divelab/Sys2Bench huggingface dataset:
Question: An American cafeteria offers 3 flavors of pizza - chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?
Options:
A)4
B)8
C)12
D)9
E)32
Rationale: 3 flavours * 3 choices = 3C1*3C1 = 3*3=9=D
Answer: D
Question: Michael is twice as old as he was 8 years ago. What is his present age?
Options:
A)10 years
B)4 years
C)8 years
D)6 years
E)16 years
Rationale: Let Michael' spresent age be x.
2 ( x - 8 ) = 8
x = 16 years
Michael's present age is 16 years.
Answer : E
Answer: E
Question: Helen went to the stationers and bought things worth Euro 21, 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)uro 16.70
B)uro 19.70
C)uro 13.70
D)uro 18.70
E)uro 15.70
Rationale: E
Euro 15.70
Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [21 - (5 + 0.30)] = Euro 15.70
Answer: E
Question: Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
Options:
A){2, 10}
B){16, 16}
C){10, 18}
D){9, 11}
E){7, 13}
Rationale: answer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is one unit. therefore accepted
answer is D mean is 10 and S.D decreases minimum.
D
Answer: D
Question: A semicircle has a radius of 14. What is the approximate perimeter of the semicircle?
Options:
A)72
B)76
C)80
D)84
E)88
Rationale: The perimeter of a circle is 2*pi*r.
The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r
The perimeter is pi*14 + 2*14 which is about 72.
The answer is A.
Answer: A
Question: 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
Options:
A)13
B)65
C)30
D)88
E)12
Rationale: 3W = 2M
15M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
15 * 21 * 8 = 14 * x * 6
x = 30. Answer: C
Answer: C
Question: If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N?
Options:
A)181
B)165
C)121
D)99
E)44
Rationale: M=10x+y
N=10y+x
M+N=11x+11y=11(x+y)
In other words the answer is a multiple of 11.
Now the question becomes " which of the following is NOT a multiple of 11?"
Answer -181
ANSWER:A
Answer: A
Question: How many terms are there in 2,4,8,16……1024?
Options:
A)10
B)12
C)14
D)16
E)15
Rationale: Clearly 2,4,8,16……..1024 form a GP. With a=2 and r = 4/2 =2.
Let the number of terms be n . Then
2 x 2^n-1 =1024 or 2^n-1=512 = 2^9.
n-1=9 or n=10
Answer is A.
Answer: A
Question: Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 8000 Find money given by 10%?
Options:
A)20000
B)40000
C)50000
D)60000
E)70000
Rationale: let first parrt is x and second part is y then x+y=50000----------eq1
total profit=profit on x +profit on y
8000=(x*10*1)/100 + (y*20*1)/100
80000=x+2y-----------------------------------eq2
80000=50000+y
so y=30000 then x =50000-30000=20000
first part =20000
ANSWER:A
Answer: A
Question: Seven cards numbered from 1 to 7 are placed in an empty bowl. First one card is drawn and then put back into the bowl, and then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 9, what is the probability that one of the two cards drawn is numbered 6?
Options:
A)1/3
B)2/3
C)1/5
D)2/5
E)2/7
Rationale: There are 6 ways to get a total sum of 9.
2 of these ways include the number 6.
The probability that one of the cards is a 6 is 2/6 = 1/3
The answer is A.
Answer: A
Question: If a number W between 0 and 1 is selected at random, which of the following will the number most likely be between?
Options:
A)0 and 3/20
B)3/20 and 1/5
C)1/5 and 1/4
D)1/4 and 3/10
E)3/10 and 1/2
Rationale: The number W will most likely be between the largest range.
A. 0 and 3/20 --> range 3/20;
B. 3/20 and 4/20 --> range 1/20;
C. 4/20 and 5/20 --> range 1/20;
D. 5/20 and 6/20 --> range 1/20;
E. 6/20 and 10/20 --> range 4/20.
Answer: E.
Answer: E
Question: A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 5 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?
Options:
A)(a) 60/11
B)(b) 5
C)(c) 26/5
D)(d) 27/5
E)(e) 28/5
Rationale: from the uphill we can find out the distance = 5*2 = 10
average speed = total distance/total time
= 20/ (2+ (10/6)) = 60/11
Answer is A.
Answer: A
Question: the perimeter of an equilateral triangle is 45.if one of the side is the side of an isoceles triangle of perimeter 40 then what is the lenght of base of isoceles triangle.
Options:
A)10 units
B)20 units
C)30 units
D)40 units
E)15 units
Rationale: base of isoceles triangle is 40-15-15= 10 units.
ANSWER:A
Answer: A
Question: What annual payment will discharge a debt of Rs. 1090 due in 2 years at the rate of 5% compound interest?
Options:
A)993.2
B)586.21
C)534.33
D)543.33
E)646.33
Rationale: Explanation:
Let each installment be Rs. x. Then,
x/(1 + 5/100) + x/(1 + 5/100)2 = 1090
820x + 1090 * 441
x = 586.21
So, value of each installment = Rs. 586.21
Answer: Option B
Answer: B
Question: The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 10, which of the following represents the maximum possible value of the largest integer?
Options:
A)4
B)6
C)20
D)10
E)1
Rationale: Let the distinct number be A,B,C, and D
Its given A > B > C > D
also A + B + C + D =40 and A + B = 10 means C + D = 30
Since the question ask for the largest possible number we should choose the least value for A and B,C. So D should be 20. If D=20 then C = 10 > A,B <10
Answer : C
Answer: C
Question: A man can row with a speed of 23 kmph in still water. If the stream flows at 9 kmph, then the speed in downstream is?
Options:
A)32
B)26
C)20
D)87
E)24
Rationale: M = 23
S = 9
DS = 23 + 9
=32
Answer: A
Answer: A
Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Options:
A)7/11
B)6/7
C)1/5
D)2/7
E)None of these
Rationale: Explanation :
Let, the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water then quantity of water in new mixture
=>3−(3x/8)+x litres.
Quantity of syrup in new mixture =5−5x/8 litres.
Therefore,
=>3−(3x/8)+x=5−5x/8.
=>5x+24=40−5x.
=>x=8/5.
So part of the mixture replaced,
=>(8/5)×(1/8)=1/5.
Answer : C
Answer: C
Question: Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 80 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take?
Options:
A)40
B)50
C)150
D)80
E)90
Rationale: L+M=M+N-80 / N=2L+10
80=M+N-L-M
80=N-L
80=2L+10-L
70=L
2(70)+10=150
C
Answer: C
Question: What approximate value should come in place of the question mark (?) in the following equation?
152√? + 795 = 8226 – 3486
Options:
A)425
B)985
C)1225
D)1025
E)675
Rationale: 152√? ≈ 8200 - 3500 - 800 = 3900
∴ √? = 3900⁄152
= slightly less than (4000⁄150) = 26.67 i.e., 26
∴ √? = (26)2 = 676 ≈ 675
Answer E
Answer: E
Question: The average of seven numbers is 27. If one number is excluded, the average becomes 25. The excluded number is
Options:
A)25
B)27
C)30
D)39
E)40
Rationale: Sol.
Therefore excluded number
= (27 × 7) - ( 25 × 6)
= 189 – 150
= 39.
Answer D
Answer: D
Question: If a young child was 14 months old one year ago, how old was the child, in months, x months ago?
Options:
A)x − 26
B)x − 12
C)14 − x
D)24 − x
E)26 − x
Rationale: The child's age today is 14 months + 12 months = 26 months
x months ago, the child's age was (26 - x) months old.
The answer is E.
Answer: E
Question: A solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally w% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar?
Options:
A)100w/(1-w)
B)80w/(1-w)
C)75w/(1-w)
D)100w/(80-0.2w)
E)100w/(80+0.2w)
Rationale: We'll go for the ALTERNATIVE approach since there are variables in all the answers (which means that any number could work). Since the question deals with percents, the easiest number to use is X = 100. Now let's say that w = 10. Before the evaporation we had 10 pound of sugar and 90 pounds of water. Since only water evaporated, after the evaporation the 10 pounds of sugar remained the same, but the water reduced by 20% of 90 (18 pounds), so we have only 72 pounds of water. 10 out of 82 is the fraction of sugar, so if we multiply it by 100 we get the percents. The correct answer is E: 100w/(80+0.2w) >>> 100x10 / 82
Answer: E
Question: In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,-5) and (t,-7). What is the least possible value of the slope of line L?
Options:
A)6
B)-1
C)-2
D)-6
E)-10
Rationale: We need to find out the value of p and L to get to the slope.
Line L and Graph y intersect at point (p,-5). hence, x= p and Y=-5 should sactisfy the graph. soliving
5 = -p2 +9
p2 = 4
p = + or - 2
simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7.
-7 = -t2+9
t = +or - 4
considering p = -2 and t =4, the least slope is (-7+5)/(4-2) = -1
IMO option B is correct answer.
Answer: B
Question: A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $30. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)
Options:
A)30xy
B)270/(xy)
C)xy/9
D)xy/30
E)270xy
Rationale: xy sq ft = $30
1 sq ft = $30/xy
multiplying by 9 on both side
9 sq ft = $270/xy
or 1 sq yard = $270/xy
Hence B.
Answer: B
Question: The roots of the equation 3x2 - 12x + 10 = 0 are?
Options:
A)rational and unequal
B)complex
C)real and equal
D)irrational and unequal
E)rational and equal
Rationale: Explanation:
The discriminant of the quadratic equation is (-12)2 - 4(3)(10) i.e., 24. As this is positive but not a perfect square, the roots are irrational and unequal.
ANSWER IS D
Answer: D
Question: A father is four times as old as his son. In twenty years, he'll be twice as old. How old are they now?
Options:
A)5,40
B)10,40
C)20,40
D)10,30
E)15,30
Rationale: If F is age of father and s is age of son
f=4s
f+20 = 2*(s+20)
4s+20 = 2s+40
2s=20
s=10
F=40
ANSWER:B
Answer: B
Question: The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
Options:
A)48.55
B)42.25
C)50
D)51.25
E)52.25
Rationale: Explanation:
Average weight of 16 boys = 50.25
Total weight of 16 boys = 50.25 × 16
Average weight of remaining 8 boys = 45.15
Total weight of remaining 8 boys = 45.15 × 8
Total weight of all boys in the class = (50.25 × 16)+ (45.15 × 8)
Total boys = 16 + 8 = 24
Average weight of all the boys = (50.25×16)+(45.15×8)/24
=(50.25×2)+(45.15×1)/3
=(16.75×2)+15.05
=33.5+15.05
=48.55
Answer: Option A
Answer: A
Question: The sum of the mean, the median, and the range of the set {5,7,9} equals which one of the following values?
Options:
A)11
B)17
C)14
D)12
E)10
Rationale: Here Mean => 5+7+9/3 => 6
median => 7
and range => 9-5 => 4
hence sum => 6+7+4=> 17
Answer: B
Answer: B
Question: If x is divisible by 4 and 6, which of the following must divide evenly into x?
I. 2
II. 35
III. 70
Options:
A)I only
B)I and II
C)II​ and III
D)II​ only
E)I, II, and III
Rationale: If x is divisible by 4,6 means it will be = or > 12, 24,48 etc...
That are not divisible by 35, 70.
So, the answer is A
Answer: A
Question: In the graph below, no axes or origin is shown. If point B's coordinates are (9,3), which of the following coordinates would most likely be A's?
Options:
A)(17, -2)
B)(10, 6)
C)(6, 8)
D)(-10, 3)
E)(-2, -17)
Rationale: wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 9.
B rules..
Answer: B
Question: 2y - x = 2xy . If x and y are integers, which of the following could equal y?
Options:
A)2
B)1
C)0
D)3
E)4
Rationale: Plug in the answer choices in the equation from the question stem.
A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE
B) y = 1 >>> 2 - x = 2x >>> Same, POE
C) y = 0 >>> -x = 0 >>> x This is the answer
Answer C
Answer: C
Question: A began business with 12500 and is joined afterwards by B with 37500. When did B join, if the profits at the end of the year are divided equally?
Options:
A)8 months
B)9 months
C)10 months
D)7 months
E)None of these
Rationale: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 12500 : (12 – x) × 37500
or 12 : 3(12 – x)
Since profit is equally divided so
12 = 3(12 – x) or x = 8. Thus B joined after 8 months.
Answer A
Answer: A
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)km
B)km
C)km
D)km
E)km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer :B
Answer: B
Question: The percent change from 29 to 43 is approximately what percent of the percent change from 43 to 57?
Options:
A)50%
B)66%
C)110%
D)133%
E)150%
Rationale: Thus, %age change from 29 to 43 = 14/29 ≈≈ 50% or 0.5 (we can approximate in this question as the options given are far apart).
%age change from 43 to 57 = 14/43 ≈≈0.33
Thus, the required value = 50/33 = 1+17/33 ≈≈ 1+0.5 = 1.5 or 150%
E is thus the correct answer.
Answer: E
Question: By selling 100 pencil, a trader gains the cost of 40 Pencil. Find his gain percentage?
Options:
A)26 1/3%
B)51 1/3%
C)40%
D)53 1/3%
E)34 1/3%
Rationale: C
40%
Let the CP of each pencil be Rs. 1.
CP of 100 pens = Rs. 100
Profit = Cost of 40 pencil = Rs. 40
Profit% = 40/100 * 100 = 40%
Answer: C
Question: at three different signals,light change after 48 sec,72 sec,108 sec respectively.if at morning 8:20:00 change together,then at what time again they will change together?
Options:
A)8:27:12
B)8:27:24
C)8:27:36
D)8:27:48
E)8:27:56
Rationale: l.c.m of 48,72,108=7min.12sec
again they will change at=8:27:12
answer A
Answer: A
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what Ɵme will it pass a bridge of 140
meter length.
Options:
A)20 seconds
B)30 seconds
C)40 seconds
D)50 seconds
E)None of these
Rationale: Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500
∗
225=40seconds
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 18 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)468
B)444
C)676
D)767
E)663
Rationale: 1h ----- 3
? ------ 60
12 h
RS = 18 + 21 = 39
T = 12
D = 39 * 12 =468
Answer: A
Answer: A
Question: The sale price sarees listed for Rs.375 after successive discount is 20% and 15% is?
Options:
A)227
B)268
C)342
D)787
E)285
Rationale: 375*(80/100)*(85/100)
= 285
Answer: E
Answer: E
Question: A boy pays Rs. 369 for an article marked at Rs. 600, by enjoying two successive discounts. If the first discount is of 25%, how much should be the second discount?
Options:
A)18
B)99
C)27
D)26
E)18
Rationale: Explanation:
First discount = 25% of 600 = Rs. 150.
Thus, the reduced price = 600 – 150 = Rs. 450.
Since the person actually paid Rs. 369, the value of the second discount must be equal to Rs. 81 (450 – 369).
Let the second discount be x
Thus, we get, 81 = x of 450
( 81/450)*100 = 18%
ANSWER: A
Answer: A
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
Options:
A)20%
B)25%
C)30%
D)15%
E)10%
Rationale: 800 --- 200
100 --- ? => 25%
ANSWER:B
Answer: B
Question: If x, y, and d are positive numbers such that 10*x/(x+y)+ 20*y/(x+y)=d and if x is less than y, which of the following could be the value of d?
Options:
A)10
B)12
C)15
D)18
E)30
Rationale: Answer choice C: d= 15
(10x + 20y)/(x+y) = 15
10x + 20y = 15x + 15y
5y = 5x
y = x
Doesn't work because the problem states that x<y.
We need y to be larger, so let's try answer choice D: d=18
10x + 20y = 18x + 18y
2y = 8x
y/x = 8/2
Success! x<y.
The correct answer is D.
Answer: D
Question: An athlete runs 200 meters race in 36sec. His speed is?
Options:
A)20km/hr
B)15km/hr
C)30km/hr
D)25km/hr
E)40km/hr
Rationale: speed = 200/36 = 50/9 m/sec
= 50/9 * 18/5 km/hr = 20km/hr
Answer is A
Answer: A
Question: When asked what the time is,a person answered that the amount of time left is 1/3 of the time already completed.what is the time.
Options:
A)2 PM
B)9 PM
C)3 PM
D)8 PM
E)6 PM
Rationale: A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x)
24−x=1/3x⇒x=18
Time is 6 PM
Answer:E
Answer: E
Question: The speed at which a man can row a boat in still water is 15 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 90 meters?
Options:
A)12
B)16
C)17
D)18
E)20
Rationale: The speed of the boat downstream = 15 + 3 = 18 km/hr
18 km/hr * 5/18 = 5 m/s
The time taken to cover 90 meters = 90/5 = 18 seconds.
The answer is D.
Answer: D
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Options:
A)4:5
B)3:5
C)6:8
D)3:5
E)5:4
Rationale: third number be x.
first no = 120% of x = 6x/5
second no = 150% of x = 3x/2
ratio in first two nos = (6x/5:3x/2)=> 4:5
ANSWER A
Answer: A
Question: A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?
Options:
A)14 days
B)5 days
C)8 days
D)4 days
E)3 days
Rationale: WC = 3:1
WT = 1:3
x 3x
1/x – 1/3x = 1/8
x = 16/3
3/16 + 1/16 = 1/4 => 4 days
ANSWER:D
Answer: D
Question: A train speeds past a pole in 15 sec and a platform 150 m long in 25 sec, its length is?
Options:
A)100
B)150
C)160
D)225
E)180
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 150)/25 = x/15 => x = 225 m.
Answer: Option D
Answer: D
Question: A shopkeeper purchased 80 kg of potatoes for Rs. 550 and sold the whole lot at the rate of Rs. 9 per kg. What will be his gain percent?
Options:
A)22.6 %
B)30.9 %
C)35.6 %
D)39.5%
E)23.6 %
Rationale: C.P. of 1 kg = 550/80 = Rs. 6.875S.P. of 1 kg = Rs. 9Gain % = 2.125/6.875 * 100 = 212.5/6.875 = 30.9 %Answer: B
Answer: B
Question: We are given the positive numbers a,b,c, which form an arithmetic progresion in the given order. We know that a+b+c=9. The numbers a+1,b+1,c+3 form a geometric progression in the given order. Find c.
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Solution:
Since a,b,c form an arithmetic progression, c=b+d=a+2d and a+b+c=a+a+d+a+2d=3a+3d=9, so a+d=b=3 and a+c=6=>c=6−a. Since a+1,b+1,c+3 form a geometric progression, we have (b+1)2=(a+1)(c+3), or 16=(a+1)(6−a+3)=(a+1)(9−a)
16=9a+9−a2−a
a2−8a+7=0, therefore a=7 or a=1. But if a=7, c=6−a=6−7=−1<0 and by definition c is positive, so a=7 is not a solution. Therefore a=1 and c=6−a=6−1=5.
Answer A
Answer: A
Question: 36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible?
Options:
A)2
B)4
C)5
D)6
E)10
Rationale: Three conditions have to be satisfied.
1. The number of students per row has to be at least 3.
2. Number of row has to be at least 3.
3. Equal number of students has to be seated in a row.
The following arrangements satisfy all 3 conditions.
Arrangement 1: 3 students to a row; 12 rows.
Arrangement 2: 4 students to a row; 9 rows.
Arrangement 3: 6 students to a row; 6 rows.
Arrangement 4: 9 students to a row; 4 rows.
Arrangement 5: 12 students to a row; 3 rows.
You will observe that the number of students in a row is a factor of 36.
So, an alternative and faster approach is to list down factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
And then start from 3 and quickly find out if the number of rows is at least 2.
Both the conditions are satisfied for the following factors : 3, 4, 6, 9, and 12. i.e., 5 arrangements.
Option C is answer
Answer: C
Question: A and B start a business with Rs.16000 and Rs.32000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)1:2
B)3:4
C)2:5
D)3:7
E)2:1
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
16000 : 32000 => 1:2
ANSWER:A
Answer: A
Question: How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: (700 – 300)/42 = 9 22/42
=> 9 Numbers
ANSWER:A
Answer: A
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
Options:
A)152
B)3^5
C)125
D)217
E)136
Rationale: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 3^5
Ans: B
Answer: B
Question: Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 342 grams of compound X?
Options:
A)54
B)162
C)250
D)270
E)280
Rationale: total number of fractions =2+10=12
element B constitutes =10 out of 12 parts of X
So in 342 gms of X have 342*10/12=280 gms of B
and 342-280=62 gms of A.
cross check:- A/B = 62/280 =2/10 (as given)
Ans E
Answer: E
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)30
B)31
C)36
D)25
E)24
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: Option C
Answer: C
Question: If n and k are integers whose product is 3600, which of the following statements must be true?
Options:
A)n+k>0
B)n does not equal k
C)Either n or k is a multiple of 10
D)If n is even, then k is odd
E)If n is odd, then k is even
Rationale: If n is odd and k is odd, then the product is odd.
The answer is E.
Answer: E
Question: How many prime numbers exist between 260 and 280?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: Straight a way lets exclude all the Even numbers between 260 and 280.
So now the number starts from 261 to 279 (Only ODD)
261 is a divisible of 3 and next odd divisible by 3 will be 261 + 6 = 267 + 6 = 273 + 6 =279.
Also we can eliminate numbers ending with '5'
So in Odd, the excluded numbers are 261,265,267,273,279, which leave us with 263,269,271,277.
Checked the above listed four numbers are divisible by any numbers till 20.
ANSWER:E
Answer: E
Question: There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 15 possible combinations in which Jim and Ellen are not selected, what is the value of k?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: There are k-2 members in the band, and k-4 members without Jim and Ellen.
(k-4)C2 = 15
(k-4)(k-5)/2 = 15
(k-4)(k-5) = 30 = 6*5
k = 10
The answer is C.
Answer: C