RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.996] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?
A.0
B.1
C.0
D.54
Answer: C.0
Explanation: K=[lCM of 80 and 45] * (any integer)
however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer
for value of k(60) * any integer unit value will be always zero .
C
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
A.15 kmph
B.18 kmph
C.85 kmph
D.17 kmph
Answer: A.15 kmph
Explanation: 90 * 10/60
=15 kmph
Answer:A
Question: A large research project was scheduled over the course of a 25-month period, and a budget of $100,000 was allotted for the course of the entire project. After 9 months, the project had spent $35,800. Was the project at this point over budget or under budget, and by how much?
A.under, $200
B.under, $1200
C.under, $7000
D.over $1800
Answer: A.under, $200
Explanation: cost per month = 100,000/25 = 4,000.
Now, multiply by nine months: 9*($4000) = $36,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is less than this, so it is under budget.
$36,000 â€“ #35,800 = $200
Answer = (A)
Question: A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets Q be in 20 years?
J-X-40/3 is my answers.
J = X + L + L + L is the initial situation
After 20 years
J + 20 = X + L + L + L + 60 ...20 years for each triplet so 60 years totally.
J - X - 40/ 3 = L is my answer.
What wrong am i doing ? Since the age asked is after 20 years i also consider adding 20 years to J .
A.(J - 50)/3
B.3(J + 20)/x
C.(J + x - 50)/3
D.(J - x + 60)/3
Answer: D.(J - x + 60)/3
Explanation: here it goes:
Oldest inhabitant = sum of age of triplets + X
J = 3L + X so L = (J - X)/3
After 20 years = L + 20
Q= (J - X)/3 + 20
= (J - X + 60)/3=D
Question: There are two numbers. If 30% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
A.5/9
B.5/6
C.5/3
D.5/8
Answer: B.5/6
Explanation: Let the two numbers be x and y.
30/100 * x + y = 5/4y
=> 3/10 x = 1/4 y => x/y
= 5/6
Answer: B
Question: John had $100 to buy drinks and sandwiches for his birhtday party. He bought 5 small boxes of drinks at $4 each box and 8 boxes of sandwiches at $6 each box. How much money was left after the shopping?
A.$68
B.$45
C.$57
D.$34
Answer: A.$68
Explanation: Money spent on drinks
5 * 4 = $20
Money spent on sandwiches
8 * 6 = $48
Total money spent
20 + 48 = $68
Money left after shopping
100 - 68 = $32
correct answer A
Question: A credit card number has 6 digits (between 1 to 9 inclusive). The first two digits are 12 in that order, the third digit is bigger than 6, the fourth digit is divisible by 2, and the fifth digit is 2 times the sixth. How many different credit card numbers are possible?
A.24
B.36
C.48
D.60
Answer: C.48
Explanation: The first two digits are fixed.
The third digit can be 7, 8, or 9 so there are 3 choices.
The fourth digit can be 2, 4, 6, or 8 so there are 4 choices.
The fifth digit depends entirely on the sixth digit.
The sixth digit can be 1, 2, 3, or 4 so there are 4 choices.
The number of possibilities is 3*4*4 = 48
The answer is C.
Question: Car A runs at the speed of 80km/hr & reaches its destination in 5hr. Car B runs at the speed of 100 km/h & reaches its destination in 2h. What is the respective ratio of distances covered by Car A & Car B?
A.11 : 5
B.11 : 8
C.2 : 1
D.15 : 7
Answer: C.2 : 1
Explanation: Sol. Distance travelled by Car A = 80 × 5 = 400 km
Distance travelled by Car B = 100 × 2 = 200 km
Ratio = 400/200 = 2 : 1
Answer : C
Question: In how many different number of ways 5 men and 4 women can sit on a shopa which can accommodate persons?
A.200
B.230
C.240
D.9
Answer: D.9
Explanation: 9p1 = 9
D
Question: Total of ages of A,B and C at present is 90 years. If ratio of this ages is 2 : 3 : 4 what will be the age of C after 8 years?
A.45 years
B.42 years
C.40 years
D.48 years
Answer: D.48 years
Explanation: 2+3+4=9
4*(90/9)=40yrs
after 8 yrs=48
ANSWER:D
Question: The ratio of present age of A and B is 4:3. A will be 26yrs old in 6yrs from now. How old is B now?
A.15yrs
B.20yrs
C.25yrs
D.10yrs
Answer: A.15yrs
Explanation: present age of A is 20yrs(26-6).
4/3=20/x;
x=15
ANSWER:A
Question: It takes Avery 4 hours to build a brick wall while Tom can do it in 2 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
A.20
B.40
C.30
D.50
Answer: C.30
Explanation: Avery takes 4 hours
Tom takes 2 hours
Efficiency of Avery is 1/4 units/hr
Efficiency of Tom is 1/2 units/hr
Combined efficiency of Tom and Avery is 1/4 +1/2 = 3/4 units/hr
Since they worked for 1 hour they completed 3/4 units of work and 1/4 units of work is left which is to be completed by Tom ( Since Avery left )
So Time taken by Tom to complete the remaining work will be 1/4/1/2 hours => 1/2*60 = 30 minutes...
Answer will be (C)
Question: Some persons can do a piece of work in 12 days. Two times the number of these people will do half of that work in?
A.3 days
B.3.5 days
C.4.5 days
D.5.5 days
Answer: B.3.5 days
Explanation: 14/ (2 * 2) = 3.5 days
ANSWER:B
Question: x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 18. Which of the following is NOT a possible value for y + b?
A.24
B.21
C.20
D.17
Answer: A.24
Explanation: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>18 --> y+b>24.
Answer: A.
Question: What is (21^7+21) / 21?
A.82216043
B.83786095
C.84316108
D.85766122
Answer: D.85766122
Explanation: (21^7+21) / 21 =
21*(21^6+1) / 21 =
21^6 + 1
Clearly this is a number which ends with a 2 in the units place.
The answer is D.
Question: Local trains leave from a station at an interval of 15 minutes at a speed of 16 km/h. A man moving from opposite side meets the trains at an interval of 12 minutes. Find the speed of the man.
A.4 km/h
B.3.5 km/h
C.4.5 km/h
D.3 km/h
Answer: A.4 km/h
Explanation: Let speed of man = S km/h. Then,
Distance covered in 15 min = Distance covered in 12 min
16 × 15⁄60 = 12⁄60[16 + S]
⇒ 16 + S = 20 ⇒ S = 4 km/h
Answer A
Question: A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius of the pool is?
A.22
B.20
C.88
D.387
Answer: B.20
Explanation: let the radius of the pool be Rft
Radius of the pool including the wall = (R+4)ft
Area of the concrete wall = {\color{Black} \Pi \left [ (R+4)^{2} -R^{2}\right ]}={\color{Black} \Pi \left [ (R+4+R)(R+4-R) \right ] =8\Pi (R+2)} sq feet
{\color{Black} \Rightarrow 8\Pi (R+2)=\frac{11}{25}\Pi R^{2}\Rightarrow 11R^{2}=200(R+2)}
Radius of the pool R = 20ft
Answer: B) 20ft
Question: Harry started a 4-mile hike with a full 6-cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Harry drank 1 cups of water during the last mile, how many cups did he drink per mile during the first 3 miles of the hike?
A.1/3
B.2/3
C.3/4
D.5/4
Answer: B.2/3
Explanation: No of cups leaked during the trip = 2 cups.
No of cups Harry drank = 3 cups.
No of cups harry drank during the first 3 miles = 2.
drink / mile = 2/3
Answer:B
Question: The average age of 3 girls is 40 years and their ages are in the proportion 1:2:3. The age of the youngest girl is?
A.22 years
B.23 years
C.21 years
D.20 years
Answer: D.20 years
Explanation: Total age of 3 boys = 40*3 =120
ratio of their ages = 1:2:3
Age of the youngest =120*1/6 = 20 years
Answer is D
Question: A group of 10 people consists of 3 married couples and 4 single men. A committee of 4 is to be formed from the 10 people. How many different committees can be formed if the committee can consist of at most 1 married couple?
A.105
B.207
C.210
D.540
Answer: B.207
Explanation: Total number of possibilities of selecting 4 people out of 10 without any restrictions = 10C4 = 10!/(4!*6!)
= (10*9*8*7)/4*3*2*1
= 10*3*7
= 210
Number of possibilities of selecting 2 married couples = 3C2 = 3!/2! = 3
Number of different committees with atmost 1 married couple that can be formed = 210 - 3 = 207
Answer B
Question: A train cross a 450 m bridge in 42 s and another bridge 650 m length in 50 s what is approximate speed of train in km/h?
A.90 Km /hr.
B.25 Km /hr.
C.30 Km /hr.
D.20 Km /hr.
Answer: A.90 Km /hr.
Explanation: Explanation:
Let the length of the train be L.
Then,
=> (450 + L)/42 = (650+L)/50.
=> L= 600 m.
Now, speed = (450+600)/42 or (650+600)/50 = 25 m/s i.e. 25*(18/5) = 90 Km /hr.
ANSWER IS A
Question: Anderson has a phone plan that charges a
monthly rate of $50 for the first 1,000 minutes
plus $0.25 for each additional minute.
Which of the following functions models
Anderson’s plan for all m > 1,000, with m as
the number of minutes per month and f(m)
as the monthly charge?
A.f(m) = 0.25m
B.f(m) = 0.25m + 50
C.f(m) = 0.25m – 200
D.f(m) = 0.25m – 950
Answer: C.f(m) = 0.25m – 200
Explanation: For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee
based on the number of minutes used plus a flat rate of $50. With this information, you can
create the following function:
f(m) = Usage fee + 50
The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for. So
the usage fee is 0.25(m – 1,000). Plug this value into the preceding function and simplify:
f(m) = 0.25(m – 1,000) + 50
f(m) = 0.25m – 250 + 50
f(m) = 0.25m – 200
correct answer C)f(m) = 0.25m – 200
Question: At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 7 pencils and 11 charts have been brought to the meeting, how many people are present?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: Say there are 'A' associate professors. So we have 2A pencils and A charts.
Say there are 'B' assistant professors. So we have B pencils and 2B charts.
Total pencils are 10 so 2A + B = 7
Total charts are 11 so A + 2B = 11
Add both: 3A + 3B = 18 so A + B = 6
Total number of people = 6
A
Question: If the President and Vice President must sit next to each other in a row with 3 other members of the Board, how many different seating arrangements are possible?
A.12
B.26
C.20
D.48
Answer: D.48
Explanation: We need to take President and VP as one unit. Therefore we have 4 people to arrange=4! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=4!*2!=48 ways
Answer D
Question: A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in
A.17 years
B.87 years
C.15 years
D.16 years
Answer: C.15 years
Explanation: P(1 + R/100)5 = 2P => (1 + R/100)5 = 2
Let P(1 + R/100)n = 8P
=> (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3
=> (1 + R/100)n = (1 + R/100)15 => n = 15 Required time
= 15 years.
Answer:C
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
A.9 3/8 days
B.4 2/8 days
C.17 9/8 days
D.12 7/8 days
Answer: A.9 3/8 days
Explanation: 1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
ANSWER:A
Question: If 0 < x > 7 and 5 < y < 9, then the lowest possible value for xy is
A.between 60 and 70
B.between 0 and 60
C.0
D.between 0 and -70
Answer: A.between 60 and 70
Explanation: If 0 < x > 7 and 5 < y < 9, then the lowest possible value for xy is
Say y = 8 (y<9)
x = 8
So xy =64 which is more than 60.
Answer is A.
Question: If a cube of dimension 4 by 4 by 4 is cut into 1 by 1 by 1 after painting it by red color then which of the following is/are true.
I) Ratio of number of painted surfaces of resultant cubes to total number of surfaces is 1/4
II) Number of cubes having no faces pointed is equal to number of cubes having three faces painted.
III) Number of cubes having 2 faces painted is same as number of cubes having one face painted
A.None
B.II and III
C.II only
D.I, II & III
Answer: D.I, II & III
Explanation: Long explanation, probably too detailed
Hypercube facts (n=3 for a cube):
2^n vertices 2n−1n edges 2+E−V faces
For a cube: 8 vertices, 12 edges and 6 faces
Let G=4be the size of the original cube.
I) Ratio of number of painted surfaces of resultant cubes to total number of surfaces is 1/4
There is 1 large cube with 6 sides of G2 painted faces.
There is G3x1 cubes with 6 sides of surface area 1.
1×6×G^2/G3×6×1=G^2/G^3=G−1=1/4
True
II) Number of cubes having no faces pointed is equal to number of cubes having three faces painted.
There are always 8 vertices on a cube, each vertex is the only 1x1 block which has 3 coloured faces.
Inside the cube, there is a secondary unpainted cube. Each side of this unpainted cube is equal to the size of the original cube minus two (on each axis, there will be two 1x1 cubes on the exterior of the larger cube). The size of this cube is (G−2)3
There are (G−2)3( cubes with 0 sides painted. =23=8
There are V=23 cubes with 3 sides painted =8
True
III) Number of cubes having 2 faces painted is same as number of cubes having one face painted
There are 12 edges on a cube. Each edge consists of G cubes, two of which are the vertices of the cube (and have 3 colours), the rest have two colours.
On each exterior face, there is a square of (G−2) cubes, surrounded by 4 vertex cubes and (G−2)×4 edge cubes.
Each square consists of (G−2)^2 coloured faces. There is 1 square per face.
There are (G−2)×E cubes with 2 sides painted. =2×12=24
There are (G−2)2×F cubes with 1 side painted. =22×6=24
True
ANSWER:D
Question: Two fill taps A and B can separately fill a cistern in 45 and 40 minutes respectively. They started to fill a cistern together but tap A is turned off after few minutes and tap B fills the rest part of cistern in 23 minutes. After how many minutes,was tap A turned-off?
A.9 min
B.10 min
C.12 min
D.7 min
Answer: A.9 min
Explanation: Let A was turned off after x min. Then,
cistern filled by A in x min + cistern filled by B in (x + 23) min = 1
⇒ x/45+x+23/40=1
⇒ 17x + 207 = 360 ⇒ x = 9 min.
Answer A
Question: If n = 6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
A. Two
B. Three
C. Four
D. Six
Answer: B. Three
Explanation: If n = 6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 6p have.
p = 3 --> 6p = 18--> 18 has 3 even divisors: 2, 6, 18.
Answer: B.
Question: A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
A.48 km/hr
B.56 km/hr
C.60 km/hr
D.52 km/hr
Answer: A.48 km/hr
Explanation: Explanation:
Method : 1
If a car covers a certain distance atxkmph and an equal distance at y kmph,
the average speed of the whole journey = 2xy/x+y kmph.
By using the same formula, we can find out the average speed quickly
Speed with which he travels from A to B = x = 40 km/hr
Speed with which he travels from B to A = x = 40×(100+50)/100 = 60 km/hr
average speed = (2×40×60)/(40+60) = 48 km/hr
Assume that distance from A to B = x km
Speed with which he travels from A to B = x = 40 km/hr
Time to travel from A to B = distance/speed = x/40 hr
Speed with which he travels from B to A = 40×(100+50)/100 = 60 km/hr
Time to travel from B to A = distance/speed = x/60
Total distance traveled = x+x = 2x
Total time taken = x/40 + x/60
Average speed = Total distance traveled/Total time taken = 2x/(x/44)+(x/60)
= 2/[(1/60)+(1/40)] = (2×2400)/(40+60) = 2×24 = 48 km/hr
Answer: Option A
Question: Marcella has 24 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?
A.21
B.20
C.19
D.16
Answer: C.19
Explanation: Marcella has 24 pairs of shoes and loses 9 shoes.
To minimize the loss of identical pairs of shoes we want Marcella to lose as many identical pairs as possible. This would yield 4 identical pairs and 1 additional shoe (destroying 5 pairs of shoes).
The 24 pairs of shoes minus the 5 'destroyed' pairs yields 19 pairs that still fulfill the requirements.
Answer: C
Question: 3 Years ago, the average age of a family of 5 members was 18 years. A baby having been born, the average age of the family is the same today. The present age of the baby is
A.1 year.
B.1.5 Years.
C.2 Years.
D.3 Years.
Answer: D.3 Years.
Explanation: We're told that 3 YEARS AGO, the average age of a family of 5 members was 17 years.
This means that the SUM of their ages was (5)(18) = 90 years.
A baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME.
This means that the sum of the ages is (6)(17) = 102 years.
We're asked for the PRESENT age of the baby.
Since each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is...
90 + (5)(3) = 108.
D
Question: John bought 2 shares and sold them for $94 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
A. a profit of $10
B. a profit of $8
C. a loss of $8
D. a loss of $12
Answer: D. a loss of $12
Explanation: $ Profit of the share sold at 20% profit =
120-94
20-?
$14 profit on the sale of 1 share.
$ Loss of the share sold at 20% loss=
80-94
20-?
$26 loss on the sale of 1 share.
14-26=Loss of $12
Answer: D
Question: If A is a positive integer greater than 1, what is the sum of the multiples of A from A to A^2, inclusive?
A. A^2(A + 1)/2
B. A(A + 1)(A-1)
C. A^2(A-1)
D. (x^3 + 2x)/2
Answer: A. A^2(A + 1)/2
Explanation: Ans :- A
I substituted 3 in all answer choices.
Option C A were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices,
A=A^2(A + 1)/2
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, 43, 46, x
A.29
B.31
C.23
D.51
Answer: D.51
Explanation: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 46 + 5 = 51
Question: The greatest number by which the product of three consecutive multiples of 2 is always divisible is
A.48
B.76
C.152
D.162
Answer: A.48
Explanation: Solution
Required number	= Product of first three multiplies of 3
= (2 Ã— 4 Ã— 6)= 48.
Answer A
Question: The roots of the equation ax(2)exponent) + bx + c = 0 will be reciprocal if:
A.c = ab.
B.a = bc
C.c = b
D.c = a
Answer: D.c = a
Explanation: Let k be one of the root of the given equation.
According to the problem,
1/k will be the other root of the given equation.
We know that, product of the roots of the equation = c/a.
Therefore, k × 1/k = c/a.
or, 1 = c/a.
or, a = c [multiplying a on both sides].
The roots of the equation ax2exponent + bx + c = 0 will be reciprocal if a = c.
Therefore, a = c or c = a.
Question: Find the value of 72519 x 9999 = m?
A.567688653
B.465768853
C.678488937
D.725117481
Answer: D.725117481
Explanation: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Question: In an election a candidate who gets 60% of the votes is elected by a majority of 1040 votes. What is the total number of votes polled?
A.A)4500
B.B)5200
C.C)6900
D.D)7520
Answer: B.B)5200
Explanation: Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 1040
20x/100 = 1040
x = 1040*100/20 = 5200
Answer is B
Question: If a(a + 5) =6 and b(b + 5) =6, where a ≠ b, then a + b =
A.−5
B.−9
C.2
D.46
Answer: A.−5
Explanation: i.e. if a = 1 then b = -6
or if a = -6 then b = 1
But in each case a+b = -6+1 = -5
Answer: option A
Question: Working alone at its constant rate, pump F pumped out ¼ of the water in a tank in 2 hours. Then pumps G and H started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump G, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump H, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?
A.6
B.12
C.15
D.18
Answer: B.12
Explanation: Rate of pump F = 1/8
3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4
Rate of F + Rate of G + Rate of H = 1/4
Rate of G + Rate of H = 1/4 - 1/8 = 1/8
G takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully.
Rate of G = 1/24
1/24 + Rate of H = 1/8
Rate of H = 1/8 - 1/24 = 1/12
Time required to pump out all the water by H = 12 hrs
Answer: B
Question: In a horticultural experiment, 200 seeds were planted in plot I and 300 were planted in plot II. If 57 percent of the seeds in plot I germinated and 42 percent of the seeds in plot II germinated, what percent of the total number of planted seeds germinated?
A.45.5%
B.46.5%
C.48.0%
D.49.5%
Answer: C.48.0%
Explanation: Plot I: 57% of 200 seeds germinated, hence 0.57*200 = 114 seeds germinated.
Plot II: 42% of 300 seeds germinated, hence 0.42*300 = 126 seeds germinated.
Thus (germinated)/(total) = (114 + 126)/(200 + 300) = 240/500 = 48% seeds germinated.
Answer: C
Question: The length of rectangle is thrice its breadth and its perimeter is 64 m, find the area of the rectangle?
A.432 sq m
B.192 sq m
C.452 sq m
D.428 sq m
Answer: B.192 sq m
Explanation: 2(3x + x) = 64
l = 24 b = 8
lb = 24 * 8 = 192
ANSWER:B
Question: Which of the following is a possible length for side AB of triangle ABC if AC = 4 and BC = 9?
I. 5
II. 9 √3
III. 12.5
A.I only
B.II only
C.III only
D.II and III
Answer: C.III only
Explanation: (9-4) < AB < (9+4)
The answer is C.
Question: A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 850.50. If each member of the club paid at least $ 42, then what is the greatest possible number of members in the club?
A.19
B.21
C.20
D.23
Answer: C.20
Explanation: Given: Each person spends $42.
By looking at the options, we see that if there were 20 members, each person will spend atleast $42.
If there were 21 members, each person will spend $41.3
Hence the greatest number of members = 20. Option C
Question: Coins are to be put into 6 pockets so that each pocket contains at least one coin. At most 2 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?
A.16
B.13
C.17
D.22
Answer: A.16
Explanation: 2 in each, so let each contain just 1 coin;
Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);
Total: 1+1++2+3+4+5=16
Answer: A
Question: If x and g are integers and 2x–g= 11, then 4x+ g CANNOT be
A. –5
B. 1
C. 13
D. 17
Answer: D. 17
Explanation: 2x-g=11....g=2x-11
4x+g=4x+2x-11=6x-11
6x-11=-5...x=1
6x-11=1... x=2
6x-11=13...x=4
6x-11=17..X is not integer
6x-11=551..X is not integer
I think the choice E is 55 not 551. Otherwise both DE CANNOT be solution=D