divelab/Sys2Bench huggingface dataset:
Question: A certain pilot flew 400 miles to City K at an average speed of 350 miles per hour with the wind and made the trip back at an average speed of 200 miles per hour against the wind. Which of the following is closest to the pilot’s average speed, in miles per hour, for the round-trip?
Options:
A)280
B)290
C)250
D)310
E)320
Rationale: Avg speed = total distance/ total time
total distance = 800
total time = 400/350 + 400/200 = 22/7
=> avg speed = (800*7)/22 = 250(approx)
ans is C
Answer: C
Question: A train is moving at a speed of 132 km/hour. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters long.
Options:
A)7 second
B)7.5 second
C)8 second
D)8.5 second
E)None of these
Rationale: Explanation:
As we need to calculate answer in seconds, so first convert speed into meter/sec.
we know 1 km/hr = 1*(5/18) m/sec
So, Speed = 132* (5/18) = 110/3 m/sec
Distance need to be covered in passing the platform =
Length of train + length of platform = 110 + 165
= 275 meters
Time = Distance/Speed
=>Time=275∗3/110=15/2=7.5seconds
Option B
Answer: B
Question: Laura's cookie recipe calls for 12 g of sugar for each 3 g of oil used. She needs to make 6 times the original recipe. If 72 g of sugar is used, then how many g of oil are needed?
Options:
A)18
B)36
C)12
D)54
E)6
Rationale: Number of g of sugar needed to make 6 times the original recipe 6x12 = 72
Number of grams of oil 3
Number of grams of oil needed 3x6 = 18
Answer 18
Answer: A
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)287 meters
B)217 meters
C)500 meters
D)278 meters
E)267 meters
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer:C
Answer: C
Question: The letters B,G,I,NB,G,I,N and RR are rearranged to form the word 'Bring'. Find its probability:
Options:
A)1/120
B)1/(5)4
C)1/24
D)1/76
E)1/32
Rationale: Solution:
There are total 5 letters. The probability that BB gets the first position is 1/5
The probability that G is in the second position is 1/4
Likewise, probability for I,NI,N and G
Hence required probability:
=1/5*1/4*1/3*1/2*1
=1/120
ANSWER IS A
Answer: A
Question: Patrick purchased 60 pencils and sold them at a loss equal to the selling price of 20 pencils. The cost of 60 pencils is how many times the selling price of 60 pencils?
Options:
A) 0.75
B) 0.8
C) 1
D) 1.33
E) 1.75
Rationale: Say the cost price of 60 pencils was $60 ($1 per pencil) and the selling price of 1 pencil was p.
Selling at a loss: 60 - 60p = 20p --> p = 3/4.
(cost price)/(selling price) = 1/(3/4) = 4/3 = 1.33.
Answer: D.
Answer: D
Question: find the last digit of 322^369
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: for calculating the unit place of these type of question (exponent)
as the power of 2 repeats after 4, so we will divide the exponent by 4
e.g, 2^1 = 2 and 2^(4+1) = 32, both have same unit place
369/4 gives the remainder as 1
so we can write 322^369 = 2^1 = 2
so, the unit place will be 2
ANSWER:B
Answer: B
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money?
Options:
A)1500
B)2277
C)2789
D)2788
E)1912
Rationale: P = 15(100/10)2 => P = 1500
Answer: A
Answer: A
Question: The difference between the two digit number and the number obtained by interchanging its digits is 54. The difference between the digits is?
Options:
A)4
B)5
C)6
D)2
E)3
Rationale: (10x + y) â€“ (10y + x) = 54
x â€“ y = 6
Answer C
Answer: C
Question: There is an increase of 30% in the production of milk chocolates in Amul Dairy in one month. If now it is 7,800 milk chocolates per month, what was it one month ago?
Options:
A)10,000 chocolates
B)6000 chocolates
C)8000 chocolates
D)7000 chocolates
E)None of these
Rationale: Let one month ago, production be x chocolates.
Then, 130 % of x = 7800
⇒ x = 7800×100/130=6000 chocolates
Answer B
Answer: B
Question: If -3<= x <= 2 and 3 <= y <= 8, which of the following represents the range of all possible values of y-x?
Options:
A) 5 <= y-x <= 6
B) 1 <= y-x <= 5
C) 1 <= y-x <= 6
D) 5 <= y-x <= 10
E) 1 <= y-x <= 11
Rationale: Maximum value of y-x= 8 - (-3)= 11
Minimum value of y-x= 3-2= 1
E mentions the correct range
Answer: E
Question: (+15) + (-11) - (+5) - (-7)
Options:
A)8
B)2
C)6
D)5
E)3
Rationale: = 15-11-57
22-16, [adding all integers with plus (+) sign together and with minus (-) sign respectively together
= +6 or simply 6. correct answer (C)
Answer: C
Question: In the rectangular coordinate system, if the line x = 3y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?
Options:
A)-2
B)0
C)1/2
D)1
E)2/3
Rationale: x = 3y+5, and thus y = x/3 - 5/3
The slope is 1/3.
The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2
p/2 = 1/3 and thus p = 2/3
The answer is E.
Answer: E
Question: The perimeter of a triangle is 44 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)76 cm2
B)56 cm2
C)18 cm2
D)98 cm2
E)55 cm2
Rationale: 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 * 44/2
= 55 cm2
Answer:E
Answer: E
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.92 at the candy store. What is John’s weekly allowance?
Options:
A)$2.55
B)$2.85
C)$3.15
D)$3.45
E)$3.75
Rationale: x = 3x/5 + 1/3*2x/5 + 92
4x/15 = 92
x = 345 = $3.45
The answer is D.
Answer: D
Question: Find the largest 5 digit number which is exactly divisible by 88?
Options:
A)98765
B)98907
C)99944
D)99954
E)99968
Rationale: Largest 5 digit number is 99999
After doing 99999 ÷ 88 we get remainder 31
Hence largest 5 digit number exactly divisible by 88 = 99999 - 31 = 99968
E
Answer: E
Question: The value for F=(0.889 × 55)/9.97 to the nearest tenth is
Options:
A)0.5
B)4.63
C)4.9
D)7.7
E)49.1
Rationale: if we read the Q, we can easily home on to the answer,,
the numerator is clearly between 40 and 50..
denomiator is close to 10..
so F=(0.889 × 55)/9.97 is between 4 and 5..
It may tempt us to solve it since ther are two values between 4 and 5..
but the catch is innearest tenth
4.63 can be called nearest to hundreth and no tenth, so can be eliminated..
4.9 is our answer...
C
Answer: C
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)565
B)444
C)676
D)767
E)663
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 =444
Answer: B
Answer: B
Question: In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 14 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?
Options:
A)102
B)114
C)126
D)138
E)150
Rationale: Initially the number of gold coins and silver coins is 2k and 6k.
After adding gold coins, the number of coins is 3k and 6k.
Thus k = 14 and the total number of coins is 9k = 126.
The answer is C.
Answer: C
Question: If 2^4, 3^3, and 12^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?
Options:
A)198
B)288
C)432
D)396
E)484
Rationale: I will go with C (pending elements to match is 2^2*3^2*12^1 =432
Answer: C
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Options:
A)99
B)77
C)12
D)66
E)45
Rationale: T = 9/45 * 60 = 12
Answer: C
Answer: C
Question: Three people of different heights are to be seated on a bench. How many different sitting arrangements are possible if the tallest one and the shortest one must sit next to each other ?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Consider T and S one. But, in this arrangement they can sit in two different combinations.
T first and S second or S first and T second.
Total we have (T and S) and third person= 2 arrangements to do.
Total arrangements= 2*2= 4
B is the answer
Answer: B
Question: Aishwarya’s mom was 38 years of age at the time of her birth, while her mom was 36 years old when her 4 years younger sister was born. The variance between the parents ages is :
Options:
A)6 years
B)11 years
C)10years
D)9 years
E)4 years
Rationale: A
6 years
Mom’s age when Aishwarya’s sister was born = 36 years.
Dad’s age when Aishwarya’s sister was born = (38 + 4) years = 42 years.
Needed Variance = (42 – 36) years = 6 years.
Answer: A
Question: 10 is added to a certain number, the sum is multiplied by 7, the product is divided by 5 and 5 is subtracted from the quotient. The remainder left is half of 88. What is the number?
Options:
A)21
B)20
C)25
D)30
E)45
Rationale: Let number is X.
When 10 added to it,
= (X+10)
7 multiplied to sum,
= 7 *(X +10)
Now,
= [{7 *(X +10)} /5]
And,
= [{7 *(X +10)} /5] - 5
According to question,
[{7 *(X +10)} /5] - 5 = half of 88
[(7X + 70) /5) = 44 +5
7X + 70 = 49 *5
X + 10 = 7 *5
X + 10 = 35
X = 35 - 10
X = 25
So, required number is: 25.
ANSWER : C
Answer: C
Question: A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 10 members, then what is the exact number of researchers required?
Options:
A)18
B)30
C)28
D)24
E)26
Rationale: l
alternatively, we have
10*3-2( because james is included in all the three teams)
=28
C
Answer: C
Question: If x<0, y>0, and |x| < |y|, which of the following must be true?
Options:
A)x > y
B)y^2 > x^2
C)x^3 > y^2
D)–x < y
E)x < –y
Rationale: Correct Answer: (E)
Let’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus –x < y is the same statement as |x| > |y|, and (D) must be true.
Answer: D
Question: Find the least value of 'a' so that 365a08 is divisible by 8.
Options:
A)9
B)8
C)0.
D)2
E)1
Rationale: Explanation:
Given, number is divisible by 8 only if 'a08' is divisible by 8.
.: Least value of a is '0'.
Answer: Option C
Answer: C
Question: A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 32 inches. Find b.
Options:
A)8
B)16
C)24
D)32
E)48
Rationale: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.
From the second premise, we know that the LCM of 12 (2^2*3) andbis 32 (2^5), sob=2^5
Combining 2 premises shows the answer is D(32).
Answer: D
Question: The mass of 1 cubic meter of a substance is 100 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: 100 kg - 1 cubic meter;
100,000 g - 1 cubic meter;
100,000 g - 1,000,000 cubic centimeters;
1 g - 1,000,000/100,000 = 10/1 = 10 cubic centimeters.
Answer: C.
Answer: C
Question: The C.P of 5 books is equal to the S.P of 20 books. Find his gain% or loss%?
Options:
A)35%
B)20%
C)5%
D)25%
E)75%
Rationale: explanation:
5 CP = 20 SP
20 --- 15 CP loss
100 --- ? => 75% loss
Answer: E
Answer: E
Question: A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, 4, and 6 at all. If repeated digits are allowed, what is the probability that it has at least one even digit?
Options:
A)23/24
B)31/36
C)55/64
D)65/81
E)75/121
Rationale: P(no even digits) = 2/3*2/3*2/3*2/3 = 16/81
P(at least one even digit) = 1 - 16/81 = 65/81
The answer is D.
Answer: D
Question: A cow and horse are bought for Rs.2,00,000. The cow is sold at a profit of 20% and the horse is sold a t a loss of 10%. The overall gain is Rs.4000, the Cost price of cow?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Ans: Overall profit = 4000200000×100=2%4000200000×100=2%
By applying alligation rule, we get
Answer:A
Answer: A
Question: Max invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded quarterly, then the amount received by Max at the end of the year will be?
Options:
A)16557.1
B)16557.19
C)16557.25
D)16557.3
E)16557.38
Rationale: P = Rs. 15000; R = 10% p.a. = 2.5% per quarter; T = 1 year = 4 quarters
Amount = [15000 * (1 + 2.5/100)4]
= (15000 * (1.025)4) = Rs. 16557.19
Answer: B
Answer: B
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150m
B)287m
C)278m
D)122m
E)121m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: A
Question: By how much does the larger root of the equation 2z^2+5z = 12 exceed the smaller root?
Options:
A) 5/2
B) 10/3
C) 7/2
D) 14/3
E) 11/2
Rationale: For 2z^2+5z = 12 Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4
= 1.5 OR -4
Hence larger root 1.5 is 1.5 - (-4) = 5.5 = 11/2 greater than smaller root (-4).
Hence option (E).
Answer: E
Question: What is the area of a square with perimeter 2P ?
Options:
A) 16p^2
B) 4P
C) P^2/5
D) P/16
E) P^2/4
Rationale: Each side is p/2
A = (p/2)^2 = (p^2)/4
Answer E
Answer: E
Question: Car A is 40 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
Options:
A)5
B)6
C)7
D)5.5
E)6.5
Rationale: Relative speed of car A is 58-50=8 miles per hour, to catch up 40 miles and drive 8 miles ahead so to drive 48 miles it'll need 48/8=6 hours.
Answer: B
Answer: B
Question: Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 54. No two digits of h are identical. How many different numbers are possible values of h?
Options:
A)24
B)28
C)30
D)36
E)48
Rationale: Answer = A = 24
Let number =abcd
Given that a*b*c*d = 54
a,b,c,d can be 1,2,3,9
Number of ways = 4*3*2 = 24
Answer: A
Question: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
Options:
A)20
B)24
C)10
D)27
E)16
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 24 kmph.
Answer: B
Answer: B
Question: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
Options:
A)17 1/7
B)17 1/9
C)17 1/2
D)17 1/7
E)17 1/5
Rationale: 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
Answer: A
Answer: A
Question: Set D consists of 19 elements. The average of set D is L. If a new element is added to the set and the average grows by K, what is the value of the new element?
Options:
A)a) L(1 + K / 5)
B)b) L * (K/100) - 20L
C)c) 20L(1+K/100)
D)d) 20(1+K/100)-19L
E)e) L*(K/5)-19
Rationale: Let's assume the value of new element to bea. So converting the word problem into equation,
(19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K
But according to the answer options, problem writer wanted to conveyk% percent rise in average value.
If we consider this case than resulting equation will be,
(19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]
==> a= 20L + KL/5 -19L
==> a= L + KL/5 , which is equivalent to option [A]
Answer: A
Question: Rahul went to a shop and bought things worth Rs. 65, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)A)19.7
B)B)19.9
C)C)39.9
D)D)49.9
E)E)59.7
Rationale: Total cost of the items he purchased = Rs.65
Given that out of this Rs.65, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (65−30/100−x)6/100 = 30/100
⇒ 6(65 −0.3 −x) = 30
⇒ (65 − 0.3 − x) = 5
⇒ x = 65 − 0.3 − 5 = 59.7
E)
Answer: E
Question: In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is/
Options:
A)20
B)22
C)24
D)26
E)27
Rationale: Number = (35 * 12) = 420
Correct quotient = 420/21 = 20
A)
Answer: A
Question: Subtracting 10% from X is the same as multiplying X by what number?
Options:
A)98%
B)90%
C)93%
D)96%
E)34%
Rationale: X - (10/100) X = X * ?
? = 90%
Answer:B
Answer: B
Question: If 2^5, 3^3, and 12^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?
Options:
A)26
B)39
C)42
D)144
E)156
Rationale: Here 156 has three two's
two three's
and one 13
rest of them must be in w
so w= 12*3*4 = 144
Smash D
Answer: D
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more?
Options:
A)22
B)40
C)99
D)88
E)66
Rationale: 760 ---- 22
760 ---- 20
x ----- 19
x*19 = 760*20
x = 800
760
-------
40
Answer: B
Answer: B
Question: A metallic sheet is of rectangular shape with dimensions 52 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
Options:
A)4830
B)5120
C)6420
D)7500
E)5760
Rationale: l = (52 - 16)m = 36 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (36 x 20 x 8) m3 = 5760 m3.
Answer: Option E
Answer: E
Question: A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability Q the piece ends no more than 7 spaces from the square numbered 49?
Options:
A) 7%
B) 8%
C) 14%
D) 15%
E) 28%
Rationale: OA is E
required prob is 7 spaces any side of 49.
so total 14 spaces are required in 7 moves which can be achieved by max 7 move on any side
so total spaces = 28
probability Q= 28%.E
Answer: E
Question: The distance between two stars is 3 × 10^5 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)
Options:
A)3.1 × 10^4
B)9.2 × 10^4
C)9.7 × 10^5
D)8.5 × 10^6
E)7.1 × 10^7
Rationale: 3 × 10^5 ly / (3.26 ly/parsec) = (3/3.26) x 10^5 = 0.92 x 10^5 = 9.2 x 10^4 parsec
The answer is B.
Answer: B
Question: How many seconds will a 1000 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)287
B)300
C)500
D)277
E)121
Rationale: Let length of tunnel is x meter
Distance = 1000+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
1000+x = (65/3) * 60
1000+x = 20 * 65 = 1300
x = 1300 - 1000 = 300 meters
Answer: B
Answer: B
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)3456
B)4567
C)4789
D)5678
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: Ram bought 50 books for Rs.1750 from one shop and 10 books for Rs.650 from another. What is the average price he paid per book ?
Options:
A)28
B)18
C)27
D)29
E)21
Rationale: Average price per book
= (1750 + 650) / (50 +10)
= 2400/ 60
= Rs.40
Answer:D
Answer: D
Question: In wardrobe Marry has 3 trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens hiswardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?
Options:
A)1/2
B)2/3
C)3/5
D)2/7
E)3/8
Rationale: Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
∴ Required probability = 2/3 x 3/4 = 1/2
A
Answer: A
Question: The letters P,O,C and Y are rearranged to form the word 'Copy'. Find its probability.
Options:
A)1/120
B)1/235
C)1/24
D)1/76
E)1/53
Rationale: Explanation :
There are total 4 letters. The probability that P gets the first position is 1/4.
The probability that O is in the second position is 1/3.
Likewise, probability for C and Y are 1/2 and 1/1.
Hence, the required probability is:-
=> (1/4) x (1/3) x (1/2) x 1.
=> 1/24.
Answer : C
Answer: C
Question: Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 7 seconds.What is the length of the fast train?
Options:
A)23 m
B)38 8/9 m
C)27m
D)27 7/9m
E)33 7/9m
Rationale: relative speed=20kmph=50/9m/sec
length of the train=50/9*7= 38 8/9
ANSWER:B
Answer: B
Question: n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1500, then what is the smallest possible value of n?
Options:
A)8
B)10
C)12
D)15
E)20
Rationale: 1500=2^2*3*5^3
5^3 means that n must be at least 15. That is, we need 5, 10, and 15.
The answer is D.
Answer: D
Question: In a small snack shop, the average (arithmetic mean) revenue was $400 per day over a 10-day period. During this period, if the average daily revenue was $360 for the first 6 days, what was the average daily revenue for the last 4 days?
Options:
A)$420
B)$440
C)$450
D)$460
E)$480
Rationale: The average revenue was $400 per day over a 10-day period --> total revenue over 10-day period is 10*$400=$4,000;
The average daily revenue was $360 for the first 6 days --> total revenue for the first 6 days is 6*$360=2,160;
Total revenue for the last 4 days is $4,000-2,160=$1,840;
Average daily revenue for the last 4 days is $1,840/4=$460.
Answer: D.
Answer: D
Question: Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 3, 16, 54, 12, 13, 64
II. 52,53,54,55,56,57
III. 8, 8, 8, 8, 8, 8
Options:
A)I, II, II
B)II, III, I
C)III, I, II
D)II, III, I
E)III, II, I
Rationale: out of three given sets,
III has all numbers same, so it has zero standard deviation hence it is Least
only answer choices A, B and D have III in least position.
II has consecutive numbers , hence all are closedly spaced hence std deviation will be less
while in I,numbers are spread widely hence std deviation should be more than III
hence order should be III, II,I
Option: E
Answer: E
Question: At the end of a business conference the 5 people present all shake hands with each other once. How many handshakes will there be altogether ?
Options:
A)20
B)45
C)55
D)90
E)10
Rationale: number of handshakes = 5C2= 5*4/2 = 10
ANSWER: E
Answer: E
Question: A card is randomly drawn from a deck of 52 cards. What is the probability getting either a King or a Diamond?
Options:
A)5/43
B)8/32
C)6/26
D)4/13
E)2/31
Rationale: Total number of cards = 52
Total Number of King Cards = 4
P(King) = 4/52
P(Diamond) = 13/52
P(King and Diamond) = 1/52
P(King or a Diamond) = P(King) + P(Diamond) â€“ P(King and Diamond)
=4/52+13/52â€“1/52=16/52=4/13
Answer D
Answer: D