divelab/Sys2Bench huggingface dataset:
Question: In western Europe, G bicycles were sold in each of the years 1990 and 1993. The bicycle producers of Western Europe had a 42 percent share of this market in 1990 and a 33 percent share in 1993. Which of the following represents the decrease in the annual number of bicycles produced and sold in Western Europe from 1990 to 1993?
Options:
A)9% of (x/100)
B)14% of (x/100)
C)75% of (x/100)
D)9% of G
E)14% of x
Rationale: Moreover is't question actually asking the the difference between the {(Quantity Produced + Quantity Sold )G in 1990 - (Quantity Produced + Quantity Sold ) in 1993}
Though the Quantity sold in both the years is same it actually boils down to (Quantity Produced in 1990 ) in (Quantity Produced in 1993)=D
Answer: D
Question: Rectangular Floors X and Y have equal area. If Floor X is 16 feet by 18 feet and Floor Y is 9 feet wide, what is the length of Floor Y, in feet?
Options:
A) 13 1/2
B) 18
C) 18 3/4
D) 21
E) 32
Rationale: The area of a rectangle is: Area = length x width
We are given that floor X is 16 feet by 18 feet and that floor Y is 9 feet wide. So we can say:
length of X = 16
width of X = 18
width of Y = 9
length of Y = n
We also can say:
Area of Floor X = Area of Floor Y
(length of X)(width of X) = (length of Y)(width of Y)
(16)(18) = 9n
(16)(2) = n
32 = n
Answer E.
Answer: E
Question: When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
Options:
A)349
B)300
C)500
D)450
E)250
Rationale: x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q - 13p = 2
q =	2 + 13p/17
Least value of p which q = 2+13p/17 => 26
x= (13*26+11) = 349
ANSWER A
Answer: A
Question: Two pipes A and B can fill a tank in 4 and 12 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Options:
A)12
B)3
C)6
D)9
E)10
Rationale: Part filled by A in 1 min. = 14
Part filled by B in 1 min. = 1/12
part filled by (A + B) in 1 min. = 1/4+ 1/12 = 1/3.
Both the pipes can fill the tank in 3 minutes.
Answer: B
Answer: B
Question: John can hit a target 3times in 6shots, Karan can hit the target 2 times in 6 shots & Ashwini can hit 4 times in 4 shots. What is the probability that at least 2 shots hit the target ?
Options:
A)1/3
B)2/5
C)2/3
D)3/5
E)3/7
Rationale: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Karan hits tha target and Raja not hit the target.
or
Karan does not hit the target and Raja hits the target.
or.
Karan hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3
C
Answer: C
Question: A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of w square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)
Options:
A)(5,280 mt) / 12 w
B)(5,280 pt) / 12m
C)(5,280 pmt) /12
D)(5,280)(12m) / pt
E)(5,280)(12p) / mt
Rationale: Given that: 1 gallon of paint covers an area ofwsquare feet. Question:how many gallonsof paint will be needed ...
In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/w, so w must be in the denominator: eliminate all but A and D.
Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.
Answer: A.
Answer: A
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
Options:
A)297
B)879
C)342
D)762
E)269
Rationale: 400*(90/100)*(95/100)
= 342
Answer: C
Answer: C
Question: The banker's discount on Rs.1250 due a certain time hence is Rs.125. Find the true discount and the banker's gain.
Options:
A)11
B)15
C)18
D)21
E)None
Rationale: Solution
Sum	=B.D x T.D/ B.D - T.D
= B.D x T.D/ B.G
T.D / B. G	=Sum / B.D
= 1250 / 125
= 10 / 1
If B.D is Rs. 11,T.D= Rs.10.
If B.D is Rs.125,
T.D	= Rs.(10 / 11 x 125)
= Rs.114.
And, B.G	= Rs(125 - 114)
= Rs.11.
Answer A
Answer: A
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1200, find the loss %?
Options:
A)18
B)16
C)26
D)17
E)20
Rationale: Explanation:
1500 ---- 300
100 ---- ? => 20%
Answer:E
Answer: E
Question: Jancy decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Jancy s savings by the end of the year from these monthly savings were five times the amount she spent per month, what should be the fraction of her salary that she spent each month?
Options:
A)15/17
B)17/12
C)10/17
D)13/17
E)12/17
Rationale: Let Jancy's monthly savings = S
Jancy's monthly pay = P
Jancy's monthly expenditure = P-S
Jancy's savings by the end of the year from these monthly savings were Five times the amount she spent per month
12S = 5*(P-S)
=>12/5 S = P-S
=> P = 17/5 S
Jancy's monthly expenditure = P-S = 17/5S-S = 12/5S
fraction of her salary that Jancy spent each month = 12/5S / 17/5S=P-S/P = 12/17. Answer is E
Answer: E
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
Options:
A)287 cm2
B)887 cm2
C)384 cm2
D)268 cm2
E)668 cm2
Rationale: Area of a parallelogram = base * height
= 24 * 16
= 384 cm2
Answer: C
Answer: C
Question: A departmental store has 7 managers and 30 associates. The 7 managers have an average salary of $4200. The 30 associates have an average salary of $6,000. What is the average salary for the departmental store?
Options:
A)$5659.46
B)$5888.56
C)$5200.26
D)$5929.25
E)$5126.98
Rationale: Number of managers is 7
Their average salary is $4200
Number of associates is 30
Their average salary is $6000
Total salary of managers is 7*4200=$29,400
Total salary of associates is 30*6000=$180,000
Total salary for the departmental store is 180,000+29,400=209400
Average salary for the departmental store is 209400/7+30=5659.46
Answer is A
Answer: A
Question: If x > y and y > z, which of the following represents the greatest number Q?
Options:
A) x − z
B) x − y
C) y − x
D) z − y
E) z − x
Rationale: Because x>y>z
thus Q= x- z wil lbe greatest
Ans: A
Answer: A
Question: If W persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
Options:
A)z
B)x
C)x/y
D)z/x
E)y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
W person can do z jobs in y days..
so W person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: E
Question: The tax on a commodity is diminished by 17% and its consumption increased by 15%. The effect on revenue is?
Options:
A)2%
B)8%
C)4.5%
D)6.5%
E)1.5%
Rationale: 100 * 100 = 10000
83 * 115 = 9545
-----------
10000-----------455
100-----------? => 4.55% decrease
Answer: C
Answer: C
Question: What is the sum Q of all 3 digit numbers that leave a remainder of '2' when divided by 3?
Options:
A)897
B)164,850
C)164,749
D)149,700
E)156,720
Rationale: The series is => 101+...998
Number of terms => 300
sum Q=> 300/2 * [101+998]
hence sum => 164850 i.e. option B
Answer: B
Question: Hari purchased 6 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Options:
A)A)910
B)B)1065
C)C)1070
D)D)1075
E)E)1080
Rationale: Cost of 6 kg grapes = 70 × 6 = 420.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 420 + 490 = 910
A
Answer: A
Question: 4, 12, 48, 240, 1440,10080,80640, 725760(...)
Options:
A)7257600
B)10080
C)6200
D)10020
E)12500
Rationale: Explanation :
Go on multiplying the given numbers by 3, 4, 5, 6, 7,8,9,10
Answer : Option A
Answer: A
Question: In a lottery, there are 12 prizes and 30 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)1/3
B)1/5
C)2/5
D)1/7
E)2/7
Rationale: P(winning a prize) = 12 / (12+30) = 12/42 = 2/7
The answer is E.
Answer: E
Question: From a group of 3 CATS and 3 DOGS, 4 animals are to be randomly selected. What is the probability that equal numbers of cats and dogs will be selected?
Options:
A)1/5
B)2/5
C)4/5
D)3/5
E)1
Rationale: Using the first example, here is the probability of THAT EXACT sequence occurring:
CCDD = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10
Each of the other 5 options will yield the exact SAME probability....
eg
CDCD = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10
So we have 6 different options that each produce a 1/10 chance of occurring.
6(1/10) = 6/10 = 3/5
Final Answer:
D
Answer: D
Question: In the Land of Oz only one or two-letter words are used. The local language has 68 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?
Options:
A)65
B)66
C)67
D)131
E)136
Rationale: The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...
The number of 1 letter words (X) that can be made from 68 letters is 68;
The number of 2 letter words (XX) that can be made from 68 letters is 68*68, since each X can take 68 values.
Total: 68+68*68.
Similarly:
The number of 1 letter words (X) that can be made from 67 letters is 67;
The number of 2 letter words (XX) that can be made from 67 letters is 67*67, since each X can take 67 values.
Total: 67+67*67.
The difference is (68+68*68)-(67+67*67)=136.
Answer: E.
Answer: E
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 3 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)s.4528
B)s.4520
C)s.4527
D)s.4530
E)s.2718
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)
= 906 sq.ft.
Total cost = 906 * 3
= Rs.2718
Answer:E
Answer: E
Question: HDFC bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?
Options:
A)1:5
B)625:3125
C)100:105
D)100^4:105^4
E)725:3225
Rationale: Hi Bunuel,
Here is my approach: is this correct?
HDFC bank offers an interest of 5% per annum compounded annually on all its deposits.
Interest earned in 4 year= 10000(1+0.05)^4
Interest earned in 5 year= 10000(1+0.05)^5
Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105
Hence Ans:C
Answer: C
Question: X, Y, and Z are consecutive numbers and X > Y > Z. Also, 2X + 3Y + 3Z = 5Y + 8. What is the value of Z?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.
2X + 3Y + 3Z = 5Y + 8
2Z+4+3Z+3+3Z = 5Z+5+8
3Z = 6
Z = 2
The answer is A.
Answer: A
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)248
B)289
C)240
D)242
E)229
Rationale: Speed = [54 * 5/18] m/sec
= 15 m/sec.
Length of the train
= (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36
= 15
x + 300 = 540
x = 240 m.
Answer: C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)2287
B)27
C)299
D)287
E)150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m
Answer: E
Answer: E
Question: 2034 - (1002 / 20.04) = ?
Options:
A)2984
B)2983
C)2982
D)2981
E)1984
Rationale: 2034-50 =1984
Answer : E
Answer: E
Question: George does 3/5th of a piece of work in 9 days. He then calls in Paul , and they finish the work in 4 days. How long would Paul take to do the work by himself?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: 100% work will be done by George in 15 days
(1/15)9+(1/15+1/x)4=1
solving this eqn.
we get x=30
hence Paul take to do the work in 30 days
ANSWER:A
Answer: A
Question: mr. depak has $419,774 in his bank account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among her six best friends?
Options:
Options:
A)$1
B)$2
C)$3
D)$4
E)$6
Rationale: To find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends,
he needs to make the total divisible by 6
Simply add the individual digits of the total = 4+1+9+7+7+4 = 32
If you add 4 , the number is divisible by 6 (32+ 4)
Correct Option : D
Answer: D
Question: If y exceeds x by 20%, then x is less than y by?
Options:
A)16%
B)16 1/3 %
C)16 2/3 %
D)16 3/5 %
E)16 4/5 %
Rationale: Explanation:
X=100	y=120
120------20
100-------? => 16 2/3%
ANSWER IS C
Answer: C
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
Options:
A)5409
B)54087
C)5400
D)546
E)5401
Rationale: 100x + 400 = 12(x – 5)
x = 50
100 * 50 + 400 = 5400
Answer: C
Answer: C
Question: Three grades of milk are 1 percent, 3 percent and 2 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
Options:
A)y + 3z
B)(y +z) / 4
C)2y + 3z
D)3y + z
E)3y + 4.5z
Rationale: Soln:
The resulting equation is
=> (.01x + .03y + .02z)/(x+y+z) = 1.5/100
=> x + 3y +2z = 1.5x + 1.5y + 1.5z
taking x to one side and y and z to other side we get
=> x = 3y + z
Ans is D
Answer: D
Question: Mrs. Rodger got a weekly raise of $165. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Options:
A)$ 165.
B)$ 146
C)$ 147
D)$ 148
E)None
Rationale: Solution:
Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 165.
So after completing the 1st week she will get $ (x+165).
Similarly after completing the 2nd week she will get $ (x + 165) + $ 165.
= $ (x + 165 + 165)
= $ (x + 330)
So in this way end of every week her salary will increase by $ 165.
Answer A
Answer: A
Question: C individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?
Options:
A)dx / C
B)x / (C-d)
C)d / (C-dx)
D)x / (C(C-d))
E)dx / (C(C-d))
Rationale: Number of individuals = C
Amount paid by each individual = n
Total expected amount = Charity's goal = nC = x
n = x/C
Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dx/C --> Additional amount
Number of individuals who are paying = C - d
Additional amount has to be divided among the (C - d) individuals --> dx/C(C - d)
Answer: E
Answer: E
Question: A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)49
B)50
C)12
D)13
E)77
Rationale: Speed of the train relative to man = (200/10) m/sec = (20) m/sec. [(20) * (18/5)] km/hr = 72 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 72 ==> x = 77 km/hr.
Answer: Option E
Answer: E
Question: Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent K of the lights that are on are supposed to be off?
Options:
A)22(2/9)%
B)16(2/3)%
C)11(1/9)%
D)10%
E)5%
Rationale: Is the Answer D.
let me try..
Let the light which are supposed to be OFF = SO
Let the light which are supposed to be ON = SN
Let the light which are ACTUALLY OFF = AO
Let the light which are ACTUALLY ON = AN
Let the total no. of lights be 100,
So ACTUALLY ON lights = 80
And ACTUALLY OFF lights = 20
Also given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON
it means >>> (60/100)*SO are ACTUALLY OFF
Also given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF
it means >>> (90/100)*SN are ACTUALLY ON
So, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80
and Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80
From here we get SO = 20
we need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.
So (8/80)*100 K= 10%.D
Answer: D
Question: The number N is 5,2H7, where H represents the ten's digit. If N is divisible by 3, what is the value of H?
Options:
A)3
B)8
C)5
D)6
E)4
Rationale: If the number is divisible by 3, the sum of the digits must also be divisible by 3. Only 4 yields such a number.
Answer: E
Answer: E
Question: The jogging track in a sports complex is 640 m in circumference. Lata and Geeta start from the same point and walk in opposite directions at 4.2 km/hr and 3.8 km/hr respectively. They will meet for the first time in?
Options:
A)2.9 min
B)3.9 min
C)4.2 min
D)4.8 min
E)5.6 min
Rationale: Clearly, the two will meet when they are 640 m apart.
To be (4.2 + 3.8) = 8.0 km apart, they take 1 hour.That is 60 min.
To be 640 m apart, they take
(640/8000 * 60) min
= 4.8 min.
Answer: D
Answer: D
Question: A man can row downstream at the rate of 12 Km/hr and upstream at 8 Km/hr. Find man's rate in still water and the rate of current?
Options:
A)9,6
B)6,3
C)9,3
D)10,2
E)None of these
Rationale: Explanation:
Rate of still water = 1/2 (12 + 8) = 10 Km/hr
Rate of current = 1/2 (12-8) = 2 Km/hr
Answer: Option D
Answer: D
Question: Which of the following CANNOT be a product of two distinct positive integers x and y?
Options:
A)x
B)y
C)3y + 2x
D)y - x
E)yx
Rationale: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with
take x = 1 and y = 2 and work with the options
xy = 2
A) x take x =2, y = 1
B) y take x = 1 y = 2
C) 3y + 2x Seems tricky, lets see other options and then come back to it.
D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?
E) yx Always true
You don't even have to worry what C is !
ans D
Answer: D
Question: How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 15 inches than that of a rectangular sheet of paper measuring 7.5 inches by 11 inches?
Options:
A)50%
B)87%
C)100%
D)187%
E)200%
Rationale: Let's just look at the dimensions (no calculation needed).
With dimension 11 the same, the other dimension 15 is twice 7.5
Then the area will be double which means 100% greater.
The answer is C.
Answer: C
Question: For which of the following values of n is (300+n)/n NOT an integer?
Options:
A) 1
B) 2
C) 3
D) 4
E) 7
Rationale: Solution:
This problem is easiest solved by plugging in each answer choice.
A) (300 + 1)/1 = 301/1 = 301
Answer choice A yields an integer.
B) (300 + 2)/2 = 302/2 = 151
Answer choice B yields an integer.
C) (300 + 3)/3 = 303/3 = 101
Answer choice C yields an integer.
D) (300 + 4)/4 = 304/4 = 76
Answer choice D yields an integer.
E) (300 + 7)/7 = 307/7 = 43, remainder 6
Answer choice E DOES NOT yield an integer.
Thus, the correct answer is answer choice E.
Answer: E
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face?
Options:
A)2/113
B)1/215
C)1/216
D)3/113
E)4/113
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: C
Question: Two trains 190 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.7
B)10.9
C)10.6
D)12.6
E)18.8
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 190 + 160 = 350 m.
Required time = 350 * 9/250
= 12.6 sec.
Answer:D
Answer: D
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent?
Options:
A)11.11%
B)25%
C)22%
D)29%
E)45%
Rationale: 900 --- 100
100 --- ? => 11.11%
Answer:A
Answer: A
Question: After running a series of television advertisements, a leading beverage producer saw its sales increase by 50% to $1 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day?
Options:
A)$1.25 million
B)$22,000
C)$750,000
D)$27,000
E)$10,000
Rationale: Let sales in previous month = X
1.5 X=1,000,000
3/2 X= 1,000,000 ..........> X=666,666
sales per day= 666,666/30= less than 25,000 so closest number is 22,000
Answer: B
Answer: B
Question: In school there are some bicycles and 4 wheeler wagons.one Tuesday there are 190 wheels in the campus.How many bicycles are there?
Options:
A)35
B)36
C)37
D)38
E)39
Rationale: Let no. of bicycles be x
& no. of wagons be y
so, 2x+4y=190
by solving, we get
no. of bicycles=39 (wheels=>2*39=78)
no. of wagons=28 (wheels=>4*28=112)
ANSWER:E
Answer: E
Question: A university cafeteria offers 4 flavors of pizza - pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?
Options:
A)4
B)8
C)12
D)16
E)32
Rationale: There are 4 flavors of pizza and each can be:
1. Without cheese and mushrooms;
2. With cheese;
3. With mushrooms;
4. With cheese and mushrooms.
So, the total number of pizza varieties is 4*4 = 16.
Answer: D.
Answer: D
Question: A feed shop sells two varieties of birdseed: Product A, which is 40% millet and 60% sunflower, and Product B, which is 65% millet and 35% safflower. If a customer purchases a mix of the both types of birdseed that is 50% millet, what percent of the mix is Product A?
Options:
A)50%
B)55%
C)60%
D)40%
E)45 %
Rationale: Yes there is a simple method :
Consider the following method
Product A : 40% millet and 60% sunflower
Product B : 65% millet and 35% safflower
Mix : 50% millet
Here the weighted average is 50%,
Now Product A has 40% millet, which is 10% less than the weighted average of mix = - 0.10 A --------------- I
Similarly, Product B has 65 % millet, which is 15 % more than the weighted average of mix = + 0.15 B ------------ II
Now, both Product A and Product B are combined to give a 50% mix containing millet, so equate I and II
implies, 0.10 A = 0.15 B
Therefore A/B = 0.15/0.10 = 3/2
A : B : (A + B) = 3 : 2 : (3+2) = 3 : 2 : 5
We have to find, percent of the mix is Product A i.e. A : (A + B) = 3 : 5 = (3 / 5) * 100 = 60 %
Here is a pictorial representation :
Product A= 40%------------------------10% or 0.10 below average, A times-----------------Total below = - 0.10 A
----------------------------------------------------------------------------------------Average = 50% or 0.50
Product B = 65 %--------------------------15% or 0.15 above average, B times-----------------Total above = + 0.15 B
Since the amount below the average has to equal the average above the average; therefore,
0.10 A = 0.15 B
A/B = 3/2
A:B: Total = 3:2:5
A/Total = 3:5 = 60 %
Answer: C
Answer: C