divelab/Sys2Bench huggingface dataset:
Question: Jenny received a 10% raise each month for three consecutive months. What was her salary after the three raises if her starting salary was $2,000 per month?
Options:
A)$2,248
B)$2,300
C)$2,331
D)$2,410
E)$2,662
Rationale: 2000 * 1.1 * 1.1 * 1.1 = 2000 * 1.331 = 2662
Answer: E
Answer: E
Question: A football team lost 5 yards and then gained 7. What is the team's progress?
Options:
A)2
B)4
C)5
D)6
E)8
Rationale: For lost, use negative. For gain, use positive.
Progress = -5 + 7 = 2 yards
A
Answer: A
Question: A train , having a length of 275 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
Options:
A)10 sec
B)8 sec
C)15 sec
D)4 sec
E)2 sec
Rationale: Explanation:
Distance = 275 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 275/(110/6) = 15 s
Answer: Option C
Answer: C
Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get?
Options:
A)2837
B)2839
C)2834
D)2822
E)2823
Rationale: Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 8720
32.5k = 32.5k/100k * 8720 = 2834
The number of valid votes polled in favour of B is 2834.
Answer:C
Answer: C
Question: Rahim bought 65 books for Rs.1150 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ?
Options:
A)38
B)18
C)99
D)277
E)22
Rationale: Average price per book = (1150 + 920) / (65 + 50) = 2070 / 115 = Rs.18.Answer:B
Answer: B
Question: Solve for x: 2x – y = (3/4)x + 6.
Options:
A)(y + 6)/5
B)4(y + 6)/5
C)(y + 6)
D)4(y - 6)/5
E)5/4(y-6)
Rationale: Solution:
2x – y = (3/4)x + 6.
or, 2x - (3/4)x = y + 6.
or, (8x -3x)/4 = y + 6.
or, 5x/4 = y + 6.
or, 5x = 4(y + 6).
or, 5x = 4y + 24.
or, x = (4y + 24)/5.
Therefore, x = 4(y + 6)/5.
correct answer B
Answer: B
Question: The average of 9 numbers is 7 and the average of 7 other numbers is 6. What is the average of all 16 numbers?
Options:
A)6 9/16
B)8
C)7 7⁄8
D)7 1⁄2
E)7 1⁄4
Rationale: The average of 9 numbers is 7....
The sum of those numbers is (9)(7) = 63.
The average of 7 other numbers is 6....
The sum of those numbers is (7)(6) = 42
The sum of ALL 16 numbers is 63+42 = 105. The average of those numbers is 105/16 = 6 9/16.
Final Answer:
[Reveal]Spoiler:
A
Answer: A
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 800 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
Options:
A)2880.
B)4860.
C)5780
D)5760
E)6380.
Rationale: Normal Day = 800 kw/h
Stormy Day = 800*1.2=960 kw/h
3 windmills for 2 hours on stormy day
960*3*2=5760
Answer: D
Answer: D
Question: 3x^2 - x - 4 =
Options:
A)(3x-4)(x-2)
B)(3x-4)(x+2)
C)(3x-4)(x-3)
D)(3x-2)(x+1)
E)none of above
Rationale: 3x^2 + 2x - 8
= 3x^2 + 3x - 4x - 4
= 3x (x + 1) - 4 (x+1)
= (3x-4) (x+1)
Option D
Answer: D
Question: In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of five metre is left from all sides of the boundary of the garden. What is the length of the garden?
Options:
A)32
B)24
C)26
D)28
E)30
Rationale: Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length
Also, 5 meter is left from all sides of the boundary of the garden.
Hence, length of the garden = (11 Ã— 2) + 5 + 5 = 32 meter
Answer is A.
Answer: A
Question: What number is that, to which, if its half be added, and from the sum 20 be subtracted, the remainder will be a fourth of the number itself?
Options:
A)16/3
B)16/2
C)16/4
D)16/1
E)None
Rationale: let x be put for the number required.
Then by the conditions proposed, x + x/2 - 20 = x/4
And reducing the equation x = 16.
Proof, 16 + 16/2 - 20 = 16/4.
Answer C
Answer: C
Question: The greatest common factor of two positive integers is B. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?
Options:
A)BY⁄Z
B)XZ + YZ
C)X⁄Z + Y
D)X + Y⁄Z
E)X + Z⁄Y
Rationale: Say other integer is W
Formula
GCF(WZ)*LCM(WZ) = W*Z
B*Y = W*Z
So W= BY/Z
Answer A
Answer: A
Question: A woman has four blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
Options:
A)8
B)22
C)16
D)17
E)18
Rationale: total ways = 4*3*2=24..
now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..
the ways in which the pink blose and green skirty are together=1*1*2=2..
total ways =24-2=22..
B
Answer: B
Question: How many of the positive factors of 33 are not factors of 45?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Factors of 33 - 1, 3, 11, 33,
factors of 45- 1, 3, 5, 9, 15, 45,
Comparing both, we have three factors of 33 which are not factors of 45- 11, 33,
The answer is C
Answer: C
Question: A box contains ten bulbs out of which 5 are defective. If five bulbs are chosen at random, find the probability that atleast one bulb is good?
Options:
A)251/252
B)242/243
C)258/259
D)265/266
E)247/248
Rationale: Required probability=1-5C5/10C5= 1 - 1/252= 251/252Answer:A
Answer: A
Question: In how many ways can 5 people, A, B, C, D, E, be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
Options:
A)384
B)396
C)576
D)24
E)696
Rationale: Number of total arrangements = 5!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
5! - (4!*2*2) = 120 - (24*2*2) = 24
Answer D
Answer: D
Question: A box contains 3 blue marbles, 4 red, 5 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Options:
A)1/364
B)2/455
C)1/91
D)4/455
E)None of these
Rationale: Given that there are three blue marbles, four red marbles, five green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = 3C₃/14C₃ = (1 * 3 * 2 * 1)/(14 * 13 * 12) = 1/364
ANSWER:A
Answer: A
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)15 sec
B)16 sec
C)18 sec
D)20 sec
E)25 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
ANSWER: B
Answer: B
Question: The cost of carpeting a room 18m long with a carpet 75cm wide at 45 paise per meter is Rs.81. The breadth of the room is:
Options:
A)7m
B)7.5metre
C)5.5m
D)6.5m
E)8.5m
Rationale: Length of the carpet= Total cost/ rate/m= 8100/45=180m
Area of the carpet= 180*75/100= 135m2
Breadth of the room = (Area/ length)= 135/18= 7.5m
ANSWER:B
Answer: B
Question: The area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?
Options:
A)40 m3
B)50 m3
C)60 m3
D)90 m3
E)40 m3
Rationale: Explanation:
lb = 20 ; lh = 15 ; fh = 12
(lbh)2 = 20 * 15 * 12 => lbh = 60 m3
Answer: Option C
Answer: C
Question: -20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 5 greater than the preceding term. Which of the following could not be a term in the sequence?
Options:
A)0
B)200
C)440
D)665
E)762
Rationale: Ans : E 762
Since 762 is not divisible by 5 , all the other options are divisible by 5
Answer: E
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
Options:
A)1200
B)2400
C)4800
D)Cannot be determined
E)None
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Solve the (ii) and (iii) equations,then will get
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
Option B
Answer: B
Question: How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?
Options:
A)376
B)367
C)297
D)268
E)198
Rationale: The smallest number in the series is 1000, a 4-digit number.
The largest number in the series is 4000, the only 4-digit number to start with 4.
The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.
Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.
Including 4000, there will be 376 such numbers.
Answer: A
Answer: A
Question: It costs $2 for the first 1/6 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $15 per hour. If a certain customer uses the laundry machine for 2 hours and 25 minutes, how much will it cost him?
Options:
A)$42.25.
B)$40.25.
C)$38.25.
D)$36.25.
E)$34.25
Rationale: 2 hrs 25 min = 145 min
First 10 min ------> $2
Time left is 135 min...
Now, 60 min costs $ 15
1 min costs $ 15/60
145 min costs $ 15/60*145 => $ 36.25
So, Total cost will be $36.25 + $2 => $ 38.25
Hence answer will be C
Answer: C
Question: The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 5 times the probability that both events A and B occur. What is the probability that event A occurs?
Options:
A)1/45
B)1/2
C)1/8
D)2/3
E)2/11
Rationale: Let us say probability of A occuring is a.
Let us say probability of B occuring is b.
a = 2b
Probability (either A or B or both) = 5 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 5*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 5*2b*b
3b-2b^2 = 110b^2
3b = 12b^2
b = 3/12 = 1/4
So, a = 2b = 1/2
Answer: B
Question: If A is the set of numbers possible for the eighth term in a sequence of eight consecutive integers that has 6 as its fourth term, which of the following is A?
Options:
A)2 and 11
B)2 and 10
C)2 and 9
D)3 and 9
E)3 and 10
Rationale: First Take 6 as the 4th term from begiining, 8th term will be 10.
Now, take 6 as the 4th last term from the beginning, 8th last term will be 2. Hence B.
Answer: B
Question: Today is Monday. After 61 days, it will be
Options:
A)Thursday
B)Sunday
C)Monday
D)Saturday
E)None of these
Rationale: Explanation :
61 days = 8 weeks 5 days = 5 odd days
Hence if today is Monday, After 61 days, it will be = (Monday + 5 odd days)
= Saturday .Answer : Option D
Answer: D
Question: A project manager needs to select a group of 3 people from a total of 3 men and 3 women. How many possible group combinations exist such that no group has all men ?
Options:
A)72
B)68
C)24
D)19
E)48
Rationale: Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).
The formula for combinations is:
N!/((N-K)!K!)
Where N = the total number of elements from which we will select, 6 people in this case.
Where K = the total number of elements to select, 3 people in this case.
The total number of combinations is therefore:
6!/((6-3)!3!) = 20
However, one of these combinations are not valid since they have all members of men
The correct answer is 20-1 = 19. Ans D
Answer: D
Question: I have twenty 3g stamps and twenty 5g stamps. Using one or more of these stamps, how many
different amounts of postage can I make?
Options:
A)150
B)152
C)154
D)396
E)400
Rationale: We need to find how many positive integers can be represented in the form 3n+5m
where n and m are integers between 0 and 20, but not with both of them 0. First, let us see
which integers divisible by 3 can be represented in this form. These are 3; 6; 9; ; 60 if we
set m = 0, and if we let m be 3; 6; 9; 12; 15; or 18, we get that the multiples of 3 we can
represent are 3; 6; 9; ; 150. There are thus 50 multiples of 3 we can represent. Working
similarly, we get that 5; 8; 11; ; 155 are the integers which give remainder 2 when divided
by 3, and which we can represent, giving 51 numbers of this form. Finally, the numbers which
give remainder 1 when divided by 3, and which can be represented in the desired form, are
10; 13; 16; ; 160. There are 51 of them. So, the answer is 50 + 51 + 51 = 152.
correct answer B
Answer: B
Question: If a, b, c, and d are integers; w, x, y, and z are prime numbers; w < x < y < z; and (wa)(xb)(yc)(zd)=660(wa)(xb)(yc)(zd)=660, what is the value of (a + b) – (c + d)?
Options:
A)–1
B)0
C)(a + b) – (c + d)=1
D)2
E)3
Rationale: 660660= 2^2 x 3^1 x 5^1 x 11^1
w < x < y < z = 2 < 3 < 5 < 11
So, can can say -
w = 2
x = 3
y = 5
z = 11
Hence a = 2 , b = c = d = 1
(a + b) – (c + d) will be (2 + 1) – (1 + 1) = 1
Answer will be (C)
Answer: C
Question: A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train?
Options:
A)370
B)782
C)278
D)270
E)881
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 150)/26 = 20
x = 370 m.
Answer: A
Answer: A
Question: A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?
Options:
A)10
B)8
C)6
D)4
E)2
Rationale: Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = 300/x
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5(300/x) - 10x - 50 = 0 => -150 + x2 + 5x = 0
multiplying both sides by -1/10x
=> x2 + 15x - 10x - 150 = 0
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.
ANSWER:A
Answer: A
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 6-letter code words?
Options:
A)1
B)1/4
C)1/5
D)1/3
E)1/2
Rationale: Method #1: Using the permutation formula
# of 5 letter code words:
nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6
# of 6 letter code words:
nPr = 10! / (10 – 6)! = 10*9*8*7*6*5
# of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7*6*5) = 1/5
C
Answer: C
Question: What is 120% of 13/24 of 960?
Options:
A)420
B)484
C)526
D)578
E)624
Rationale: 120% * 13/24 * 360 = 1.2 * 13 * 40 = 624
The answer is E.
Answer: E
Question: A man can row 40km upstream and 55km downstream in 13 hours also, he can row 30km upstream and 44km downstream in 10 hours. find the speed of the man in still water and the speed of the current.
Options:
A)5 and 3
B)8 and 3
C)3 and 8
D)3 and 5
E)None of them
Rationale: let rate upstream=x km/hr and rate downstream=y km/hr.
Then,40/x +55/y =13…(i) and 30/x +44/y =10
Multiplying (ii) by 4 and (i) by 3 and subtracting ,we get:11/y=1 or y=11.
Substituting y=11 in (i),we get:x=5.
Rate in still water =1/2(11+5)kmph=8kmph.
Rate of current=1/2(11-5)kmph=3kmph
Answer is B.
Answer: B
Question: A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40,000 liters of petrol is used daily, the suply fails in 90 days.If 32,000 liters of petrol is used daily, it fails in 60 days. How much petrol can be used daily with out the supply ever failing?
Options:
A)64000 liters
B)56000 liters of petrol
C)78000 liters
D)60000 liters
E)None of these
Rationale: Explanation:
Let x liter be the per day filling and v litr be the capacity of the reservoir, then
90x + v = 40000 × 90 -----(1)
60x + v= 32000 × 60 ------(2)
solving eq.(1) and (2) , we get
x = 56000
Hence , 56000 liters per day can be used without the failure of supply.
Answer: B
Answer: B
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)180 m
B)200 m
C)240 m
D)320 m
E)None
Rationale: Sol.
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 metres.
Then, x + 300 / 36 = 15 ⇔ x + 300 = 540 ⇔ x = 240 m.
Answer C
Answer: C
Question: If p#q denotes the least common multiple of p and q, then T=((12#16)#(18#24)) = ?
Options:
A) 216
B) 180
C) 144
D) 108
E) 72
Rationale: There are several ways to find the Least Common Multiple of two numbers. In this case, the most efficient method is to use the Greatest Common Factor: (A * B) / (GCF AB) = LCM AB
The greatest common factor of 12 and 16 is 4. So, 12#16 = 12*16/4 = 48.
The greatest common factor of 18 and 24 is 6. So, 18#24 = 18*24/6 = 72
Finally, the greatest common factor of 48 and 72 is 24. So,T= ((12#16)#(18#24)) = 48#72 = (48*72)/24 = 2*72 = 144
The correct answer is C.
Answer: C
Question: In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 4 rows in all and a total of 134 bricks in the wall, how many bricks does the bottom row contain ?
Options:
A)30
B)31
C)32
D)33
E)34
Rationale: The bottom row has x bricks
x+x-1+x-2+x-3 = 134
4x-6=134
4x=128
x=32
Answer:C
Answer: C
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Options:
A)Rs.14000
B)Rs.1000
C)Rs.10500
D)Rs.2050
E)Rs.5500
Rationale: Explanation:
25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = Rs.14000
ANSWER:A
Answer: A
Question: Machine A can finish a job in 6 hours, Machine В can finish the job in 12 hours, and Machine С can finish the job in 8 hours. How many hours will it take for A, B, and С together to finish the job?
Options:
A)6/5
B)7/4
C)8/3
D)9/2
E)12/5
Rationale: The combined rate is 1/6+1/12+1/8 = 9/24 of the job per hour.
The time to complete the job is 24/9 = 8/3 hours.
The answer is C.
Answer: C
Question: How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 2 ?
Options:
A)2
B)3
C)4
D)5
E)0
Rationale: A number ending with 2 can never be a perfect square.
Answer: E
Answer: E
Question: Diesel costs Rs.4 per lit and petrol costs 6.83 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol.
Options:
A)9 months
B)5 months
C)6 months
D)3 months
E)2 months
Rationale: Explanation :
=>In the First Month the price of the diesel would be 4*110/100 = 4.4
=>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84
=>In the Third Month the price of the diesel would be 4.84*110/100 = 5.324
=>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85
=>In the fifth Month the price of the diesel would be 5.85*110/100 = 6.44
=>In the sixth Month the price of the diesel would be 6.44*110/100 = 7.08 which is higher than the price of petrol
Answer : C
Answer: C
Question: y = 248 - 343x
Which of the following values of x gives the greatest value of y in the equation above?
Options:
A) 200
B) 100
C) -7
D) 0
E) 10
Rationale: Clearly, the negative value of x will result in maximum value of y.
Don't even look at the rest of the answer choices as only one negative value is being present.
Answer is C
Answer: C
Question: Reena took a loan of 1000 with simple interest for as many years as the rate of interest. If she paid 40 as interest at the end of the loan period, what was the rate of interest?
Options:
A)3.8
B)2
C)6
D)Cannot be determined
E)None
Rationale: Explanation: Let rate = R% and time = R years.
Then, (1000 x R x R)/100 = 40
10RÂ² = 40
RÂ² = 4
R = 2.
Answer: Option B
Answer: B
Question: Evaluate 28% of 450 + 45% of 280
Options:
A)232
B)242
C)252
D)262
E)250
Rationale: Explanation:
= (28/100) * 450 + (45/100) * 280
= 126 + 126 = 252
Answer IS C
Answer: C
Question: If a:b = 4:1, then find (a - 3b)/(2a - b)?
Options:
A)6/7
B)1/7
C)5/7
D)3/2
E)4/7
Rationale: Answer: Option B
a/b = 4/1 => a = 4b
(a - 3b)/(2a - b) = (4b - 3b)/(8b - b)
= b/7b => 1/7
Answer: B
Question: In a car wheel, two spokes cover 10 degree. Then for the entire car,how many spokes are there?
Options:
A)128
B)168
C)248
D)268
E)288
Rationale: given, 2 spokes cover 10degrees,
so for 360 degrees.---->360*2/10=72..
so, for entire car, 4*72=288
ANSWER:E
Answer: E
Question: If one-third of one-fourth of a number is 15, then three-tenth of that number is
Options:
A)35
B)15
C)60
D)54
E)57
Rationale: Let the number be x. then 1/3 of ¼ of x=15
X=15x12=180
The required number=(3/10)*180=54
ANSWER D 54
Answer: D
Question: If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?
(i) x is prime
(ii) y is even
(iii) xy is positive
Options:
A)ii only
B)iii only
C)i and iii only
D)ii and iii only
E)i, ii and iii
Rationale: Effectively y = 36x/41
(i) x is prime: now if y = 36x/41 and both x and y are integers; then if x= 41, 36(41)/41 .....so the 41s cancel each other out and you get x=36. Hunky dory. But if x = 82; you get y =72 which also works. Hence x is not necessarily prime.
(ii) y is even: y = 36(41)/41 = 36 (even). Or try 36(82)/41 = 72 (even). When you multiply even with odd, answer is even. So Y HAS TO BE EVEN.
(iii) xy is positive. Hmm. So if y is positive, then x is positive. Because if you have a -ve value of x, it leads to -ve value of y. Hence I would say iii is the answer. ANSWER:B
Answer: B
Question: A certain company has budgeted $1560 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $420, how much was the company under budget or over budget?
Options:
A)$60 under budget
B)$30 under budget
C)$30 over budget
D)$60 over budget
E)$180 over budget
Rationale: The budget for 3 months is (3/12)*$1560 = $390
The company is $30 over budget.
The answer is C.
Answer: C
Question: In a consignment of eggs 552 were cracked, which was 12 percent of the total consignment. How many eggs were in the consignment?
Options:
A)4400
B)4800
C)4300
D)4600
E)4900
Rationale: D
4600
(552 ÷ 12) × 100 = 4600.
Answer: D
Question: P,Q and R together earn Rs.1800 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
Options:
A)s.50
B)s.70
C)s.90
D)s.100
E)s.120
Rationale: Explanation :
Amount Earned by P,Q and R in 1 day = 1800/9 = 200 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120	---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130	---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
- Amount Earned by P,Q and R in 1 day = 120+130-200 = 50
=>Amount Earned by R in 1 day = 50
Answer : Option A
Answer: A
Question: A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 6 volts, what was the smallest possible recording in volts?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: if average of 3 is 6 so sum of 3 should be 18
3 recording can be from 0-10 inclusive
to find one smallest other two should be highest
so, lets assume three var are a,b,c
say a is smallest and give b and c greatest readings say 8 and 8
so a has to be 2
A
Answer: A