divelab/Sys2Bench huggingface dataset:
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 36 days. If 40 more cows and 15 more buffaloes are brought in, how many days will the fodder last?
Options:
A)15 days
B)18 days
C)21 days
D)24 days
E)27 days
Rationale: 2 oxen = 3 buffaloes = 4 cows
Also: 15 buffaloes + 8 oxen + 24 cows
= 10 oxen + 8 oxen + 12 oxen = 30 oxen
There is enough fodder for 1 oxen for 30*36 days.
40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen
The new total is equal to 60 oxen instead of 30 oxen.
30*36 / 60 oxen = 18 days
The answer is B.
Answer: B
Question: The average age 10 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Options:
A)20
B)99
C)77
D)26
E)12
Rationale: 10 * 2 = 20 years
Answer: A
Answer: A
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
Options:
A)19 : 6
B)19 : 4
C)19 : 1
D)19 : 5
E)19 : 3
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
Answer:D
Answer: D
Question: Kelly and Jody packed boxes with books. If Jody packed 30% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?
Options:
A)1 to 6
B)1 to 4
C)3 to 7
D)3 to 5
E)2 to 3
Rationale: Explanation:
If Jody packed 30% of the boxes then Kelly packed 70%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 30%/70%=3/7
Answer: Option C
Answer: C
Question: A clock is started at noon. By 10 minutes past 5, the hour hand has turned through how much?
Options:
A)175°
B)155°
C)145°
D)165°
E)195°
Rationale: We know that angle traced by hour hand in 12 hrs = 360°
Time duration from noon to 10 minutes past 5
= 5 hours 10 minutes
=5(10/60) hour =31/6 hour
Hence the angle traced by hour hand from noon to 10 minutes past 5
=31/6×360/12=31/6×30
=31×5=155°
Answer is B.
Answer: B
Question: A plot ABCD is as shown in figure, where AF = 30 m, CE = 40 m, ED = 50 m, AE = 120 m. Find the area of the plot ABCD?
Options:
A)1828 sq.m
B)2767 sq.m
C)2789 sq.m
D)7200 sq.m
E)2651 sq.m
Rationale: Area of plot ABCD = Area of ADE + Area of AFB + Area of BCEF
= 1/2 * 50 * 120 + 1/2 * 40 * 30 + 40 * 90
= 3000 + 600 + 3600
= 7200 sq.m
Answer:D
Answer: D
Question: The cost of 5 kgs. of sugar is Rs.279. What is the cost of 1 kg of sugar?
Options:
A)Rs.55
B)Rs.55.80
C)Rs.65.80
D)Rs.65
E)Rs.75
Rationale: Explanation:
The cost of kgs. of sugar = 279x 1/5= Rs.55.80
Answer: Option :B
Answer: B
Question: By how much is three-fifth of 350 greater than four- seventh of 210 ?
Options:
A)95
B)110
C)120
D)None of these
E)Cannot be determined
Rationale: Solution
3/5of 350 - 4/7of 210 - 120 = 90.
Answer D
Answer: D
Question: What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12% p.a.?
Options:
A)Rs.10123.77
B)Rs.10123.21
C)Rs.10123.20
D)Rs.10123.28
E)Rs.10123.21
Rationale: Amount = [25000 * (1 + 12/100)3]
= 25000 * 28/25 * 28/25 * 28/25
= Rs. 35123.20
C.I. = (35123.20 - 25000)
= Rs. 10123.20
Answer:C
Answer: C
Question: Among 250 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 80 watch exactly two channels. How many watch exactly one channel?
Options:
A)185
B)160
C)175
D)190
E)195
Rationale: 250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
250 = n(Exactly 1 channel) + 80 + n(Exactly 3 channels)
Let's find the value of n(Exactly 3 channels) = x
250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
250 = 116 + 127 + 107 - 80 - 2x
x = 25
250 = n(Exactly 1 channel) + 80 + 25
n(Exactly 1 channel) = 160
Answer (B)
Answer: B
Question: A bag contains 4 yellow, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?
Options:
A)1/5
B)2/9
C)3/11
D)4/17
E)2/3
Rationale: Total number of balls = 4+2 = 6
n(S) = 6C3 = 6*5*4 / 3*2 = 20
n(E) = 2C2* 4C1 = 4
Probability = 4/20 = 1/5
Answer is A
Answer: A
Question: Surekha started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajesh joined him with an amount of Rs. 35,000. In 2001, Surekha invested another additional amount of Rs.10,000 and Jay joined them with an amount of Rs.35,000. What will be Rajesh's share in the profit of Rs.2,10,000 earned at the end of 3 years from the start of the business in 1999?
Options:
A)Rs 45000
B)Rs 50000
C)Rs 70000
D)Rs 75000
E)None
Rationale: Surekha:Rajesh:Jay= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajesh's share =Rs.(210000×2/6) = Rs.70000.
Answer C
Answer: C
Question: How many integers from 0 to 56, inclusive, have a remainder of 1 when divided by 3 ?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: My ans is also C.17.
Explanation:
1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.
Hence we have an arithmetic progression: 1, 4, 7, 10,..... 55, which are in the form 3n+1.
Now we have to find out number of terms.
tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.
so, 55 = 1+(n-1)3
or, (n-1)3 = 54
or, n-1 = 18
or, n = 19
E
Answer: E
Question: How much interest can a person get on Rs. 8200 at 17.5% p.a. simple interest for a period of two years and six months?
Options:
A)3587.58
B)3587.59
C)3587.5
D)3587.52
E)3587.56
Rationale: I = (8200 * 2.5 * 17.5)/100 = (8200 * 5 * 35)/(100 * 2 * 2) = Rs. 3587.50.Answer: C
Answer: C
Question: N number of persons decide to raise 3 lakhs by equal contributions from each. If they contributed 50 each extra, the contribution would be 3.25 lakhs. How many persons are there?
Options:
A)600
B)400
C)450
D)Cannot be determined
E)None of these
Rationale: Required persons = 325000−300000/50 = 500
Answer E
Answer: E
Question: If the sales tax be reduced from 4 (1/3) % to 2 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 8000?
Options:
A)146.69
B)146.66
C)146.62
D)146.61
E)146.6
Rationale: Explanation:
Required difference = (4 (1/3) of Rs. 8000) - (2 (1/2) of Rs. 8000)
= (13/3 – 5/2) % of Rs. 8000
= (11/6) x (1/100) x 8000
= Rs. 146.66
ANSWER: B
Answer: B
Question: In how many ways can you seat 8 people on a bench if one of them does not want to sit in one of the two middle seats or at either end?
Options:
A)17,540
B)18,360
C)19,320
D)20,160
E)21,480
Rationale: One person can choose 4 possible chairs to sit. The remaining 7 people can sit in 7! ways.
The number of arrangements is 4*7! = 20,160.
The answer is D.
Answer: D
Question: Express 25 mps in kmph?
Options:
A)22
B)87
C)90
D)77
E)22
Rationale: 25 * 18/5 = 90 kmph
Answer: C
Answer: C
Question: How many odd factors does 250 have?
Options:
A) 3
B) 4
C) 5
D) 6
E) 8
Rationale: Start with the prime factorization: 250 = 2*5*7
For odd factors, we put aside the factor of two, and look at the other prime factors.
set of exponents = {1, 1}
plus 1 to each = {2, 2}
product = 2*2 = 4
Therefore, there are 4 odd factors of 250.
Answer: B.
Answer: B
Question: A mirror 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches. What is the area of the frame, in square inches?
Options:
A)96
B)94
C)28
D)44
E)18
Rationale: This question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.
We're told that a mirror 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches. We're asked for the area of the mirror , in square inches.
Area of a rectangle = (length)(width)
So the area of the paper is... (8)(12) = 96
The mrror 'adds' 2 inches to the top, bottom, left and right 'sides' of the picture, so the area of EVERYTHING is...
(8+2+2)(12+2+2) = (12)(16) = 196
When we 'punch out' the area of the paper, we'll be left with the area of the FRAME:
192 - 96 = 96
Final Answer:
A
Answer: A
Question: If the perimeter of a rectangular garden is 700 m, its length when its breadth is 100 m is?
Options:
A)299 m
B)777 m
C)200 m
D)250 m
E)128 m
Rationale: 2(l + 100) = 700 => l
= 250 m
Answer:D
Answer: D
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds Q that it is an ace?
Options:
A)1/52
B)1/26
C)1/13
D)1/4
E)5/13
Rationale: The question should ask about the probability not the odds.
There are 13 spades, the probability Q that the spade we already have is an ace is therefore 1/13.
Answer: C.
Answer: C
Question: A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 10 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?
Options:
A)1200
B)996
C)1110
D)896
E)1400
Rationale: Pretty simple actually
Number of 1 letter symbols = 10
Number of 2 letter symbols = 10*10
Number of 3 letter symbols = 10*10*10
The answer is sum of the 3. = 10+100+1000 =1110
So the answer is C.
Answer: C
Question: In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?
Options:
A)8
B)9
C)7
D)6
E)2
Rationale: Since A beats B by 200 m or 25 seconds, i
t implies that B covers 200 m in 25 seconds.
Hence speed of B = 200/25 = 8 m/s.
Answer: A
Answer: A
Question: Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose?
Options:
A)1.25%
B)2.1%
C)2.25%
D)2.65%
E)3%
Rationale: Generally in such cases, there is always loss.
So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss.
Loss% = Common loss and gain% 2 = x 2
10 10
Therefore, here common loss and gain % = 15%
Hence,
Loss% = 15 2 = 2.25%
C
Answer: C
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Options:
A)3 : 1
B)3 : 2
C)3 : 6
D)3 : 7
E)3 : 9
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: Option B
Answer: B
Question: A no.when divided by 222 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
Options:
A)2
B)7
C)9
D)10
E)15
Rationale: 222 + 43 = 265/17 = 10 (Remainder)
D
Answer: D
Question: How many cuboids of length 5 m, width 4 m and height 3 m can be farmed from a cuboid of 16 m length, 10 m width and 12 m height.
Options:
A)32
B)28
C)36
D)40
E)50
Rationale: (16 Ã— 10 Ã— 12)/(5 Ã— 4 Ã— 3) = 32
Answer is A.
Answer: A
Question: A school has received 50% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
Options:
A)$400
B)$177.78
C)$320
D)$277
E)$200
Rationale: Let us suppose there are 100 people. 40% of them donated $16000 ( 400 * 40 )
$16000 is 50% of total amount.
So total amount = 16000 * 100/50
Remaining amount is 50% of total amount.
50% of total amount = 16000 * (100/50) * (50/100) =16000
This amount has to be divided by 50 ( remaining people are 50 )
So per head amount is 16000 / 50 = 320
ANSWER:C
Answer: C
Question: If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a × b × c < a^3
II. 5b < bc
III. a + b + c > a^3
Options:
A)I only
B)II only
C)III only
D)II and III
E)I, II, and III
Rationale: Only 'C' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4
Putting the values in the answers only 'C' seems valid.
Answer: C
Question: Jerome anticipated that the WebWeb.com stock price would fall and sold all his WebWeb.com stocks for $5 per stock. He paid $10,000 tax on the revenue. A week later, Jerome became convinced that the WebWeb.com stock price would rise, and he used the money that he had gotten from selling the WebWeb.com stocks to purchase them again, this time at $6 per stock. If Jerome ended up having 7000 WebWeb.com stocks fewer than the number he had before selling them, how many WebWeb.com stocks did he have originally?
Options:
A)10,000
B)11,600
C)17,000
D)14,000
E)16,400
Rationale: Let the number of shares be x.
5*x -10000(money paid in taxes) = 6(x- 7000)
Solving for x, we get the shares as 17000.
Ans :(Option C)
Answer: C
Question: 72 hens cost Rs. __ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand?
Options:
A)Rs. 3.23
B)Rs. 5.11
C)Rs. 5.51
D)Rs. 7.22
E)None
Rationale: Explanation :
The best way to solve this question is to multiply the alternatives by 72 and find which one gives the middle three digits 96.7.
To cut time, you can choose to multiply 72 by integer values only, e.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504.
It must be remembered that the decimal part of the answer will be multiplied by 72 and the actual answer will increase .
Let us now roughly multiply the decimal values of the options also by 72,
e.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2 and 72 × 0.5 = 36.
So, option (1) will yield (216 + 14) = 230 (approximately),
option(2) will yield (360 + 7) = 367 (approximately),
option(3) will yield (360 + 36) = 396 (approximately),
and option(4) will yield (504 + 14) = 528 (approximately).
Of these only option (3) satisfies our requirement of 2nd and 3rd digits being 96.
Answer : C
Answer: C
Question: what is the nearest no. to 2304 which is divisible by 21?
Options:
A)2289
B)2310
C)2333
D)2456
E)2309
Rationale: remainder when 2304 is divided by 21=15
so,no. should added to make 15 to 21=6
no.=2304+6=2310
answer B
Answer: B
Question: A manufacturer of a certain type of screw rejects any screw whose length is less than 2.47 centimeters or greater than 2.53 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?
Options:
A)|k + 0.03| > 2.5
B)|k — 0.03| <= 2.5
C)|k — 2.5| > 0.03
D)|k — 2.5| >= 0.06
E)|k — 2.5| <= 0.03
Rationale: So, let's go through this step by step:
Any screw that is less than: 2.47 or greater than 2.53 will be rejected.
If k represents the length of a screw
In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:
2.47 ≤ K ≤ 2.53
You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.
Let's look at (E):
|k — 2.5| <= 0.03
For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53
For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47
2.47 ≤ k ≤ 2.53
(E)
Answer: E
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
Options:
A)22
B)77
C)40
D)26
E)18
Rationale: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) => x = 40
Answer: C
Answer: C
Question: The least perfect square, which is divisible by each of 21, 36 and 66 is
Options:
A)213414
B)213424
C)213434
D)213444
E)None of these
Rationale: Explanation:
L.C.M. of 21, 36, 66 = 2772
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444
Option D
Answer: D
Question: What is the perimeter of a triangle with sides 7 and 4 that has the maximum possible area?
Options:
A)11 + √5
B)11 + √6
C)11 + 4√7
D)11 + √65
E)11 + 3√17
Rationale: We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+16) = √65
The perimeter is 11 + √65
The answer is D.
Answer: D
Question: A certain collage has total of 700 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
Options:
A)100
B)80
C)75
D)155
E)50
Rationale: Answer D
700 = 525 + 20 + x => x = 155
= 3/4 * 700 in 4 subjects + 20 min for 5th subject + x = 700
Answer: D
Question: If 20% of a = b, then b% of 20 is the same as:
Options:
A)4% of a
B)5% of a
C)6% of a
D)3% of a
E)2% of a
Rationale: Here, 20% of a=b i.e.,(20/100)a=b
then, b% 20 i.e.,(b/100)x20---I
then sub b=(20/100)a in I
we get,
=(20/100)a x (1/100) * 20
=(20/100)a x (20/100)
=(400/10000)a
=(4/100)a
= 4% of a
ANSWER :A
Answer: A
Question: If (1+y)x=xwhich of the following must be true?
Options:
A)x=-1 or y=0
B)x=0 or y=-1
C)x=1 or y=1
D)x=-1 or y=-1
E)y=0 or x=0
Rationale: We have (1+y)x=x
If x=0, y=y. True
If y=0, (1+x)*0=0 True
So, E will be the answer.
Answer: E
Question: If −2≤e≤0 and n > 19, which of the following CANNOT be the value of en?
Options:
A)-48
B)-38
C)-20
D)0
E)19
Rationale: value of en not equal to -19=E -19....Rest all are achievable
Answer: E
Question: A 8% stock yielding 10% is quoted at :
Options:
A)80
B)110
C)112
D)120
E)160
Rationale: Solution
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 8, money invested = Rs.(100/10X8) = Rs. 80.
âˆ´ Market value of Rs. 100 stock =Rs. 80
Answer A
Answer: A
Question: A women paid $1650 a year in interest on a loan with an annual rate of 11%. How w\much more money could she have borrowed for the same amount of interest if she had been able to get a loan amount with an annual rate of 10%?
Options:
A)$165
B)$1500
C)$1815
D)$ 15000
E)$16500
Rationale: Let P = Principal amount
R1 = Interest Rate for case 1
R2 = Interest Rate for case 2
Time = T = 1year
Now Interest = (P * R1* T)/ 100
We have 1650 = (P*11*1)/100 => we get P = 15000$
now Case 2 : P = 15000 R2= 10% T= 1year
Interest Amount is $1650( Interest Amount Remains same)
Now on $15000 with 10% Interest Amount is $1500.
We get, Difference in Interest Amount's is $ 150
Solve for
150 = (P * 10 * 1)/100
P = $ 1500 . So the women can borrow $1500 more.
Answer: B
Answer: B
Question: Train A left station T at 3:30 p.m. and traveled on straight tracks at a constant speed of 60 miles per hour. Train B left station T on adjacent straight tracks in the same direction that train A traveled on. Train B left station T 40 minutes after train A, and traveled at a constant speed of 75 miles per hour. Train B overtook train A on these straight tracks. At what time did train B overtake train A?
Options:
A)4:10
B)5:40
C)6:10
D)6:50
E)7:30
Rationale: Train A left 40 mins before Train B at a speed of 60 mph
So distance traveled by Train A in 40 mins= 40 miles
Let's say the total distance at the point of overtaking is x
So, the time taken for covering the remaining distance x-40 by Train A=x-40/60
Time taken for covering the distance x at 75 mph by Train B=x/75
Both Time should be equal which gives us,
x-40/60=x/75
x=160 mins=2 hr 40 mins
Time when train B overtake train A = 3:30+40 mins+ 2 hr 40 mins= 6:50
Correct Answer is D.
Answer: D
Question: An error 2% in excess is made while measuring the side of asquare. The % of error in the calculated area of the square is?
Options:
A)4.00%
B)4.04%
C)4.26%
D)4.56%
E)4.67%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Answer: B
Question: Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 38 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
Options:
A)2:5
B)5:16
C)3:5
D)4:7
E)14:5
Rationale: Answer = B) 5:16
........................ Rum ..................... Coke ................. Total
First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)
Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)
Total .................. 10 ............................. 28 .................... 38
Ratio = 10:32= 5:16
B
Answer: B
Question: What is the unit digit in (4137)754?
Options:
A)1
B)3
C)7
D)9
E)6
Rationale: Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}
=Unit digit in { 292915317923361 x 17114769 }
= (1 x 9) = 9
Option D
Answer: D
Question: If x and y are integers and x + y = 6, which of the following must be true?
Options:
A)x and y are consecutive integers.
B)If x < 0, then y > 0.
C)If x > 0, then y < 0.
D)Both x and y are even.
E)Both x and y are less than 5.
Rationale: In option C if x > 0,then y<0 means x is +ve and y is -ve
In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.
How option B is right could you explain
B
Answer: B
Question: The greatest possible length which can be used to measure exactly the length 6m, 3m 85cm, 12 m 95 cm is
Options:
A)2
B)7
C)5
D)8
E)9
Rationale: Explanation:
Required Length = H.C.F of 600 cm, 385 cm and 1295 c
= 5 cm.
Answer: C) 5 cm
Answer: C
Question: A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.
Options:
A)1 ½ days
B)2 ½ days
C)3 ½ days
D)4 ½ days
E)5 ½ days
Rationale: A
1 ½ days
3/20 * 2 + (2 + x)/5 = 1
x = 1 ½ days
Answer: A
Question: The probability of having a girl is identical to the probability of having a boy. In a family with four children, what is the probability that all the children are of the same gender?
Options:
A)1/8.
B)1/3
C)1/4
D)1/6
E)1/2
Rationale: There are two cases. All boys and all girls
case 1. all boys.
1/2*1/2*1/2*1/2= 1/16
case 2 .all girls.
1/2*1/2*1/2*1/2=1/16
We will add the cases to get 1/8
Answer: A
Question: The sum of two consecutive number is 67. Which is the larger number?
Options:
A)34
B)43
C)44
D)45
E)46
Rationale: Let consecutive number be x, x+1
Therefore sum of the consecutive number is x + x+1=67
2x+1=67
2x=66
x=33
Therefore larger number is x+1=34
ANSWER:A
Answer: A
Question: A train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the train?
Options:
A)270 m
B)210 m
C)340 m
D)130 m
E)140 m
Rationale: Explanation:
Speed= 72 kmph = 72×10/36 = 20 m/s
Distance covered = 250+ x where x is the length of the train
Time = 26 s
(250+x)/26 = 20
250+x = 26×20 = 520 m
x = 520-250 = 270 m
Answer: Option A
Answer: A
Question: Simplify (3^y + 3^y + 3^y) (3^y + 3^y + 3^y)
Options:
A) 4^4y * 3^3y
B) 9^y+1
C) 16^y + 9^y
D) 12^y
E) 4^y * 12^y
Rationale: B
(3^y + 3^y + 3^y) (3^y + 3^y + 3^y)
(3*3^y)(3*3^y)
9*9^y=9^(y+1)..
Answer: B