divelab/Sys2Bench huggingface dataset:
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?
Options:
A)3 days
B)3.5 days
C)4.5 days
D)5.5 days
E)2.5 days
Rationale: 14/ (2 * 2) = 3.5 days
ANSWER:B
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?
Options:
A)24
B)21
C)20
D)17
E)15
Rationale: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>18 --> y+b>24.
Answer: A.
Answer: A
Question: What is (21^7+21) / 21?
Options:
A)82216043
B)83786095
C)84316108
D)85766122
E)86426237
Rationale: (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.
Answer: 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.
Options:
A)4 km/h
B)3.5 km/h
C)4.5 km/h
D)3 km/h
E)None of these
Rationale: 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
Answer: A
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 42 kg and that of B and C be 43 kg, then the weight of B is:
Options:
A)33 kg
B)31 kg
C)32 kg
D)36 kg
E)35 kg
Rationale: Let A, B, C represent their respective weights.
Then, we have: A + B + C = (45 x 3) = 135 .... (i)
A + B = (42 x 2) = 84 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 170 .... (iv)
Subtracting (i) from (iv), we get : B = 35
B's weight = 35 kg.
E
Answer: E
Question: A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:
Options:
A)Rs. 207.40
B)Rs. 534.60
C)Rs. 648
D)Rs. 655.60
E)Rs. 755.60
Rationale: No. of shares= 4455/8.25 =540
income on shares=540*10=5400
annual income=12*5400/100=648
ANSWER:C
Answer: C
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?
Options:
A)22
B)20
C)88
D)387
E)19
Rationale: 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
Answer: B
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?
Options:
A)1/3
B)2/3
C)3/4
D)5/4
E)4/3
Rationale: 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
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?
Options:
A)22 years
B)23 years
C)21 years
D)20 years
E)25 years
Rationale: 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
Answer: 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?
Options:
A)105
B)207
C)210
D)540
E)5,040
Rationale: 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
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?
Options:
A)90 Km /hr.
B)25 Km /hr.
C)30 Km /hr.
D)20 Km /hr.
E)None of these
Rationale: 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
Answer: 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?
Options:
A)f(m) = 0.25m
B)f(m) = 0.25m + 50
C)f(m) = 0.25m – 200
D)f(m) = 0.25m – 950
E)f(m) = 0.25m + 1,000
Rationale: 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
Answer: C
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?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: 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
Answer: 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?
Options:
A)12
B)26
C)20
D)48
E)32
Rationale: 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
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
Options:
A)17 years
B)87 years
C)15 years
D)16 years
E)19 years
Rationale: 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
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?
Options:
A)9 3/8 days
B)4 2/8 days
C)17 9/8 days
D)12 7/8 days
E)16 9/8 days
Rationale: 1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
ANSWER:A
Answer: A
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
Options:
A)7000
B)7200
C)7400
D)7600
E)8000
Rationale: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
E)
Answer: E
Question: If 0 < x > 7 and 5 < y < 9, then the lowest possible value for xy is
Options:
A)between 60 and 70
B)between 0 and 60
C)0
D)between 0 and -70
E)less than -70
Rationale: 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.
Answer: 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
Options:
A)None
B)II and III
C)II only
D)I, II & III
E)I & III only
Rationale: 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
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?
Options:
A)9 min
B)10 min
C)12 min
D)7 min
E)None of these
Rationale: 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
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 ?
Options:
A) Two
B) Three
C) Four
D) Six
E) Eight
Rationale: 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.
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?
Options:
A)48 km/hr
B)56 km/hr
C)60 km/hr
D)52 km/hr
E)None of these
Rationale: 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
Answer: 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?
Options:
A)21
B)20
C)19
D)16
E)15
Rationale: 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
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
Options:
A)1 year.
B)1.5 Years.
C)2 Years.
D)3 Years.
E)4 Years.
Rationale: 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
Answer: D
Question: On her annual road trip to visit her family in Seal Beach, California, Alice stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination. What was the total distance, in miles, from Alice’s starting point to Seal Beach?
Options:
A) 250
B) 300
C) 350
D) 450
E) 400
Rationale: Let D = total distance
Traci traveled 1/3 = D/3
i.e. remaining distance = 2D/3
She traveled 1/4 th of 2D/3 = D/6
Thus:
D = (D/3) + (D/6) + 200
D = 400
ANSWER: E
Answer: E
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
Options:
A) a profit of $10
B) a profit of $8
C) a loss of $8
D) a loss of $12
E) neither a profit nor a loss
Rationale: $ 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
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?
Options:
A) A^2(A + 1)/2
B) A(A + 1)(A-1)
C) A^2(A-1)
D) (x^3 + 2x)/2
E) x(x-1)^2
Rationale: 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
Answer: A
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
Options:
A)29
B)31
C)23
D)51
E)69
Rationale: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 46 + 5 = 51
Answer: D
Question: The greatest number by which the product of three consecutive multiples of 2 is always divisible is
Options:
A)48
B)76
C)152
D)162
E)None of these
Rationale: Solution
Required number	= Product of first three multiplies of 3
= (2 Ã— 4 Ã— 6)= 48.
Answer A
Answer: A
Question: The roots of the equation ax(2)exponent) + bx + c = 0 will be reciprocal if:
Options:
A)c = ab.
B)a = bc
C)c = b
D)c = a
E)a = b
Rationale: 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.
Answer: D
Question: Find the value of 72519 x 9999 = m?
Options:
A)567688653
B)465768853
C)678488937
D)725117481
E)789458695
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: 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?
Options:
A)A)4500
B)B)5200
C)C)6900
D)D)7520
E)E)6000
Rationale: 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
Answer: B
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 5 people take the trip rather than 15, how many more dollars, in terms of x, will it cost per person?
Options:
A) x/6
B) x/16
C) x/40
D) 3x/40
E) 3x/22
Rationale: Just plugging in values
X= 75
Cost per person if we consider 5 = 15
Cost per person if we consider 15 = 5
Difference between costs is 10 dollars.
Plugging in the value of x into the answer choices, let's see which one yields a result of 10. And that is E.
Answer: E
Question: If a(a + 5) =6 and b(b + 5) =6, where a ≠ b, then a + b =
Options:
A)−5
B)−9
C)2
D)46
E)48
Rationale: 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
Answer: 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?
Options:
A)6
B)12
C)15
D)18
E)24
Rationale: 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
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?
Options:
A)45.5%
B)46.5%
C)48.0%
D)49.5%
E)51.0%
Rationale: 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
Answer: C
Question: A pharmaceutical company received $8 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
Options:
A)8%
B)15%
C)45%
D)52%
E)79%
Rationale: Solution:
This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.
We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales, and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.
First 20 Million
royalties/sales =8/20
Next 108 Million
royalties/sales = 9/108 = 1/12
Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents.
First 20 Million
royalties/sales = (8/20) x 60 = 24
Next 108 Million
royalties/sales = 9/108 = (1/12) x 60 = 5
We can plug 24 and 5 into our percent change formula:
(new – old)/old x 100
[(5 – 24)/24] x 100
-475/6 x 100
At this point we can stop and consider the answer choices. Since we know that 475/6 is just a bit less than ½, we know that -475/6 x 100 is about a 79% decrease.
Answer E.
Answer: E
Question: The length of rectangle is thrice its breadth and its perimeter is 64 m, find the area of the rectangle?
Options:
A)432 sq m
B)192 sq m
C)452 sq m
D)428 sq m
E)528 sq m
Rationale: 2(3x + x) = 64
l = 24 b = 8
lb = 24 * 8 = 192
ANSWER:B
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
Options:
A)I only
B)II only
C)III only
D)II and III
E)I, II, and III
Rationale: (9-4) < AB < (9+4)
The answer is C.
Answer: 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?
Options:
A)19
B)21
C)20
D)23
E)25
Rationale: 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
Answer: 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?
Options:
A)16
B)13
C)17
D)22
E)28
Rationale: 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
Answer: A
Question: If x and g are integers and 2x–g= 11, then 4x+ g CANNOT be
Options:
A) –5
B) 1
C) 13
D) 17
E) 551
Rationale: 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
Answer: D
Question: The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability R that the next couple the maitre 'd seats will not order dessert?
Options:
A) 20%
B) 25%
C) 40%
D) 60%
E) 75%
Rationale: could you use a venn diagram and just go with the number 100.
60 people order dessert and coffee... which is the union of D and C.
R=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.
B 25%
Answer: B
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
Options:
A)33
B)44
C)39
D)66
E)none of these
Rationale: Let the average after 7th inning = x
Then average after 16th inning = x - 3
inline fn_jvn therefore 16(x-3)+87 = 17x
inline fn_jvn therefore x = 87 - 48 = 39 Answer C
Answer: C