divelab/Sys2Bench huggingface dataset:
Question: Rahul went to a shop and bought things worth Rs. 30, out of which 40 Paise went on sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items?
Options:
A)17.6
B)24.6
C)21.6
D)18.6
E)20.6
Rationale: Total cost of the items he purchased = Rs.30
Given that out of this Rs.30, 40 Paise is given as tax
=> Total tax incurred = 40 Paise = Rs.40/100
Let the cost of the tax free items = x
Given that tax rate = 8%
∴ (30−40/100−x)8/100 = 40/100
⇒ 8(30 −0.4−x) = 40
⇒ (30− 0.4 − x) = 5
⇒ x = 30 − 0.4 − 5 = 24.6.
B)
Answer: B
Question: a dealer buys 4 varieties of wheat costing rs. 20,rs.25,rs.30 and rs.35 per kg in the ratio 6:4:3:1 and mixes all the four varieties and sells at 40% profit. What is the selling price per kg of wheat?
Options:
A)30.5
B)31.0
C)32.0
D)33.0
E)34.5
Rationale: CP = 20*6+25*4+30*3+35*1=345
SP = 1.4*345=483
Total no.of kgs=6+4+3+1=14
SP per kg=483/14 = 34.50
ANSWER:E
Answer: E
Question: If the quantity (p − 4) is 5 times the quantity (q − 5), then what is the relationship between p and q?
Options:
A)p = 5q + 30
B)p = 5q − 21
C)5p = q + 20
D)p = 5q
E)p = 5q − 20
Rationale: p-4=5(q-5)
p-4=5q-25
p=5q-21
option B
Answer: B
Question: Kyle, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/8, 1/4 and 3/5, respectively, what is the probability no one will solve the problem?
Options:
A)3/80
B)21/80
C)5/16
D)25/76
E)9/80
Rationale: P(Kyle will not solve)=1 - 1/8 = 7/8
P(David will not solve)= 1 - 1/4 = 3/4
P(Catherine will not solve) = 1- 3/5 = 2/5
P= (7/8)*(3/4)*(2/5) = 42/160 = 21/80
Answer:B
Answer: B
Question: What percent of a day is nine hours?
Options:
A)20.83%
B)16x1/2%
C)18x2/3%
D)37.5%
E)None of these
Rationale: Explanation :
Required percentage = (9/24100)%
= 37.5%.
Answer : D
Answer: D
Question: If 10 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a four-percent vinegar solution, what was the concentration of the original solution?
Options:
A)20%
B)24%
C)25%
D)28%
E)30%
Rationale: Let x be the concentration of the original solution.
10x = 0.04(60)
x = 0.24
The answer is B.
Answer: B
Question: 1/x+1/y=1/z where x=12 and y,z positive integer how many possible value of y and z ?
Options:
A)4
B)7
C)12
D)15
E)infinite
Rationale: 1/12 = 1/z - 1/y
y = 12 * z / ( 12 - z )
0 < z < 12
Only for z = 3 ,4 ,6 ,8 , 9 ,10 and 11 , y is intiger
Hence seven solutions
ANSWER:B
Answer: B
Question: For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 94 Θ 33 ) Θ 17 ) - ( 96 Θ (33 Θ 17)) ?
Options:
A)-10
B)-2
C)8
D)13
E)17
Rationale: (( 94 Θ 33 ) Θ 17 )
The remainder of 98 divided by 33 is 28;
The remainder of 28 divided by 17 is 11;
( 96 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
The remainder of 96 divided by 16 is 0.
11 - 0 = 11.
Answer: D.
Answer: D
Question: Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 4 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?
Options:
A)5
B)7
C)15
D)20
E)25
Rationale: Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12
Collective work Time = 12/7 = 1.7 Hrs
Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 4 breaks
=.3/4=.07 hrs = 7 m
so Answer is B) 10 mins
Answer: B
Question: 1370 , 1320 , X, -180, -6430
Options:
A)1070
B)6530
C)6630
D)6730
E)6830
Rationale: 1370-50*(5^0)=1320
1320-50*(5^1)=1070
1070-50*(5^2)=-180
-180-50*(5^3)=-6430
ANSWER:A.
Answer: A
Question: The product of the digits of the four-digit number Q is 36. No two digits of are identical. How many different numbers are possible values of Q ?
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: The main question here is how can you arrange 4 different digits Q. We don't even need to find the number. from the question itself we know that there are 4 different digits and none of them is 0 as the product is non-zero.
Therefore no of ways to arrange 4 diff. digits is 4! which is 24
hence C
Answer: C
Question: If x is a positive integer, which of the following must be odd?
Options:
A)x+1
B)x^2+x
C)x^2+x+11
D)x^2−1
E)3x^2−3
Rationale: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 11 = ODD
Hence C.
Answer: C
Question: A school committee consists of 2 teachers and 4 students. The number of different committees that can be formed from 5 teachers and 10 students is
Options:
A)3000
B)2520
C)2100
D)2510
E)2210
Rationale: There are C(5,2) ways to select 2 teachers from 5 and C(10,4) ways to select 4 students from 10 where C(n,r) is the combinations of n items taken r at the time. Using the multiplication counting principle,the number of different committees that can be formed is given by
C(5,2)*C(10,4) = 2100
Answer: C
Question: A garrison of 2000 men has provisions for 54 days. At the end of 18 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
Options:
A)1977
B)1600
C)1979
D)1900
E)1278
Rationale: 2000 ---- 54
2000 ---- 36
x ----- 20
x*20 = 2000*36
x = 3600
2000
-------
1600
Answer: B
Answer: B
Question: In a group of cows and hens, the number of legs are 12 more than twice the number of heads. The number of cows is :
Options:
A)5
B)6
C)7
D)10
E)12
Rationale: Let no of cows be x, no of hens be y.
So heads=x+y
Legs=4x+2y
Now, 4x+2y = 2(x+y)+ 12
2x = 12
x = 6.
ANSWER:B
Answer: B
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.7 the sixth number is?
Options:
A)11.4
B)11.3
C)13.3
D)11.5
E)11.1
Rationale: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.7 = 70.2
63 + 70.2 = 133.2 – 119.9 = 13.3
6th number = 13.3
Answer: C
Answer: C
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 17% microphotonics; 24% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
Options:
A)8°
B)10°
C)26°
D)36°
E)52°
Rationale: Here all percentage when summed we need to get 100% . As per data 17+24+15+29+8 = 93%.
So remaining 7% is the balance for the astrophysics.
Since this is a circle all percentage must be equal to 360 degrees.
100% ---- 360 degrees
Then 7% will be 26 degrees..
IMO option C.
Answer: C
Question: A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $2,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002?
Options:
A)$18,400
B)$19,500
C)$20,200
D)$20,700
E)$21,100
Rationale: Price in 96 = 22000
Price decrease each year = 2.5/100*22000 = 550
Price in 97 = 22000 - 550
Price in 98 = 22000 - 2*550
Price in 99 = 22000 - 3*550
Price in 00 = 22000 - 4*550
Price in 01 = 22000 - 5*550
Price in 02 = 22000 - 6*550 = 18700
Investment in the car = 1500
Net price of the car in 02 = 18700 + 2000 = $20700
Correct Option: D
Answer: D
Question: A reduction of 23% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
Options:
A)s.2.99
B)s.2.4
C)s.2.5
D)s.2.2
E)s.2.1
Rationale: 100*(23/100) = 23 --- 10
? --- 1 => Rs.2.3
100 --- 77
? --- 2.3 => Rs.2.99
Answer:A
Answer: A
Question: 60% of a number is added to 120, the result is the same number. Find the number?
Options:
A)300
B)788
C)677
D)256
E)261
Rationale: (60/100) * X + 120 = X
2X = 600
X = 300
Answer: A
Answer: A
Question: If A lends Rs.3200 to B at 12% per annum and B lends the same sum to C at 14.5% per annum then the gain of B in a period of 5 years is?
Options:
A)157.78
B)157.98
C)400
D)420
E)430
Rationale: (3200*2.5*5)/100
=> 400
Answer: C
Answer: C
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 45min will be.
Options:
A)60 km/h
B)53 km/h
C)40 km/h
D)70 km/h
E)65 km/h
Rationale: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=45/60hr=3/4hr
New speed = 40* 4/3 kmph= 53kmph
Answer : B
Answer: B
Question: A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 2.5 grams per cubic centimeter and mineral Y weighs 3 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)
Options:
A)5,500,000
B)2,800,000
C)55,000
D)28,000
E)280
Rationale: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3
By volume
40% is X = 400,000 cm^3
60% is Y = 600,000 cm^3
By weight,
In 1 cm^3, X is 2.5 gms
In 400,000 cm^3 , X = 2.5 * 400,000 = 1,000,000 grams
In 1 cm^3, Y is 3 gms
In 600,000 cm^3, Y = 3 * 600,000 = 1,800,000 gms
Total gms in 1 m^3 = 1,000,000 + 1,800,000 = 2,800,000
ANSWER:B
Answer: B
Question: A, B and C have Rs.900 between them, A and C together have Rs.400 and B and C Rs.750. How much does C have?
Options:
A)100
B)150
C)200
D)250
E)350
Rationale: A+B+C = 900
A+C = 400
B+C = 750
--------------
A+B+2C = 1150
A+B+C = 900
----------------
C = 250
ANSWER:D
Answer: D
Question: Mohan purchased 14 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?
Options:
A)A)Rs.572
B)B)Rs.594
C)C)Rs.596
D)D)Rs.595
E)E)of these
Rationale: Explanation:
Price of 14 kgs of rice at Rs.26/kg = 14x26 = Rs.364
Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208
Therefore, Total amount = Rs.364+Rs.208 = Rs.572.
Answer: Option A
Answer: A
Question: If |20x-10| = 170, then find the product of the values of x?
Options:
A)-45
B)50
C)-72
D)35
E)-30
Rationale: |20x-10| = 170
20x-10 = 170 or 20x-10 = -170
20x = 180 or 20x = -160
x = 9 or x = -8
product = -8*9 = -72
Answer is C
Answer: C
Question: 0.35 represents what percent of 0.7?
Options:
A)0.05%
B)0.5%
C)50%
D)500%
E)5000%
Rationale: One more method
0.35 represents what percent of 0.7?
Adjusting the decimal
3.5 represents what percent of 7?
Divide by 7
0.5 represents what percent of 1?
Answer = 0.5*100 = 50% = C
Answer: C
Question: A pipe can fill a tank in 15 minutes and another one in 10 minutes. A third pipe can empty the tank in 5 minutes. The first two pipes are kept open for 4 minutes in the beginning and then the third pipe is also opened. In what time will the tank be empited ?
Options:
A)35 min
B)15 min
C)20 min
D)Cannot be emptied
E)None of these
Rationale: Proportion of the volume of the tank filled by both the
pipes in 4 min = 4(1⁄15 + 1⁄10) = 2⁄3rd of the tank
Volume of the tank filled by all the pipes working together = 1⁄15 + 1⁄10 - 1⁄5 = -1⁄30
i.e. 1⁄30 tank is emptied in 1 min.
∴ 2⁄3 rd of the tank can be emptied in 2×30/3=20min
Answer C
Answer: C
Question: Find the value of y from given equation: (12)^3 x 6^4 ÷ 432 = y?
Options:
A)2345
B)2790
C)3490
D)7389
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: A volume of 11780 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?
Options:
A)2812
B)8231
C)2734
D)4222
E)2945
Rationale: a volume of 4l can be kept in 1 hemisphere
therefore, a volume of 11780l can be kept in (11780/4) hemispheres
ans.2945
ANSWER:E
Answer: E
Question: Two heavily loaded sixteen-wheeler transport trucks are 855 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway?
Options:
A)90
B)130
C)135
D)320
E)450
Rationale: I've been reading the website for a while and I'm always keen to see different approaches so I would like to share one that works for me:
Short version:
Truck A travels for an hour.
Distance remaining = 855-90 = 765k
Ratio of speeds 9:8 -> 765/17 = 45
Truck A = 90 + 45*9 = 495
Truck B = 45*8 = 360
Delta = 135km
Answer C
Answer: C
Question: If x/(12p) is an odd prime number, where x is a positive integer and p is a prime number, what is the least value of x?
Options:
A) 22
B) 33
C) 44
D) 66
E) 72
Rationale: x/(12p) = odd prime number
x = odd prime number * 11p
Least value of x = Lowest odd prime number * 11 * Lowest value of p
= 3 * 12* 2 = 72
Answer E
Answer: E
Question: For a certain set, the value range of its members is 96.8. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?
Options:
A)21.2
B)24.2
C)36.3
D)48.4
E)96.8
Rationale: Let x and z be the smallest and largest of the original set, respectively.
z - x = 96.8
The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.
Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 96.8 / 4 = 24.2
The answer is B.
Answer: B
Question: A regular hexagon is there. The mid points of the sides were joined and formed another hexagon.Then What is the percentage reduction in area.
Options:
A)25%
B)35%
C)45%
D)55%
E)65%
Rationale: Let ABCDEF be the regular hexagon with sides AB and ED parallel. P and Q are mid points of AF and EF resp.
AE=root(3) * s (s is side of hexagon)
then PQ =(root(3) * s)/2 mid point theorem
Now u know side of inner hexagon
use formula area of hexagon = (3 * root(3))2 * s^2
and find diff in area of two hexagon multiply by 100 and divide the product by area of bigger hexagon
Ans 25%
ANSWER:A
Answer: A
Question: In a garden, 26 trees are planted at equal distances along a yard 400 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?
Options:
A)10
B)8
C)12
D)14
E)16
Rationale: 26 trees have 25 gaps between them.
Length of each gap = 400/25 = 16
i.e., distance between two consecutive trees = 16
Answer is E.
Answer: E
Question: The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 68 kg. What is the correct weight?
Options:
A)58kgs
B)58.85kgs
C)58.95kgs
D)59kgs
E)59.85kgs
Rationale: Actual total weight is (20X 58.4 - 56 + 68) = 1180 Kgs
Actual average weight is 1180/20 = 59kgs
D
Answer: D
Question: The ratio between b and y is 7/9; b and y are increased by 4, what is the ratio between the new values of b and y?
Options:
A)7/9
B)14/9
C)7/18
D)11/13
E)It Cannot Be Determined
Rationale: Ratio = 7k/9k = 7/9, 14/18, etc.
b and y are increased by 4 --> (7k + 4)/(9k + 4)
New ratio can be 11/13, 18/22, etc.
Answer: E
Answer: E
Question: A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.
Options:
A)50 km/hr
B)60 km/hr
C)65 km/hr
D)70 km/hr
E)None of these
Rationale: Explanation:
We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.
Lets solve it.
Time = 50/60 hr = 5/6 hr
Speed = 48 mph
Distance = S × T = 48 × 5/6 = 40 km
New time will be 40 minutes so,
Time = 40/60 hr = 2/3 hr
Now we know,
Speed = Distance/Time
New speed = 40 × 3/2 kmph = 60kmph
Answer: B
Answer: B
Question: If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 6, and 7, what is the greatest number of four-digit extensions that the company can have?
Options:
A)4
B)6
C)11
D)12
E)24
Rationale: Since the phone number must be even, the unit's digit can be either 2 or 6.
When the unit's digit is 2 --> number of possibilities is 3! = 6
When the unit's digit is 6 --> number of possibilities is 3! = 6
Largest number of extensions = 6 + 6 =12
Answer:D
Answer: D
Question: Barbara has 8 shirts and 11 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
Options:
A)41
B)86
C)100
D)70
E)104
Rationale: 8 shirts
9 pants
we can combine 2 shirts with (11-3) pants
2*8=16
we can combine the other shirts (6) with any pants (9)
8*11=88
Thus total :16+88=104	ANS:E
Answer: E
Question: Alice is now 10 years older than Bob. If in 6 years Alice will be twice as old as Bob, how old will Alice be in 5 years?
Options:
A)19
B)21
C)23
D)25
E)27
Rationale: A=B+10 so B=A-10.
A+6=2(B+6).
A+6=2(A-10+6).
A+6=2A-8.
A=14.
In 5 years, Alice will be 19 years old.
The answer is A.
Answer: A
Question: The sides of a square region, measured to the nearest centimeter, are 4 centimeters long. The least possible value of the actual area of the square region is
Options:
A)15.25 sq cm
B)18.25 sq cm
C)12.25 sq cm
D)21.25 sq cm
E)25.25 sq cm
Rationale: Though there might be some technicalities concerning the termnearest(as 3.5 is equidistant from both 3 and 4) the answer still should be : 3.5^2=12.25.
Answer: C
Answer: C
Question: A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 5^12 and 5^16, respectively, what is the value of A?
Options:
A)-24(5^12)
B)-27(5^12)
C)-24(5^6)
D)23(5^12)
E)24(5^12)
Rationale: Ans : B
Assume that the numbers appear as shown below on the number line
A-----B-----C-----D-----E-----F-----G-----H
(5^12) (5^13)
As the values for G and H are given , we can calculate the difference between any two terms of the series .
Common Difference ,d = (5^13) - (5^12)
= (5^12) *[ 5-1 ]
= (5^12)*(4)
Also F + d = G as the terms are in equidistant and in increasing order.
So F + (5^12)*(4) = (5^12).
That is , F = (5^12) - (5^12)*(4)
= (5^12)[ 1-4]
= (5^12) (-3)
Similarly , E = F - d
= (5^12)[-3-4]
= (5^12)*(-7)
You can see a -4 getting added to the non-exponent part of the values . That is , according to the pattern , D SHOULD BE (5^12)*(-7-4)= (5^12)*(-11)
Following this pattern , A = (5^12)*(-27)
B
Answer: B
Question: The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
Options:
A)2333
B)1015
C)2683
D)2693
E)1113
Rationale: Explanation:
Required Number = (L.C.M of 12, 16, 18,21,28)+7
= 1008 + 7
= 1015
Answer: B) 1015
Answer: B
Question: A certain toy store's revenue in November was 1/5 of its revenue in December and its revenue in January was 3/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
Options:
A) 1/4
B) 1/2
C) 2/3
D) 2
E) 6
Rationale: Let Dec rev =100
Then Nov rev is 1/5 (100) => 20
Therefore Jan rev = 3/4(Nov rev) = 3/4(20) => 15
Hence Dec rev = x*( Nov rev+Jan rev)/2
100 = x* (20+15)/2
x = 100/17.5 => 5.71=6
Ans) E
Answer: E
Question: If the probability of rain on any given day in City X is 40%, what is probability that it rains on exactly 3 days in a 4 day period?
Options:
A)16/25
B)48/125
C)96/625
D)108/625
E)132/625
Rationale: One possible way is rain-rain-rain-no rain.
The probability of this is 2/5*2/5*2/5*3/5 = 24/625
The number of possible ways is 4C3 = 4, so we multiply this by 4.
P(rain on exactly 3 days) = 4*24/625 = 96/625
The answer is C.
Answer: C
Question: What are the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?
Options:
A)714
B)814
C)850
D)866
E)None of these
Rationale: Explanation:
In this type of questions, first we need to calculate the area of tiles. With we can get by obtaining the length of largest tile.
Length of largest tile can be obtained from HCF of length and breadth.
So lets solve this,
Length of largest tile = HCF of (1517 cm and 902 cm)
= 41 cm
Required number of tiles =
Area of floor/Area of tile=(1517×902/41×41)=814
Option B
Answer: B
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
Options:
A)14 years
B)10 years
C)8 years
D)17 years
E)None of these
Rationale: Explanation:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x = 20
⇒ x = 4.
⇒ Age of the youngest child = x = 4 years.
Answer: A
Answer: A
Question: What is the minimum value of |x-4| + |x+7| + |x-5| ?
Options:
A)-3
B)3
C)5
D)-12
E)12
Rationale: A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative.
|x-4| >= 0 --> Minimum occurs at x = 4
|x+7| >= 0 --> Minimum occurs at x = -7
|x-5| >= 0 --> Minimum occurs at x = 5
x = -7 --> Result = 11 + 0 + 12 = 23. Also any negative value will push the combined value of |x-4| + |x-5| to a value > 9.
x = 4 --> Result = 0 + 11 + 1 =12
x = 5 --> Result = 1 + 12 + 0 = 13
x = 7 --> Result = 3 + 14 + 2 = 19
So minimum value of the expression occurs at x = 4 and the resultant value = 12
Answer: E
Answer: E
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is
Options:
A)21/25
B)17/25
C)4/25
D)8/25
E)9/25
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
ANSWER:B
Answer: B
Question: If you spend 1/4 of your salary during the first week of the month and 20% of it during each of the coming 3 weeks, what part(fraction) of your salary will leave unspent at the end of the month?
Options:
A)2/20
B)3/20
C)4/20
D)5/20
E)None
Rationale: Solution:
1/4+3(20/100)=1/4+3/5=5+12/20=17/20
The sallary that will be spent = 17/20
Unspend will be = 1−17/20 =20−17/20 =3/20
Answer B
Answer: B
Question: Given the sum 195 of 13 consecutive integers, find the sum of 4th number and 7th number of the sequence
Options:
A)65
B)54
C)26
D)30
E)27
Rationale: The median is: 195/13 = 15.
The middle position is: 13/2 = 6.5, rounded up: 7th position. So 15 is the value of the 7th position
Difference between 7th and 4th position = 3 positions less
15 - 3 = 12 = is the value of the 4th position
15 + 12 = 27 = sum of 4th and 7th number.
Answer: E
Answer: E
Question: A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 2
matches are totally played, how many teams participated?
Options:
A)4
B)5
C)6
D)2
E)3
Rationale: 2 ways to solve this problem..
summation(x)=n(n-1)/2
n(n-1)/2=2;
n^2-n-4=0
Ans : 2
ANSWER:D
Answer: D
Question: The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 432 sq meters, then what is the width (in meters) of the rectangular plot?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Area = L*W = 3W^2 = 432
W^2 = 144
W = 12
The answer is C.
Answer: C
Question: The total number of digits used in numbering the pages of a book having 360 pages is
Options:
A)972
B)990
C)1098
D)1305
E)1405
Rationale: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 261) = (9 + 180 + 783) = 972.
ANSWER:A
Answer: A