the sum of digits is 18 the only possible remainder is 9 in case of 99. Similarly, if the sum of digits is 17 the maximum possible remainder is 14 in case of 98.Similarly, if the sum of digits is 16 the maximum possible remainder is 15 in case of 79. The remainder we have already got is 15 and all other sums of digits will be 15 or less than 15. So 15 has to be the answer. Answer C
Answer: C
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
Options:
A)2/3
B)8/21
C)3/7
D)9/22
E)None of these
Rationale: Explanation:
Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Option B
Answer: B
Question: A child has 36 blue marbles and 10 red marbles, and he kept they into a bag. If he asks you to pick up 3 marbles, what is the probability that all the 3 marbles will be red?
Options:
A) 1/253
B) 2/253
C) 3/253
D) 1/153
E) 2/153
Rationale: There are 10 red marbles in a group of 36 + 10 that is 46. Thus the probability of picking all 3 red marbles is: (10/46)(9/45)(8/44) = 2/253. The correct answer is B.
Answer: B
Question: The average of 5 quantities is 6. The average of 3 of them is 4. What is the average of remaining 2 numbers?
Options:
A)9
B)10
C)8
D)9.5
E)None of these
Rationale: ANSWER: A
Answer: A