divelab/Sys2Bench huggingface dataset:
Question: Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed?
Options:
A)110
B)1,100
C)9,900
D)10,000
E)12,100
Rationale: P can take a total of 10*11 co-ordinates.
for a given P, R can take a total of 9 co-ordinates and Q can take a total of 10 co-ordinates.
Hence, total = 110*9*10 = 9900
ANS:C
Answer: C
Question: How many cases do you need if you have to pack 50 dozens of bar soaps into cases that each hold 50 soaps?
Options:
A)15
B)14
C)13
D)12
E)10
Rationale: D
12
50 dozens of bar soaps = 600 soaps
600 ÷ 50 = 12.
Answer: D
Question: If 3^w - 3^(w-1) = 162 then w(w-1) =
Options:
A)12
B)16
C)20
D)30
E)81
Rationale: It seems like you were really close but you solved for w - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of w(w -1), e.g. (3)(4) = 12. Even then, had you figured w has to be a little bigger (plugging in 4 for w gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (w - 1) exponent place.
Again, a quick plugging in should get you (C) 20 as, the only other answer with consecutive integers as factors is far too big.
Answer: C
Question: In how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together?
Options:
A)610
B)720
C)825
D)920
E)925
Rationale: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
ANSWER:B
Answer: B
Question: For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.
Options:
A)13
B)42
C)55
D)27
E)19
Rationale: f(x) = -3(x - 10)(x - 4) = -3x2*square* + 42x - 120 : expand and obtain a quadratic function
h = -b/2a = -42/-6 = 7 : h is the value of x for which f has a maximum value
f(h) = f(7) = 27 : maximum value of f.
correct answer D
Answer: D
Question: Find the average of first 60 natural numbers.
Options:
A)20.5
B)18
C)30.5
D)19
E)17
Rationale: Exp. Sum of first n natural numbers = n( n+1)/2
So, sum of first 60 natural numbers = 60*61/2 = 1830
Required average =1830/60 =30.5
Answer:C
Answer: C
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 16 more transactions than Cal. How much transactions did Jade handled?
Options:
A)82
B)83
C)84
D)85
E)86
Rationale: Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 16 more transactions than Cal.
Jade = 66 + 16
= 82
Jade handled = 82 transactions.
Correct Answer:A)82
Answer: A
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job. How long should it take both A and B, working together but independently, to do the same job?
Options:
A)6 days
B)40 days
C)5 days
D)12 days
E)40/9 days
Rationale: A’s 1 hour's work = 1/8
B's 1 hour's work = 1/10
(A + B)'s 1 hour's work = (1/8) +(1/10)=9/40
Both A and B will finish the work in 40/9 days.
Ans: E
Answer: E
Question: A says " the horse is not black".
B says " the horse is either brown or grey."
c says " the horse is brown"
At least one is telling truth and atleast one is lying. Tell the colour of horse?
Options:
A)Black
B)grey
C)Brown
D)White
E)blue
Rationale: The color of the horse can be any color other than Black and Brown.
If the color of the horse is Black - all are lying. If the color of the horse is Brown - all are telling truth. Thus, the horse is neither Black nor Brown. If the color of the horse is Grey - A and B are telling truth whereas C is lying. If the color of the horse is other than Black, Brown and Grey - A is telling truth whereas B and C are lying. You must have noticed that for the given conditions, A is always telling truth whereas C is always lying.
So ans is grey.
ANSWER:B
Answer: B
Question: If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 10 men in 3 days?
Options:
A)65mtr.
B)28mtr
C)70mtr.
D)78mtr.
E)17mtr.
Rationale: 20 men is 6 days can build 112 metres
10 men in 3 days can build = 112*(10/20)x(3/6)
= 28 meters
Answer: B.
Answer: B
Question: The value of x + x(x^x) when x = 2 is
Options:
A)10
B)16
C)18
D)36
E)64
Rationale: Solution:
x + x(x^x)
Put the value of x = 2 in the above expression we get,
2 + 2(2^2)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer: (a)
Answer: A
Question: Geetha 's home has One tap, working alone at its maximum constant rate, can fill a certain sink in 210 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 214 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to
Options:
A)106 seconds
B)130 seconds
C)177 seconds
D)200 seconds
E)270 seconds
Rationale: Tap 1 : 210 secs
Tap 2 : 214 secs
Considering the average of these 2 taps : 212 secs.
So 1 tap can fill the tank in 212 secs, so 2 taps can fill the tank in 212/2 = 106 secs.
Closest answer is A.
Answer: A
Question: Solution for 2.75+.003+.158
Options:
A)2.91
B)2.911
C)2.938
D)2.986
E)2.999
Rationale: 2.75+.003+.158=0
0=0-2.75-0.003-0.158
0=-2.911
answer :B
Answer: B
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
Options:
A)1898
B)1098
C)1000
D)2008
E)1082
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 10 * 10 * 10 = 1000
Answer:C
Answer: C
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
Options:
A)42 6/9%
B)42 3/7%
C)42 7/7%
D)42 6/7%
E)22 6/7%
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Answer: D
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is
Options:
A)3.34
B)3.39
C)3.37
D)3.33
E)3.31
Rationale: Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16
= 3.34 sq m
Answer:A
Answer: A
Question: If 40% of a number is equal to two-thirds of another number, what is the ratio of the first number to the second?
Options:
A)7 : 3
B)3 : 7
C)2 : 5
D)5 : 3
E)None of these
Rationale: Suppose the first number is x and the second numbery.
Therefore, 40% of x = 2⁄3 of y
∴ x⁄y = 2⁄3 × 100⁄40 = 5⁄3
Answer D
Answer: D
Question: Two trains having length of 140 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)10.2
B)10.4
C)10.6
D)10.8
E)11.2
Rationale: Distance = 140+160 = 300 m
Relative speed = 60+40 = 100 km/hr = (100×10)/36 m/s
Time = distance/speed = 300 / (100×10)/36 = 300×36 / 1000 = 3×36/10 = 10.8 s
Answer is D.
Answer: D
Question: In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
Options:
A)11 Years
B)12.6 Years
C)13 Years
D)13.5 Years
E)14 Years
Rationale: Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years
B)
Answer: B
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
Options:
A)5768
B)5760
C)5762
D)5766
E)5712
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
Answer: B
Answer: B
Question: On his first 4 tests, Rajeev received an average score of X points. If on his fifth test, he exceeds his previous average score by 20 points, what is his average score for his first 5 tests?
Options:
A)X + 5
B)X + 1
C)X + 4
D)X + 2
E)X + 3
Rationale: Total of 1st 4 tests= 4X
5th test score = X + 20
Total of all 5 tests = 5X + 20
Average = X + 4
Answer : C
Answer: C
Question: One train is traveling 18 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
Options:
A)1:2
B)5:6
C)5:0
D)5:4
E)5:1
Rationale: 18 * 5/18 = 10
5:10 => 1:2
Answer: A
Answer: A
Question: What approximate value should come in plce of question mark (?) in the following equations ?
728.038 x 54.978 - 72.016 x 85.250 = ?
Options:
A)31400
B)32700
C)33900
D)34400
E)32400
Rationale: Explanation :
? = 728 x 55 - 72 x 85.25
= 40040 - 6138 = 339900
Answer : Option C
Answer: C
Question: A train cruising at 50 km/hr takes 9 seconds to pass a platform. Next, it takes 3 seconds to pass a man walking at 3 km/hr in the same direction. Find the length of the train and that of the platform.
Options:
A)200/3m175/3m
B)40m85m
C)50m45m
D)100/3 m200/3
E)none of these
Rationale: A train running at 50 km/hr takes 9 seconds to pass a platform. Next, it takes 3 seconds to pass a man walking at 3 km/hr in the same direction. Find the length of the train and that of the platform.
Distance = Speed*time
It's probably best to convert to meters so we can find the length of the platform.
Distance = 50000 meters/h * 9 seconds*(1/60*60)
Distance =(55000*9 / [3600] ) = 125m
I'm not sure how we take the length of the train into account (if we do at all) to solve this problem. For example, If we were measuring by the time the very front of the train passed one end of the platform to the time the very front of the train passed the other end, the result would be different than if we counted when the very front of the train passed one end of the platform to the time the back side of the train passed the end.
As for the problem involving the man, the man is moving forward at a speed of 3km/h while the train is moving forward at a speed of 50km/h. Therefore, the train is moving past the man at a total speed of 47km/h.
distance = speed * time
distance = 47km/h * 3 seconds
distance (length of train) = 39.16 m
We know the length of the train is roughly 39.16m and the distance covered passing the platform was 125m. However, The platform isn't 125m long - it is 125m minus the length of the train long (or so I think) which is 125-39.16 or roughly 85m. Both of these answers are in A so I think that is the right answer. I am still having a bit of trouble conceptualizing why we have to subtract out the length of the train, however.
ANSWER: B) 40m85m
Answer: B
Question: What is the area of a regular hexagon with sides 1 in. long?
Options:
A)1.59 square inch
B)2.59 square inch
C)3.59 square inch
D)4.59 square inch
E)2.69 square inch
Rationale: A regular hexagon of side 1 inch can be divided in to 6 equilateral triangle of side 1 inch.
Area of each triangle = (root 3/4)* side^2 = (root 3/4)
Area of 6 triangles = 6*(root 3/4)= 1.5 root 3= 2.59 square inch
ANSWER:B
Answer: B
Question: In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2, If Rs 157300 was their profit, how much amount did B receive.
Options:
A)Rs 48000
B)Rs 47000
C)Rs 47400
D)Rs 48400
E)None of these
Rationale: Explanation:
A:B = 3:2 = 6:4
=> A:C = 2:1 = 6:3
=> A:B:C = 6:4:3
B share = (4/13)*157300
= 48400
Option D
Answer: D
Question: Average of 10 matches is 32, How many runs one should should score to increase his average by 6 runs.
Options:
A)A)70
B)B)76
C)C)78
D)D)98
E)E)88
Rationale: Explanation:
Average after 11 innings should be 38
So, Required score = (11 * 38) - (10 * 32)
= 418 - 320 = 98
Answer: Option D
Answer: D
Question: What is the probability of getting a sum 9 from two throws of a dice?
Options:
A)1/6
B)1/8
C)1/9
D)1/12
E)None
Rationale: Solution
In two throws of a die, n(S) = (6×6)
= 36.
Let E = event of getting a sum 9= {{3,6),(4,5),(5,4),(6,3)}
P(E)	= n(E) / n(S)
= 4/36
‹=›1/9.
Answer C
Answer: C
Question: The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
Options:
A)5.025%
B)5.25%
C)6.125%
D)7.34%
E)8.43%
Rationale: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W
Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%
C
Answer: C
Question: Three cubes of metal whose edges are 5, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
Options:
A)28
B)77
C)17.3
D)18
E)99
Rationale: 53 + 123 + 153 = a3 => a
= 17.3
Answer: C
Answer: C
Question: (3x + 4) (2x - 5) = ax^2 + kx + n . What is the value of a - n + k ?
Options:
A)5
B)8
C)9
D)10
E)15
Rationale: Expanding we have 6x^2 -15x + 8x -20
6x^2 - 7x - 20
Taking coefficients, a = 6, k= -7, n = -20
Therefore a - n + k = 6 - (-20) - 11 = 26 - 11 = 15
The answer is E.
Answer: E
Question: A number is missing from the number series below.
Can you find it ?
84, 155, 258, ? , 584, 819.
Options:
A)275
B)350
C)399
D)421
E)449
Rationale: C
The missing number is 399.
84 = 4^3 + 3^2 + 4
155 = 5^3 + 5^2 + 5
258 = 6^3 + 6^2 + 6
584 = 8^3 + 8^2 + 8
819 = 9^3 + 9^2 + 9
Thus,
399 = 7^3 + 7^2 + 7
Answer: C
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen?
Options:
A)3
B)6
C)7
D)8
E)12
Rationale: Sol. lie purchases 6a bananas mere for 4096 of Rs 40 or, Rs 16. Reduced price per do,. 3
A
Answer: A
Question: If 35% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
Options:
A)110
B)330
C)572
D)430
E)880
Rationale: Students enrolled in biology are 35% and therefore not enrolled are 65%. so of 880 is 880*.65 = 572
Answer is C 572
Answer: C
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
Options:
A)1.44%
B)1.43%
C)1.34%
D)4.44%
E)1.74%
Rationale: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
Answer: A
Answer: A
Question: Eighteen dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we make from these 18 dots that do not form an equilateral triangle?
Options:
A)792
B)798
C)804
D)810
E)816
Rationale: The total number of ways we can choose three dots is 18C3=816.
We can form six equilateral triangles from these eighteen dots.
There are 816 - 6 = 810 combinations which do not form an equilateral triangle.
The answer is D.
Answer: D
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph?
Options:
A)21.4 sec
B)77 sec
C)25 sec
D)18 sec
E)17 sec
Rationale: D = 100 + 150 = 250
S = 42 * 5/18 = 11.7 mps
T = 250/11.7 = 21.4 sec
Answer:A
Answer: A
Question: What is the smallest positive integer x such that 108x is the cube of a positive integer?
Options:
A)2
B)4
C)8
D)10
E)7
Rationale: Given 108x is a perfect cube
so we will take 216 = 6*6*6
108x = 216
x = 216/108 = 2
correct option is A
Answer: A
Question: Calculate the sum of first 89 natural numbers.
Options:
A)2017
B)2647
C)2147
D)2045
E)4005
Rationale: Solution
We know that(1+2+3+.....+89)	= n(n+1)/2
Therefore (1+2+3+....+89)	=(89×90 / 2)
= 4005.
Answer E
Answer: E
Question: A and B can do a work in 18 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?
Options:
A)360/13 days
B)350/13 days
C)160/13 days
D)260/13 days
E)960/13 days
Rationale: One day work of A and B = 1/18
One day work of B and C = 1/30
One day work of C and A = 1/36
2(A + B + C) = 1/18 + 1/30 + 1/36
2(A + B + C) = 21/180
(A + B + C) = 13/360
Number of days required = 360/13 days.
ANSWER:A
Answer: A
Question: Einstein walks on an escalator at a rate of 5steps per second and reaches the other end in 10 sec. while coming back, walking at the same speed he reaches the starting point in 40secs. What is the number of steps on the escalator?
Options:
A)22
B)80
C)28
D)17
E)11
Rationale: Escalator problems are similar to boats and streams problems. If we assume man's speed as 'a m/s' and escalator speed as 'b m/sec' then while going up man's speed becomes 'a -b' and while coming down 'a + b'.
In this question, Let the speed of escalator be b steps per sec. And length of escalator be L. Einstein's speed = 5 steps/ sec
While going down, L5+x=10L5+x=10 ⇒⇒ L = 50 + 10x
While coming up, L5−x=40L5−x=40 ⇒⇒ L = 200 - 40x
Multiply the first equation by 4, and add to the second, we get L = 80
Answer:B
Answer: B
Question: If n is a natural number, then (7(n2) + 7n) is always divisible by:
Options:
A)3 and 7
B)14 only
C)7 only
D)7 and 14
E)NONE
Rationale: Solution
(7n2 + 7n) = 7n(n + 1), which is always divisible by 7 and 14 both, since n(n + 1) is always even.
Answer D
Answer: D
Question: a * b = 2a - 3b + ab, then 3*5 + 5*3 = ?
Options:
A)20
B)21
C)22
D)Bedford is at one end.
E)Mercedes is at one end.
Rationale: Explanation:
= 2(3)-3(5)+(3*5) + 2(5)-3(3)+(5*3)
= 6-15+15+10-9+15 = 31-9 = 22
Option E
Answer: E
Question: If |y + 5| = 8, what is the sum of all the possible values of y?
Options:
A)-14
B)-13
C)-8
D)-12
E)-10
Rationale: There will be two cases
y+5 = 8 or y+5 = -8
=> y = 3 or y= -13
sum of both the values will be -13 + 3 = -10
Answer: E
Answer: E
Question: How many positive integers between 1 and 200 are there such that they are multiples of 17?
Options:
A)9
B)11
C)13
D)10
E)8
Rationale: Multiples of 17= 17,34,51,-----187
Number of multiples of 17 => 17*11= 187
Answer is B
Answer: B
Question: A discount of 10 percent on an order of goods followed by a discount of 20 percent amounts to
Options:
A)the same as one 45 percent discount
B)the same as one 38 percent discount
C)the same as one 36 percent discount
D)the same as one 30 percent discount
E)the same as one 28 percent discount
Rationale: 0.9*0.8*x=0.72x from initial value, meaning 0.28 or 36% discount
E
Answer: E
Question: Divide Rs. 3364 between A and B, so that A's Share at the end of 5 years may equal to B's share at the end of 7 years, compound interest being at 5 percent.
Options:
A)Rs. 1764 and Rs.1600
B)Rs. 1756 and Rs.1608
C)Rs. 1722 and Rs.1642
D)Rs. 1732 and Rs.1842
E)None of these
Rationale: Explanation: A's share after 5 years = B's share after 7 years
(A's present share)(1+5100)5 = (B's present share)(1+5100)7
=>(A's present share)/(B's present share) = (1+5/100)7/(1+5/100)5 = (1+5/100)(7−5) = (1+5/100)2 =(21/20)2 =441/400
i.e, A's present share : B's present share = 441 : 400
Since the total present amount is Rs.3364, A's share = 3364 × 441/(441 + 400)
= (3364 × 441)/841 = 4 × 441 = Rs. 1764
B's present share = 3364 - 1764 = Rs.1600
Answer: Option A
Answer: A
Question: A train passes a station platform in 37 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)328
B)255
C)240
D)288
E)231
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 / 37 = 15
x + 300 = 555
x = 255 m. Answer:B
Answer: B
Question: A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many Q apples did each person get before 45 people joined the feast?
Options:
A)20.
B)21.
C)22.
D)23.
E)24.
Rationale: Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13.
Since number of apples per person * total persons Q= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.C
Answer: C
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Options:
A)180 sec
B)190 sec
C)170 sec
D)175 sec
E)195 sec
Rationale: Explanation:
L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
ANSWER IS B
Answer: B
Question: A tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes. The inlet pipe fills water into the tank at the rate of 3 cubic inches/min and the 2 outlet pipes empty it out at the rates of 12 cubic inches/min and 6 cubic inches/min respectively. If all 3 pipes are opened when the tank is full, how many minutes does it take to empty the tank? (1 foot = 12 inches)
Options:
A)2345
B)3456
C)4567
D)5678
E)6789
Rationale: The tank is emptied at this rate: 12 + 6 - 3 = 15 cubic inches/min
The tank has a volume of 30*12*12*12 = 51840 cubic inches.
The time it takes to empty the tank is 51840/15 = 3456 minutes.
The answer is B.
Answer: B
Question: In an exam, Libi scored 78 percent, Nibi scored 75 percent and Catherine 85 percent. The maximum score awarded in the exam is 1100. Find the average mark scored by all the three boys?
Options:
A)874.65
B)873.66
C)871.22
D)872.67
E)870.2
Rationale: Average mark scored by all the three boys =
[78/100 (1100) + 75/100 (1100) + 85/100 (1100)] / 3
(858+825+935)/3= 872.67
Answer: D
Answer: D
Question: The ratio of the amount of the oil bill for the month of February to the amount of the oil bill for the month of January was 3:2. If the oil bill for February had been $30 more, the corresponding ratio would have been 5:3. How much was the oil bill for January?
Options:
A)$120
B)$150
C)$180
D)$210
E)$240
Rationale: 3:2 = 9:6 and 5:3 = 10:6.
An increase in $30 increases the ratio by 1:6.
Therefore, January's bill was 6($30) = $180.
The answer is C.
Answer: C
Question: A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of B square inches. Which of the following equations must be true?
Options:
A)2W^2 + PW + 2B = 0
B)2W^2 − PW + 2B = 0
C)2W^2 − PW − 2B = 0
D)W^2 + PW + B = 0
E)W^2 − PW + 2B = 0
Rationale: P = 2(L+W)-----------------1)
B= LW------------------------2)
option A is not possible why ?? because all the terms are positive.
lets try option B , put value of P and B from 1 and 2 we have,
2W^2-2(L+W)W + 2(LW)
2W^2 - 2LW - 2W^2 + 2LW=0.
hence answer is B.
Answer: B
Question: If the milk and water ware added in the ratio 5:4 then how much more water should be added so he gets the ratio of 6:7.
Options:
A)5/6
B)11/6
C)7/6
D)11/5
E)5/11
Rationale: let quantity of water should added be x then
A/Q
5/(4+x)= 6/7
=> 35=24+6x
=> x=11/6
ANSWER:B
Answer: B