divelab/Sys2Bench huggingface dataset:
Question: In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes X of the competition are possible?
Options:
A)18
B)20
C)54
D)84
E)120
Rationale: the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total X=84 outcomes
D
Answer: D
Question: ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,35) and (-5,15). Which can be the coordinate of fourth vertex?
Options:
A)(-5,-5)
B)(5,15)
C)(-5,-35)
D)(-5,10)
E)(15,35)
Rationale: A(-5, 15)
B(5, 15)
C(5, 35)
X(-5, 35): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB
Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB
Z(15, 35): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB
Ans:E
Answer: E
Question: X^Y + Y^X =2408
Find the values of X ?
Options:
A)2407
B)2408
C)2409
D)2405
E)32
Rationale: 2407^1+1^2407=2408
ANSWER:A
Answer: A
Question: 30 pens and 75 pencils were purchased for 750. If the average price of a pencil was 2.00, find the average price of a pen.
Options:
A)20
B)11
C)12
D)13
E)14
Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (750 – 150) = 600
∴ Average price of a pen = 600⁄60 = 20
Answer A
Answer: A
Question: The length and breadth of a square are increased by 40% and 30% respectively. The area of the rectangle so formed exceeds the area of the square by ?
Options:
A)82%
B)78%
C)80%
D)90%
E)none of these
Rationale: Since Side1 x Side2 = Area
Therefore, net% change in area
= ( x + y + xy/100) %
= [40 + 30 + (40 x 30)/100]% or 82%.
Therefore, area is increased by 82%.
ANSWER:A
Answer: A
Question: How many odd integers X between 200 and 600 are there such that their tens digit is even?
Options:
A)20
B)25
C)100
D)150
E)200
Rationale: The hundreds digit can take 4 values: 2, 3, 4 and 5;
The tens digit can take 5 values: 0, 2, 4, 6 and 8;
The units digit can take 5 values: 1, 3, 5, 7 and 9;
Total X: 4*5*5=100.
Answer: C.
Answer: C
Question: Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but one contained 7 books and the last shelf contained 11 books, how many shelves does the bookcase have?
Options:
A)7
B)6
C)4
D)5
E)3
Rationale: Let x be the number of shelves.
No of books in the beginning =12*x
After taking out 21 books No of remaining books = 12x -21
when the remaining books are rearranged, each shelf except the last shelf has 8 books and the last shelf has 11 books. So No of remaining books is also equal to 7*(x-1)+11
12x-21=7(x-1)+11
5x=25
x=5. Answer D
Answer: D
Question: The population of a town increased from 1,45,000 to 2,30,500 in a decade. The average percent increase of population per year is:
Options:
A)4.37%
B)5.8%
C)6.8%
D)8.75%
E)None
Rationale: Explanation: Increase in 10 years = (230500 - 145000) = 85500.
Increase% = (85500/145000 x 100)% = 58%.
Required average = (58/10)% = 5.8%.
Answer: Option B
Answer: B
Question: An article is bought for Rs.600 and sold for Rs.900, find the gain percent?
Options:
A)33 1/7%
B)33 1/6%
C)50%
D)38 1/3%
E)33 2/3%
Rationale: 600 ---- 300
100 ---- ? => 50%
Answer:C
Answer: C
Question: If x ≠ 0 and x - (2+ x^2)/x = y/x, then y =
Options:
A)-5
B)-2
C)-4
D)-3
E)-1
Rationale: x - (2+ x^2)/x = y/x
x^2 -2 - x^2/x = y/x
y= -2
Answer : B
Answer: B
Question: tell the smaller no. if its subtraction is 5 and ration is 4:3.
Options:
A)15
B)10
C)8
D)5
E)4
Rationale: 4x-3x=5
x=5
smaller no.=15
answer A
Answer: A
Question: Vinay got thrice as many marks in Maths as in English. The proportion of his marks in Maths and History is 4:3. If his total marks in Maths, English and History are 250, what are his marks in English ?
Options:
A)120
B)90
C)40
D)80
E)70
Rationale: Explanation:
M=3E and M/H=4/3
H=3/4M=3/4×3E=9/4E
Now, M+E+H=250⇒ 3E+E+9/4E=250
25E = 1000 or E = 40
Correct Option: C
Answer: C
Question: When positive integer N is divided by positive integer J, the remainder is 16. If N/J = 134.08, what is value of J?
Options:
A)22
B)56
C)78
D)112
E)200
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 134.08
Here 134 is the quotient.
Given that Remainder = 16
So, 134.08 = 134 + 16/J
So, J = 200 ANS E
Answer: E
Question: The difference between the ages of A and B is 10 years. Ten years ago, A was twice as old as B. Find the age of A, 10 years hence.
Options:
A)20 years
B)30 years
C)40 years
D)50 years
E)60 years
Rationale: given that A-B=10 ->(1)
A-10=2(B-10)
A=2B-10 ->(2)
by solving 1&2
we get A=30,B=20
After 10 years age of A is 40 years
ANSWER:C
Answer: C
Question: What is the sum of natural numbers between 40 and 100
Options:
A)4800
B)4270
C)5000
D)5500
E)5550
Rationale: a = first number
l = last number
Sn = n/2[a + l]
between 40 and 100 numbers = 61 => 100 - 40 = 60 + 1 = 61
Sn = 61/2 Ã— 140 = 61 Ã— 70 = 4270
Answer : B
Answer: B
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
Options:
A)8.5 m
B)17 m
C)34 m
D)51 m
E)None of these
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
ANSWER:B
Answer: B
Question: If e is a positive integer, then 3^e + 3^(e +1) =
Options:
A)4^a
B)3^a − 1
C)3^(2a) + 1
D)3^a*(a − 1)
E)4(3^e)
Rationale: 3^e + 3^(e +1)
= 3^e + (3^e * 3^1)
= 3^e (1 + 3)
= 3^e(4)
Ans. E) 4(3^e)
Answer: E
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 400 m?
Options:
A)122.9 m
B)127.5 m.
C)122.2 m
D)85 m
E)12289 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800
= 6300/8
= 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 400 m, the number of meters by which A beats C = (400 * 212.5)/1000
= 85m.
Answer:D
Answer: D
Question: Two representatives must be selected from each of two groups of students. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ?
Options:
A)1/6
B)1/4
C)2/7
D)1/3
E)1/2
Rationale: Group 1: 3 Men and 1 Woman
Group 2: 1 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 2 women from group 2 - 3C2*2C2 = 3 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 3*1*1*2 = 6 ways
Total Favorable cases = 3+6 = 9
Total Possible ways of selecting students 2 from each group = 4C2*3C2 = 6*3 = 18
Probability = 9/18 = 1/2
Answer : Option E
Answer: E
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITH', if repetition of letters is not allowed?
Options:
A)690
B)336
C)740
D)760
E)780
Rationale: The word 'LOGARITH' has 8 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 8P3
=
8
×
7
×
6
=
336
Option B
Answer: B
Question: Janet has to pay back her bank loan over 10 months following the below sequence.
$50, $55, $65, $80, $85, $95, $110, $115, $125, ?
How much will she pay back on the tenth month?
Options:
A)$155
B)$140
C)$135
D)$125
E)$130
Rationale: The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 10th Month is $140
Ans B
Answer: B
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A)2:5
B)2:6
C)2:9
D)2:1
E)2:4
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer:A
Answer: A
Question: If taxi fares were $1.00 for the first 1/5 mile and $0.20 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was
Options:
A)$1.56
B)$2.40
C)$3.80
D)$4.20
E)$2.80
Rationale: In 3 miles , initial 1/5 mile charge is $1
rest of the distance = 3 - (1/5) = 14/5
rest of the distance charge = 14(0.2) = $2.8 (as the charge is 0.2 for every 1/5 mile)
=> total charge for 3 miles = 1+2.8 = 3.8
Answer is C.
Answer: C
Question: The average of 20, 100 and 180 is twice the average of 10, 30, and which of the following ?
Options:
A)1)110
B)2)30
C)3)60
D)4)90
E)5)180
Rationale: 20 100 180 = 180+120 = 300/3 = 100
100/2 = 50
10 30 x = 40+x/3 should be smaller than 50
cross multiply 50*3-40 = 110
A
Answer: A
Question: A person was dialing a telephone. He forgot the last three digits of the six-digit telephone number but rembered that the number formed by the last three digits in the same order was a perfect square. What is the probability he dialed a right number?
Options:
A)1/32
B)1/46
C)1/49
D)1/36
E)1/18
Rationale: There are following perfect squares less than 1,000:
000 (0^2);
001 (1^1);
004;
009;
016;
025;
036;
049;
064;
081;
100;
121;
144;
...
961 (31^2).
Total of 32 perfect squares.
The probability = 1/32.
Answer: A.
Answer: A
Question: A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 550 ?
Options:
A)249
B)498
C)676
D)823
E)274
Rationale: slope of 2 and a y-intercept of 2
y-coordinate is 550
y = 2x + 2
548 = 2x
x = 274
Answer:
E. 274
Answer: E
Question: A grandmother lent $20,000 to her grandson at the beginning of the year. At the end of the year, she received y dollars more than than the amount she lent due to interest. She also received an additional amount $300, as a gift. In terms of y, what fraction of the amount that grandmother received was the gift?
Options:
A)50Y
B)300/(20300+Y)
C)300Y/20000Y
D)2/3Y
E)300Y/(Y+1)
Rationale: The amount of money the grandmother received was (20,000 + 300+ y) dollars. The $300 gift as a fraction of the amount received was, therefore, 300/(20,300 + y).
Answer: B.
Answer: B
Question: The diagonal of a rectangle is sqrt(41) cm. and its area is 20 sq. cm. The perimeter of the rectangle must be:
Options:
A)22
B)18
C)19
D)27
E)62
Rationale: Explanation:
\inline {\color{Black}\sqrt{l^{2}+b^{2}}=\sqrt{41}}
Also, lb=20
\inline {\color{Black}(l+b)^2=(l^{2}+b^{2})+2lb=41+40=81}
(l + b) = 9.
Perimeter = 2(l + b) = 18 cm.
Answer: B) 18 cm
Answer: B
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 0
II. x = 0
III. x =y
Options:
A)I only
B)II only
C)III only
D)I and III only
E)I, II, and III
Rationale: Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer B
Answer: B
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
Options:
A)600
B)729
C)278
D)268
E)308
Rationale: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A
Answer: A
Question: The L.C.M. of 2 numbers is 40. The numbers are in the ratio 4:5. Find their sum?
Options:
A)18
B)40
C)48
D)32
E)56
Rationale: Let the numbers be 4x and 5x
L.C.M. = 20x
20x = 40
x = 2
The numbers are = 8 and 10
Required sum = 8+10 = 18
Answer is A
Answer: A
Question: For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.5?
Options:
A)12.6.
B)14.4.
C)15.8.
D)15.7.
E)16.4.
Rationale: [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.5
= 6*0 + 2*7.2 + 8 - 6.5
= 0 +14.4 +1.5
15.7
Answer D
Answer: D
Question: The mean proportional between 4 and 9 is?
Options:
A)33
B)77
C)35
D)88
E)29
Rationale: 7/20 * 100 = 35
Answer:B
Answer: B
Question: How many different committees can be formed from a group of four women and eight men if three people are on the committee and at least one member must be a man?
Options:
A)215
B)220
C)225
D)216
E)210
Rationale: 4 Women and 8 Men. Three people needed
It is always better to subtract the total from none in case of at least one problems.
Total ways = 12C3 = 220
Total ways without any men = 4C3 = 4
Hence ways in which at least one man will be present = 220 - 4 = 216
Correct option: D
Answer: D
Question: The square root of 636 is between which set of integers?
Options:
A)24 and 25
B)25 and 26
C)26 and 27
D)27 and 28
E)28 and 29
Rationale: 25^2=625
26^2=676
Hence 636 lies between 25^2 & 26^2
ANSWER:B
Answer: B
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
Options:
A)560
B)240
C)329
D)443
E)544
Rationale: Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2xkilograms. So, the total is x+2x=3x This must be equal to 360.
3x=360
x=360/3
x=120
Therefore, the salesman sold 120 kg in the morning and 2⋅120=240 kg in the afternoon.
Answer: B
Question: What is the place value of 7 in the numeral 57468?
Options:
A)7000
B)5000
C)7
D)700
E)70
Rationale: place value of 7 = 7 * 1000 = 7000
Answer is A
Answer: A
Question: Which of the following is closer to (7!+5!)-(7!-5!)?
Options:
A)120
B)150
C)200
D)240
E)360
Rationale: (7!+5!)-(7!-5!)=5040+120-5040+120
= 240
Answer: D
Answer: D
Question: For what k value(s) is the following equation satisfied: 2k-9-k = 4k+6-3k
Options:
A)a. -5
B)b. 0 only
C)c. 5/2 only
D)d. No value
E)e. Any value
Rationale: 9k-9-8k = 4k+4-3k
k - 9 = k + 4
-9 = 4, which is false.
So, no k satisfies given equation.
Answer: D.
Answer: D
Question: x+(1/x) = 2.5 find x^2 + (1/x^2)
Options:
A)2.25
B)3.25
C)4.25
D)5.25
E)6.25
Rationale: squaring on both sides (x+1/x)^2=2.5^2
x^2+1/X^2=6.25-2
x^2+1/X^2=4.25
ANSWER:C
Answer: C
Question: A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?
Options:
A)1
B)4
C)3
D)2
E)6
Rationale: D
Just 2
Day One: You make your first cut at the 1/7th mark and give that to the worker.
Day Two: You cut 2/7ths and pay that to the worker and receive the original 1/7th in change.
Day three: You give the worker the 1/7th you received as change on the previous day.
Day four: You give the worker 4/7ths and he returns his 1/7th cut and his 2/7th cut as change.
Day Five: You give the worker back the 1/7th cut of gold.
Day Six: You give the worker the 2/7th cut and receive the 1/7th cut back in change.
Day Seven: You pay the worker his final 1/7th.
Answer: D
Question: How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 20% solution?
Options:
A)6.7
B)1.3
C)9.6
D)12.5
E)7.9
Rationale: Amount salt in 100kg solution = 10*100/100 = 10 kg
Let x kg of pure salt be added
then(10+x)/(100+x)=20/100
100+10x=200+2x
8x = 100
x = 12.5
Answer is D
Answer: D
Question: On a trip covering 350 km, a bicyclist travels the first 200 km at 20 km per hour and the remainder of the distance at 15 km per hour. What is the average speed, in km per hour, for the entire trip?
Options:
A)15.5
B)16.0
C)17.5
D)19.0
E)18.5
Rationale: time 1 = 200 / 20 = 10 hours
time 2 = 150 / 15 = 10 hours
total time = 20 hours
average speed = 350 / 20 = 17.5 km/hr
The answer is C.
Answer: C
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 360 votes. Find the number of votes casted to the winning candidate?
Options:
A)288
B)744
C)788
D)298
E)930
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 360
62% -------- ? => 930
Answer: E
Answer: E
Question: A researcher computed the mean, the median, and the standard deviation W for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
Options:
A)The mean only
B)The median only
C)The standard deviation only
D)The mean and the median
E)The mean and the standard deviation
Rationale: If we add or subtract a constant to each term in a set the standard deviation W will not change..
If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.
Answer: D.
Answer: D
Question: If 9 ministers are to be seated at a round table conference, then how many different ways can they be seated?
Options:
A)24
B)60
C)40320
D)720
E)180
Rationale: Simple formula:
There are (n - 1)! ways to arrange n distinct objects in a circle.
so its (9-1)! = 8! = 40320=C
Answer: C
Question: If the productivity of a brigade grows by 12% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade?
Options:
A)0.21
B)0.82
C)1.2
D)1.232
E)1.44
Rationale: B = 10-men brigade
p = increase in the productivity = 12%
Solution: B x p = B x 1.12 = 1.12B -------> the productivity of 11 men brigade
1.12B x p = 1.12B x 1.1 = 1.232B -----> the productivity of 12 men brigade
The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.232B/B = 1.232
D
Answer: D
Question: The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
Options:
A)5 : 12
B)5 : 14
C)5 : 17
D)5 : 18
E)5 : 16
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128 = 5 : 16
Answer: Option E
Answer: E
Question: A mixture containing 6% boric acid is to be mixed with 2 quarts of a mixture which is 15% acid in
order to obtain a solution which is 12% acid. How much of the 6% solution must be used?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: This is a mixture problem.
The question asks, “How much of the 6% solution”.
Let x the number of quarts of 6% solution needed.
Write the equation and solve.
0.06+0.15(2)=0.12(x+2)
0.06x+0.30=0.12x+0.24
6x+30=12x+24
6=6x
x=1
The answer: 1 qt of 6% boric acid solution must be used.
correct answer A
Answer: A
Question: In a basket of apples, 12% of them are rotten and 66 are in good condition. Find the total number of apples in the basket.
Options:
A)33
B)75
C)23
D)20
E)287
Rationale: Let the total number of apples in the basket be m
12 % of the apples are rotten, and apples in good condition are 66
Therefore, according to the question,
88% of m = 66
88/100 × m = 66
m = (66 × 100)/88
m = 3 × 25
m = 75
Therefore, total number of apples in the basket is 75.
Answer:B
Answer: B
Question: A train speeds past a pole in 15 seconds and a platform 140 meters long in 25 seconds. What is the length of the train (in meters)?
Options:
A)190
B)200
C)210
D)220
E)230
Rationale: Let the length of the train be x meters.
The speed of the train is x / 15.
Then, x + 140 = 25*(x / 15)
10x = 2100
x = 210 meters
The answer is C.
Answer: C
Question: On a ranch, a rancher can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 4 attempts?
Options:
A)3/4
B)5/8
C)7/8
D)11/16
E)15/16
Rationale: P(missing all 4)=(1/2)^4=1/16
P(success on at least one attempt)=1-1/16=15/16
The answer is E.
Answer: E
Question: (525 + 275) Ã— 4 Ã— (3 + 2) = ?
Options:
A)12000
B)24000
C)16000
D)14000
E)16200
Rationale: (525 + 275) Ã— 4 Ã— (3 + 2) = ?
or, ? = 800 Ã— 4 Ã— 5 = 16000
Answer C
Answer: C
Question: A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and one-legged captain) to a nearby port. Altogether, these passengers have 15 heads and 43 legs. How many cats does the ship host?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: sa's +co +ca +cats = 15. sa's + 1 +1 +cats =15 or sa's +cats =13.
sa's(2) +2 +1 +cats*4 =43 sa's*2 +cats*4 = 40 or sa's +cats*2 =20 or 13-cats +cat*2 =20
then cats =7
D
Answer: D
Question: How long will a boy take to run round a square field of side 40 meters, if he runs at the rate of 9km/hr?
Options:
A)64sec
B)45sec
C)1min
D)32sec
E)25sec
Rationale: Speed = 9 km/hr = 9*5/18 = 5/2 m/sec
Distance = 40*4 = 160m
Time taken = 160*2/5 = 64sec
Answer is A
Answer: A
Question: A triangle has a perimeter 17. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
Options:
A)4
B)5
C)6
D)7
E)3
Rationale: The SHORTER sides have integral lengths equal to x and x + 1
Let the longest side be 'a'
So, a + x + (x +1) = 17
a + 2x = 17.......eqn (1)
We know that the sum of the lengths of the shorter sides has to be more than the length of the longer one. i.e 2x+1> a
a =7
D
Answer: D
Question: For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?
Options:
A)8/5
B)5/2
C)3
D)33/25
E)4
Rationale: Let monthly salary for each of the 11 months except December was x, then
11x*1/10 + Nx*1/3 = 1/8(11x + Nx);
11/10 + N/3 = 1/8(11 + N)
33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66
N = 66/50=33/25
Answer: D.
Answer: D
Question: The average of first nine prime numbers is?
Options:
A)10
B)11.1
C)12.5
D)15.8
E)13.6
Rationale: Average = (2+3+5+7+11+13+17+19+23)/9= 100/9 = 11.1
Answer is B
Answer: B
Question: If an integer t is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that t(t + 1)(t + 2) will be divisible by 8?
Options:
A)1/4
B)3/8
C)1/2
D)5/8
E)3/4
Rationale: for t Total numbers 8*12
There are 12 numbers divisible by 8 -> 3*12 (if 8 is an example - (6,7,8), (7,8,9), (8,9,10))
and 12 numbers divisible by 4 but not divisible by 8 -> 2*12 (if 4 is an example (2,3,4) and (4,5,6))
The answer 5/8 -> D
Answer: D
Question: If integers w and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. wb + b^2
II. (w+ b)^2
III. w + b
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II, and III
Rationale: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
I. wb + b^2 --> if w=1 and b=2 then wb + b^2=6, which is a factor of 30. OK;
II. (w + b)^2 --> (w + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;
III. w + b --> if w=1 and b=2 then w + b=3, which is a factor of 30. OK.
Answer: B.
Answer: B
Question: Find the invalid no.from the following series 3, 6, 15, 31, 63, 127, 255
Options:
A)6
B)7
C)27
D)63
E)127
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 6 is wrong.
A
Answer: A