divelab/Sys2Bench huggingface dataset:
Question: The distance between a food bank and a church is approximately 8.0 x 10^5 inches. Which of the following is closest to the distance between the food bank and the church, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
Options:
A)22.8
B)23.4
C)19.86
D)20.5
E)23.9
Rationale: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).
We also know that the distance between the food bank and the church is approximately 8.0x10^5 inches. To convert inches to kilometers, we need to multiply 8.0x10^5 inches by the ratio we just found out.
kilometers = 8.0x10^5 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]
km = 8.0x10^5/3.9x10^4 km
km = 20.51 = 20.5 km
Therefore, we can see that the closest answer is D.
Answer: D
Question: The equation x = 2y^2 + 5y - 18, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
Options:
A)3x + y + 15 = 0
B)y - 3x - 11 = 0
C)-2x - y - 7 = 0
D)-3x + y - 18 = 0
E)-3x + y + 13.5 = 0
Rationale: The question is made to look difficult though it is pretty simple if you focus on just the line and use process of elimination. (Remember that GMAT does not focus on parabolas so basically, the question should be quite do-able even if someone doesn't know how to handle parabolas.)
We need equation of l. Its slope must be 3.
Slope in option A and C is not 3 so we are left with B, D and E
The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B and E, if you put x = -5, you get -ve value for y co-ordinate. So ignore them.
Answer must be (D)
Answer: D
Question: The average ageof A, B and their C 3 years ago was 25 years and that of B and the C 5 years ago was 10 years. The present age of the A is:
Options:
A)46 years
B)56 years
C)51 years
D)58 years
E)60 years
Rationale: Sum of the present ages of husband, wife and child = (25 x 3 + 3 x 3) years = 81 years.
Sum of the present ages of wife and child = (10 x 2 + 5 x 2) years = 30 years.
Husband's present age = (81 - 30) years = 51 years.
C
Answer: C
Question: David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 4 family members in a row for the picture?
Options:
A)9!
B)9×8!
C)8×9!
D)10!/2!
E)9x10!
Rationale: In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, 5, 6, 7, 8, 9 which can be arranged in 11! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 10!*2! ways.
Total - Restriction =
= 11! - 10!*2! =
= 10!(11 - 2!) =
= 9*10!.
Answer: E.
Answer: E
Question: The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu?
Options:
A)10
B)20
C)40
D)80
E)100
Rationale: Q=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C
Answer: C
Question: The present ages of Tim and Lee are in the ratio of 5:6 respectively. Seven years hence, the ratio of their ages will be 6:7 respectively. What is Tim's present age?
Options:
A)40 years
B)32 years
C)35 years
D)34 years
E)39 years
Rationale: Let x be the Tim's age.
And y be the Lee's age.
Then, x/y = 5/6 ===> y = 6x/5
And, x+7/y+7 = 6/7
==> 7x+49 = 6y+42
==> 7x = 67-7
By substituting 7x=(36x/5)-7
==>35x-36x=-35
Therefore, x=35
ANSWER:C
Answer: C
Question: On decreasing the price of a colour TV by 15%, its sale is increased by 30%. The effect on the revenue is?
Options:
A)20 % decrease
B)25.5 % increase
C)16% decrease
D)30 % increase
E)none of these
Rationale: Net% change in revenue
= ( x + y + xy/100) %
= [-15 + 30 + ( -15 x 30)/100]% or 25.5%
ANSWER:B
Answer: B
Question: The perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
Options:
A)A)72
B)B)45
C)C)729
D)D)34
E)E)35
Rationale: Explanation:
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 36/2 = 45 cm2
Answer: Option B
Answer: B
Question: Find the arithmetic mean W of all roots of the following equation- see an attachment.
Options:
A)2
B)1
C)0.5
D)-1/3
E)0.3
Rationale: arithmetic mean W your answer C and E are same, can you correct one of them please. thanks.C
Answer: C
Question: The youngest of 4 children has siblings who are 1, 4, and 7 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 17, what is the age of the youngest sibling?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: x + (x+1) + (x+4) + (x+8) = 68
4x + 12 = 68
4x = 56
x = 14
The answer is E.
Answer: E
Question: judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 9th position from either end of the row.
Can you find out how many girls are practicing together?
Options:
A)4
B)9
C)17
D)18
E)20
Rationale: As judith is 9th from either end of the row, it means that 8 girls are on one of her sides and 8 are present on the other.
8 + 8 + 1(judith herself) = 17.
Hence, 17 girls are practicing the dance together.
correct answer is C)17
Answer: C
Question: A certain number X when divided by 243 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81?
Options:
A)17
B)27
C)37
D)47
E)57
Rationale: X=243y+98
so X/81 = 243y/81 + 98/81
since 243 is divisible by 81 the remainder of X/81 is remainder of 98/81 that is 17
Therefore subtracting 17 from X will make it divisible by 81
hence A is the answer
Answer: A
Question: If selling price is doubled, the profit triples. Find the profit percent?
Options:
A)108%
B)100%
C)120%
D)900%
E)160%
Rationale: Let C.P. be Rs. x and S.P. be Rx. y.
Then, 3(y - x) = (2y - x) => y = 2x
Profit = (y - x) = Rs. (2x - x) = Rs. x
Profit % = x/x * 100 = 100%.
Answer: B
Answer: B
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 4 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)3:1
B)19:4
C)19:8
D)19:5
E)19:2
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 4 = 5/2 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/2 + 7/2 = 6 litres
As 8 litres of mixture is formed, ratio of alcohol and water in the mixture formed
= 600 : 200 = 3:1.
Answer: A
Answer: A
Question: Which term of the AP: 121, 117, 113, ...... is its first negative term?
Options:
A)-1
B)-2
C)-3
D)-5
E)-7
Rationale: 121,117,113,......5,1,-3
ANSWER:C
Answer: C
Question: Divide Rs. 1600 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Options:
A)346
B)368
C)375
D)337
E)400
Rationale: A+B+C = 1600
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1600 => 400
Answer:E
Answer: E
Question: If a person walks at 16 km/hr instead of 8 km/hr, he would have walked 20 km more. The distance traveled by him if he walked at 16 km/hr?
Options:
A)50 km
B)58 km
C)60 km
D)70 km
E)40 km
Rationale: Let the actual distance traveled be x km. Then,
x/8 = (x + 20)/16
2x - x = 20 =>x = 20 km.
The required distance is = (20+20) km = 40 km
Answer :E
Answer: E
Question: Of a certain group of 100 people, 40 graduated from High School O, 65 graduated from College Y, and 30 live in City Z. What is the greatest possible number of people in this group who did not graduate from High School O, did not graduate from College Y, and do not live in City Z ?
Options:
A) 5
B) 15
C) 35
D) 65
E) 85
Rationale: 1. o+y+z+oy+yz+oz+oyz+ none=100. Fornoneto be maximum others have to be minimum
2. We know the underlined portions sum to 65 and that is the minimum value of others
3. Maximumnone= 100-65=35=C
Answer: C
Question: Kim is taking a math class, and the teacher gives a multiple choice test consisting of 7 questions. If each question has 4 answer choices, and Kim answers every question, in how many different ways can she complete the test?
Options:
A)a 40
B)b 400
C)c 4^7
D)d 8^5
E)e 40^40
Rationale: different ways to solve each question is 4.
So, 4*4*4*4.. 7 times ----> 5^8
Answer will be C.
Answer: C
Question: If there are n rays and all of them are reversed after 2006 reversals, then a possible value of n is
Options:
A)2237
B)3777
C)2002
D)3772
E)8822
Rationale: has to be same number less than (or equal to) k and of the same type as k.
k = 2006 then n = 2002.
Answer:C
Answer: C
Question: If you keep rolling a pair of dice together till a sum of 5 or 7 is obtained, then what is the probability that a sum of 5 comes before a sum of 7?
Options:
A)5/5
B)4/5
C)3/5
D)2/5
E)1/5
Rationale: This can be solved in a generic and complex way but let us not go into all that.
There can be four ways through which the pair of dice results in a sum of 5. There can be six ways through which the pair of dice can result in a sum of 7.
Now, we want the probability of the pair of dice resulting in a sum of 5 before a sum of 7. Thus probability = 4/(4+6) = 4/10 or 2/5.
correct answer is D)2/5
Answer: D
Question: A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 16%. What is the value of x?
Options:
A)37.5 litres
B)36.67 litres
C)37.67 litres
D)36.5 litres
E)33.33 litres
Rationale: Working formula ...
Initial Concentration*Initial Volume=Final Concentration*Final Volume.
Let X is the part removed from 100 lts.
36%(1-X/100)^2 = 16% * 100%
(1-x/100)^2=16/36------>(1-x/100)^2=(4/6)^2
100-X=400/6
x=33.33...
Ans E
Answer: E
Question: An inspector rejects 0.08% of the meters as defective. How many will he examine to reject 2?
Options:
A)1500
B)2000
C)2500
D)3000
E)3100
Rationale: Let the number of meters to be examined be x
Then, 0.08% of x = 2
(8/100)*((1/100)*x = 2
x = 2500
Answer is C
Answer: C
Question: A car during its journey travels 30 minutes at a speed of 40 kmph, another 45 minutes at a speed of 60 kmph, and 2 hours at a speed of 70 kmph.The average speed of the car is
Options:
A)63.07 kmph
B)64 kmph
C)62.02 kmph
D)64.02 kmph
E)None of these
Rationale: First car travels 30 min at speed of 40 kmph
distance = 40 x 1/2 = 20 m
Then car travels 45 min at a speed of 60 kmph
distance = 45 min at speed of 60 kmph
distance = 60 x 3/4 = 45 m
at last it travels 2 hours at speed of 70 kmph
distance = 70 x 2 = 140 m
Total distance = 20 + 45 + 140 = 205
Total time= 1/2 + 3/4 + 2 = 3.25
Average speed of the car = 205/3.25 = 63.07
ANSWER:A
Answer: A
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)34
B)35
C)36
D)37
E)38
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: Option C
Answer: C
Question: Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 4 screws and 2 nails?
Options:
A)4
B)5/2
C)2
D)3/2
E)5/4
Rationale: let the weight of nail be n and that of screw be s..
so s+w=1/2 * (6s+1n)...
or 1n = 4s..
lets see the weight of 3 s and 3n= 3s+3*4s=15s..
and weight of 4s and 2n= 4s+2*4s=12s..
ratio= 15s/12s=15/12=5/4
ANSWER:E
Answer: E
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Options:
A)2.87
B)2.88
C)2.67
D)2.21
E)2.82
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Answer: B
Question: In how many V ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?
Options:
A)6
B)12
C)18
D)24
E)30
Rationale: Number of ways of arranging the word GMAT = 4! = 24
Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6
Number of ways of arranging GMAT so that A is not in the beginning V= 24 - 6 = 18
Answer: C
Answer: C
Question: A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
Options:
A)1/3
B)1/4
C)1/5
D)1/6
E)1/10
Rationale: The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 5*4*1=20.
P(dispensing one of each color)=20/120=1/6.
The answer is D.
Answer: D
Question: What is the maximum number E of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Options:
A)36
B)32
C)24
D)21
E)15
Rationale: 27 cubic centimetre cubes gives side = 3cm
so if:
L*W*H is 9*12*8, then max. cube we can have are 3*4*2 = 24
L*W*H is 9*8*12, then max. cube we can have are 3*2*4 = 24
L*W*H is 12*8*9, then max. cube we can have are 4*2*3 = 24
L*W*H is 12*9*8, then max. cube we can have are 4*3*2 = 24
L*W*H is 8*12*9, then max. cube we can have are 2*4*3 = 24
L*W*H is 8*9*12, then max. cube we can have are 2*3*4 = 24
In all cases we get E=24 cubes.
Ans. C
Answer: C
Question: A person can swim in still water at 20 km/h. If the speed of water 12 km/h, how many hours will the man take to swim back against the current for 40km?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: M = 20
S = 12
US = 20 - 12 = 8
D = 40
T = 40/8 = 5 Answer:C
Answer: C
Question: Evaluate: 11 + sqrt(- 4 + 6×4÷3)
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: According to order of operations, inner brackets first where 6×4÷3 is first calculated since it has a multiplication and a division.
6×4÷3 = 24÷3 = 8
Hence
11 + sqrt(- 4 + 6×4÷3) = 11 + sqrt(- 4 + 8)
= 11 + sqrt(4) = 11 + 2 = 13
correct answer E)13
Answer: E
Question: If n = 2p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ?
Options:
A) Two
B) Three
C) Four
D) Six
E) Eight
Rationale: This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:
n = 4 x 3
n = 12
Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.
1, 12, 6, 2, 4, 3
From this we see that we have 4 even divisors: 12, 6, 2, and 4.
If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so
n = 4 x 5
n = 20
The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.
No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.
The answer is A.
Answer: A
Question: The product of all the prime numbers less than 25 is closest to which of the following powers of 10?
Options:
A)a) 10^9
B)b) 10^8
C)c) 10^8*2.23
D)d) 10^6
E)e) 10^5
Rationale: Group these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11*19)(13*17)*23 or 10*21*209*221* 23
Now take out power of 10 from each number and rewrite
10*10*100*100*10 (1*2.1*2.09*2.21*2.3) or 10^7*(1*2.1*2.09*2.21*2.3)=10^7*10*2.23
=2.23*10^8
C
Answer: C
Question: Somehow or other I got talked into buying something on the installment plan. I'm notsure I got a good deal. The payments to date,according to my checkbook, have reached Rs.96.The second year cost Rs.2.00 more than the first year; the third year cost Rs.3.00 more thanthe second; and the fourth year cost me Rs.4.00 more than the third. What were mypayments the first year?
Options:
A)18
B)20
C)22
D)24
E)26
Rationale: let payments for the first year=x
given,x+x+2+x+5+x+9=96
4x+16=96
x=20
ANSWER:B
Answer: B
Question: A cubical block of metal weighs 7 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
Options:
A)48
B)32
C)24
D)56
E)12
Rationale: For example our cube have a side 1 meter, so we have 1 cubical meter in this cube
and this cubical meter weigth 7 pounds
If we take cube with side 2 meters we will have 8 cubical meters in this cube
8 meters * 7 pounds = 56 pounds
So answer is D
And similar but more theoretical approach:
if we have sides a and b than they have equal ration with their areas:
a/b = a^2/b^2
and they have equal ration with their volumes:
a/b = a^3/b^3
we have two sides 1/2 so their volume will be in ratio 1/8
weight of one cube * volume of another cube
7 * 8 = 56
So answer is D
Answer: D
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 2500 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140
B)150
C)160
D)170
E)200
Rationale: Given that the area of the square =2500 sq.units
=> Side of square = √2500 = 50 units
The radius of the circle = side of the square = 50 units
Length of the rectangle = 2/5 * 50 = 20 units
Given that breadth = 10 units
Area of the rectangle = lb = 20 * 10 = 200 sq.units
Answer: Option E
Answer: E
Question: A, B and C shared profits in ratio of 5 : 7 : 8. Theypartnered for 10months, 8months and 7months respectively. What was he ratio of their investments ?
Options:
A)10 : 49 : 45
B)20 : 49 : 64
C)10 : 19 : 64
D)20 : 35 : 64
E)30 : 29 : 63
Rationale: Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.
Let X is the total investment
â‡’10 x = 5
â‡’ 8 x = 7
â‡’ 7x = 8
â‡’ Final investment ratio = 20 : 35 : 64
D
Answer: D
Question: In a 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 B receive 18000,how much amount was their profit?
Options:
A)58000
B)48200
C)60400
D)58500
E)None of these
Rationale: Explanation :
Assume that investment of C = x
Then, investment of A =2x
Investment of B = 4x/3
A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3
Let their profit was y
18000 = y*4/(6+4+3)
y = 18000*13/4 = 58500
Answer : Option D
Answer: D
Question: Arun makes a popular brand of ice cream in a rectangular shaped bar 6cm long, 5cm wide and 2cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain same, but the length and width will be decreased by some percentage. The new width will be,
Options:
A)33
B)87
C)99
D)367
E)72
Rationale: Answer:A
Answer: A
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 26. Which of the following integers is the higher of the remaining two integers?
Options:
A)32
B)85
C)44
D)22
E)55
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 26
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -26 = 144
B = (144 + 26)/2 = 85
Answer:Option B
Answer: B
Question: Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 5 days before the completion of the work. How long did the work last?
Options:
A)6
B)7
C)8
D)8 1/9
E)10
Rationale: Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains
Then if Ben had to leave 5 days before the completion, this means that Carla had to work alone for these 5 days in which she completed 1/3 of the job.
Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 7/15
3/20 (t) = 7/15 ---> t = 3 1/9
Therefore, these 3 1/9 days worked plus the 5 days that Carla had to work by herself add to 8 1/9 days
Answer: D
Answer: D
Question: Robert ate 13 chocolates, Nickel ate 4 chocolates. How many more chocolates did Robert ate than nickel?
Options:
A)A)4
B)B)7
C)C)9
D)D)5
E)E)2
Rationale: 13-4=9. Answer is C
Answer: C
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 54. What is the rate of interest per annum?
Options:
A)8
B)2
C)9
D)4
E)6
Rationale: Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 54
15000[(1 + R/100)2 - 1 - 2R/100] = 54
15000[(100 + R)2 - 10000 - 200R]/10000 = 54
R2 = (54 * 2)/3 = 36 => R = 6
Rate = 6%
Answer: Option E
Answer: E
Question: The average age of 21 students of a class is 21 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 21th student is
Options:
A)164
B)152
C)100
D)182
E)195
Rationale: Explanation:
Age of the 21th student = [21 * 21 - (14 * 5 + 16 * 9)] = (378-214) = 164 years.
Answer: A
Answer: A
Question: The average (arithmetic mean) of 20, 40, and 60 is 9 more than the average of 10, 70, and what number?
Options:
A)15
B)25
C)35
D)13
E)55
Rationale: a1 = 120/3 = 40
a2 = a1 -9 = 31
sum of second list = 31*3 = 93
therefore the number = 93 -80 = 13
ANSWER:D
Answer: D
Question: What is the unit digit in(7^95 - 3^58)?
Options:
A)6
B)4
C)7
D)9
E)10
Rationale: Explanation:
Unit digit in 7^95 = Unit digit in [(7^4)23 x 73]
= Unit digit in [(Unit digit in(2401))23 x (343)]
= Unit digit in (123 x 343)
= Unit digit in (343)
= 3
Unit digit in 3^58 = Unit digit in [(3^4)14 x 32]
= Unit digit in [Unit digit in (81)14 x 32]
= Unit digit in [(1)14 x 32]
= Unit digit in (1 x 9)
= Unit digit in (9)
= 9
Unit digit in (795 - 358) = Unit digit in (343 - 9) = Unit digit in (334) = 4.
B
Answer: B
Question: Ben and Shari have invited three other couples to their apartment for a game of charades. Everyone is to be split into two equal teams, but each team must consist of either two couples or no couples. How many different pairs of teams are possible?
Options:
A)11
B)14
C)22
D)35
E)70
Rationale: Ben and Shari can be paired with any of the other three couples, leaving the remaining two for the other team. So, the number of ways to split 4 couples into two teams is 3:
{1, 2} - {3, 4}
{1, 3} - {2, 4}
{1, 4} - {2, 3}
The number of teams where there are no couples:
{Ben, any from couple 2, any from couple 3, any from couple 4} and the remaining 4 people form team #2. The number of team for Ben = 2*2*2 = 8.
Total = 3 + 8 = 11.
Answer: A
Answer: A
Question: If xx is chosen at random from the set {1,2,3,4} and yy is to be chosen at random from the set {5,6,7}, what is the probability that xy will be even?
Options:
A)24
B)29
C)28
D)23
E)22
Rationale: SS ={(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)}
Total element n(S)=12
xy will be even when even xx or yy or both will be even.
Events of x,y being even is E.
E ={(1,6),(2,5),(2,6),(2,7),(3,6),(4,5),(4,6),(4,7)}
n(E)=8
So, Probability,
P=n(E)n(S)
P=812
P=23
D
Answer: D
Question: 7^b + 7^b + 7^b + 7^b + 7^b + 7^b + 7^b =
Options:
A)7^b
B)7^(b + 1)
C)7^(7b)
D)8^b
E)49^B
Rationale: Easy one.
7*7^b = 7^(b+1)
Ans. B
Answer: B
Question: Calculate the circumference of a circular field whose radius is 5 centimeters.
Options:
A)5 π cm
B)6 π cm
C)7 π cm
D)8 π cm
E)10 π cm
Rationale: Circumference C is given by
C = 2πr = 2π*5 = 10 π cm
correct answer B
Answer: B
Question: Find the odd man out. 9, 12, 15, 18, 21, 25
Options:
A)9
B)25
C)12
D)15
E)18
Rationale: All numbers except 25 are multiples of 3
Answer is B
Answer: B