divelab/Sys2Bench huggingface dataset:
Question: If 21,394 + x is a multiple of 3, which of the following could be the value of x?
Options:
A)1
B)2
C)3
D)4
E)6
Rationale: Sum of the digits of 21,394 is 2+1+3+9+4 = 19
Now 19 is not a multiple of 3, the next multiple of 3 close to 19 is 21, which is 2 added to 19.
So the least number to be added to 21,394 is 2
B
Answer: B
Question: Emily has a cylindrical water bottle that can hold 1000π cubic centimeters of water. Right now,
the bottle is holding 100π cubic centimeters of water, and the height of the water is 1 centimeter.
Compute the radius of the water bottle.
Options:
A)8
B)10
C)15
D)22
E)13
Rationale: if the height of the water is 1 centimeter when there are 100π cubic centimeters
of water, then the height of the water would be 10 centimeters when the water bottle is full.
Therefore,πr2 * 10 = 1000π and r2 = 100, so r = 10 .
correct answer B
Answer: B
Question: A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?
Options:
A)95%
B)90%
C)80%
D)75%
E)60%
Rationale: According to the matrix the probability of selecting a colorblind person is 0.6 and the probability of NOT selecting a colorblind person is 0.4.
{The probability of selecting a colorblind person in three tries} = 1 - {the probability of NOT selecting a colorblind person in three tries} = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936 = 93.6%.
We are asked to find the approximate probability, so the answer is 95%.
Answer: A.
Answer: A
Question: The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
Options:
A)4.2
B)4.4
C)4.6
D)5.6
E)5.7
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
C
Answer: C
Question: For which of the following values of n is (200+n)/n NOT an integer?
Options:
A) 1
B) 2
C) 3
D) 4
E) 5
Rationale: Solution:
This problem is easiest solved by plugging in each answer choice.
A) (200 + 1)/1 = 101/1 = 201
Answer choice A yields an integer.
B) (200 + 2)/2 = 202/2 = 101
Answer choice B yields an integer.
C) (200 + 3)/3 = 203/3 = 67, remainder 2
Answer choice C DOES NOT yield an integer.
Although we believe answer choice C is correct, we should still test the other answer choices.
D) (200 + 4)/4 = 204/4 = 51
Answer choice D yields an integer.
E) (200 + 5)/5 = 205/5 = 41
Answer choice E yields an integer.
Thus, the correct answer is answer choice C.
Answer: C
Question: If x is negative and y is positive, which of the following cannot be positive?
Options:
A)-x/y
B)x/-y
C)-xy
D)x*(-y)
E)x^3*y
Rationale: -*-*-= -
x^3*y is negative.
Answer : E
Answer: E
Question: What is the smallest number which when increased by 3 is divisible by 12, 15, 35, and 40?
Options:
A)837
B)947
C)1027
D)1155
E)1231
Rationale: Factor each of the numbers 8, 15, 35, and 40 into primes:
12=2*2*3; 15=3*5; 35=5*7; 40=2*2*2*5
The smallest number divisible by all of them is thus 2*2*2*3*5*7 = 840
837 + 3 = 840
A
Answer: A
Question: The fourth proportional to 12, 14 and 18 is?
Options:
A)21
B)66
C)77
D)88
E)99
Rationale: (14*18)/12 = 21
Answer: A
Answer: A
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 30 seconds. Its length is?
Options:
A)188 m
B)876 m
C)251 m
D)200 m
E)145 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 30= x / 15
x = 200 m.
Answer: D
Answer: D
Question: A car drives 60 miles on local roads at 20 mph, and 195 miles on the highway at 65 mph, what is the average speed of the entire trip?
Options:
A)36 mph
B)40 mph
C)44 mph
D)43 mph
E)58 mph
Rationale: So The Answer is Plainly D....
we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance)
for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20*t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles
in the same way we should divide 195 to 65 to find the needed time to cover 195 miles ,so t= 3 hours
so the total time for covering total distance would be 3+3 = 6 hours and total distance is 60+195= 255 miles
Final stage : average speed is total distance divide to total time : 255/6 = 42.5 miles per hour rounded up to 43 MPH....
Answer: D
Question: A certain airline's fleet consisted of 100 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: Let x be the number of years.
4x > 100 - 3x
7x > 100
x > 14 + 2/7
The answer is B.
Answer: B
Question: Find the next number in the Sequence
5, 16, 49, 104, ?
Options:
A)111
B)224
C)133
D)181
E)231
Rationale: D
181
+11 =>16
+33 =>49
+55 =>104
+77 =>181
Answer: D
Question: In the xy-plane, a line has slope 3 and x-intercept 5. What is the y-intercept of the line?
Options:
A)-15
B)-3
C)0
D)3
E)9
Rationale: Let the line be represented by a general equation y=mx+b, where m = slope (3) and b=y intercept. We are also given the value of x-intercept 5.
Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.
Putting these values in the equation : 0 = 3*5 + b => b = -15. Hence A.
Answer: A
Question: 100 identical coins, each with probability P of showing 'heads' are tossed once. If 0<P<1 and the probability of 'heads' showing on 50 coins is equal to that of 'heads' showing on 50 coins, then find the value of P.
Options:
A)51/101.
B)51/100
C)32/81
D)None of these
E)Cannot be determined
Rationale: Explanation :
Let X be the number of coins showing 'heads', then X follows a binomial distribution with parameters n = 100 and P.
As given, P(X=50) = P(X=51)
=> 100C50P50(1-P)50 = 100C51P51(1-P)49 .
=> 51/50 = P / (1-P)
=> p = 51/101.
Hence, the value of p is 51/101.
Answer : A
Answer: A
Question: At what rate percent on simple interest will a sum of money double itself in 30 years?
Options:
A)3 1/3%
B)3 1/9%
C)3 9/3%
D)3 2/3%
E)3 6/3%
Rationale: P = (P*30*R)/100
R = 3 1/3%
Answer: A
Answer: A
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)?
Options:
A)28 years
B)29 years
C)20 years
D)26 years
E)21 years
Rationale: Present total age of the members = 26(5) = 130 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 130 -10 = 120 years
Their average age at the time of the birth of the youngest member = [120 - (4 * 10)] / 4
= 30 - 10 = 20 years.
Answer:C
Answer: C
Question: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 50 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
Options:
A)105
B)120
C)140
D)147
E)98
Rationale: Car Y began travelling after 72 minutes or 1.2 hours.
Let t be the time for which car Y travelled before it stopped.
Both cars stop when they have travelled the same distance.
So,
35(t+1.2) = 50t
t=2.8
Distance travelled by car X from the time car Y began traveling until both cars stopped is
35 x 2.8
= 98 miles
Answer:- E
Answer: E
Question: A boat goes 100 km downstream in 10 hours, and 75 Km upstream in 25 hours. The speed of the stream is?
Options:
A)22 1/9
B)6
C)5
D)3.5
E)4.5
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 25 US = 3
? ----- 1 S = (10 - 3)/2
= 3.5 kmph.
Answer:D
Answer: D
Question: If (y - 4)(z - 8) + 9(z - 8) = 0, then which of the following must be true?
Options:
A) y = -4 and z = -3
B) y = -4 or z = 8
C) y = -4 or z = 3
D) y = 1 and z = 3
E) y = 1 or z = 3
Rationale: factor out:
(z-8)(y-4+9)=0
(z-8) (y+5) = 0
So by checking options we get ,
B.
Answer: B
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is
Options:
A)25/42
B)25/40
C)25/49
D)25/47
E)25/44
Rationale: Explanation:
Total fruits = 9
Since there must be at least two apples,
= 25/42.
Answer: A
Answer: A
Question: How many distinct integer values of n satisfy the inequality||n-3| + 4| ≤ 15?
Options:
A)15
B)16
C)17
D)18
E)13
Rationale: so i can write this as In-3I+4<=15
or In-3I<=11
so n can have -8 to 14 = 13 true values....
E
Answer: E
Question: The area of a square is 4356 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)5:28
B)5:19
C)7:12
D)5:13
E)7:22
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 = 4356
a = 66
L = 2a and b = a - 24
b : l = a - 24 : 2a = 42 : 132
= 7:22
Answer:E
Answer: E
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 1000 revolutions. How many revolutions does the second wheel make in covering d feet?
Options:
A)1000xy
B)1000x/y
C)1000x - y
D)1000y/x
E)1000y - x
Rationale: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
1000 = d/(x*pi)
d = 1000 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (1000 * x * pi) / (y*pi) = 1000x/y
Answer (B)
Answer: B
Question: The average marks of a class of 25 students is 50 and that of another class of 40 students is 65. Find the average marks of all the students?
Options:
A)52.6
B)52.4
C)52.1
D)59
E)52.9
Rationale: Sum of the marks for the class of 25 students = 25 * 50 = 1250
Sum of the marks for the class of 40 students = 40 * 65 = 2600
Sum of the marks for the class of 65 students =
1250 + 2600 = 3850
Average marks of all the students = 4850/65 = 59.Answer: D
Answer: D
Question: The speed of a train is 60 kmph. What is the distance covered by it in 20 minutes?
Options:
A)21 kmph
B)22 kmph
C)20 kmph
D)23 kmph
E)24 kmph
Rationale: 60 * 20/60
=20 kmph
Answer: C
Answer: C
Question: A car covers a distance of 624 km in 4 hours. Find its speed?
Options:
A)156
B)288
C)271
D)276
E)128
Rationale: 624/4 = 156 kmph
Answer: A
Answer: A
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
Options:
A)70
B)65
C)25
D)30
E)40
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
ANSWER A
Answer: A
Question: Reduce
368/598
to the lowest terms
Options:
A)30/25
B)28/13
C)28/29
D)8/13
E)None of these
Rationale: Explanation:
We can do it easily by in two steps
Step1: We get the HCF of 368 and 598 which is 46
Step2: Divide both by 46, we will get the answer 8/13
Answer: Option D
Answer: D
Question: A Complany provides health insurance that pays 50.0% of the cost, with a $180.00 deductible. This means that the employees pays the first $180.00, after which the insurance company pays 150.0%. How much will an employee pay if his total medical bill is $1400.00?
Options:
A)$790
B)$780
C)$770
D)$760
E)$750
Rationale: Amount employee pays = 180 + 50/100* (1400-180)
= 180 + 50/100*1220
= 180+610
= $790
ANSWER:A
Answer: A
Question: In a school of 700 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
Options:
A)173
B)126
C)153
D)143
E)133
Rationale: 44 + 28 + 10 = 82%
100 – 82 = 18%
700 * 18/100 = 126
ANSWER:B
Answer: B
Question: The sum of the mean, the median, and the range of the set {1,5,6} equals which one of the following values?
Options:
A)7
B)12
C)14
D)17
E)20
Rationale: Here Mean => 1+5+6/3 => 4
median => 5
and range => 6-1 => 5
hence sum => 4+5+5=> 14
Answer: C
Answer: C
Question: If we have 9 people in a meeting, in how many ways they can sit around a table?
Options:
A)10*9!
B)9*8!
C)8*7!
D)7*6!
E)6*5!
Rationale: If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=9
(n-1)!=8!=8*7!
Ans:C
Answer: C
Question: At a dinner party, 3 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
Options:
A)2
B)10
C)24
D)32
E)120
Rationale: Soln: Since the arrangement is circular and 2 seating arrangements are considered different only when the positions of the people are different relative to each other, we can find the total number of possible seating arrangements, by fixing one person's position and arranging the others.
Thus if one person's position is fixed, the others can be arranged in 2! =2 ways.
Ans is A.
Answer: A
Question: Of the people who responded to a market survey, 60 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 3 to 1, how many people responded to the survey?
Options:
A)80
B)150
C)240
D)360
E)480
Rationale: Ratio = 3:1 => 3x respondents preferred Brand X and x preferred Brand Y
Since, no. of respondents who preferred Brand X = 60 => 3x=60 => x=20
Hence Total no. of respondents = 60 + 20 = 80
Hence A is the answer.
Answer: A
Question: A solution of 70 litres contains oil and water in the ratio 9:x. If six litres of water is added to the solution, the ratio becomes 6:4, find the value of x?
Options:
A)6
B)8.5
C)9
D)6.5
E)5
Rationale: Exp. Total new quantity = original sol + water =70+6 =76
New ratio = 6:4, New quantity of oil =6/10*76 = 45.6 Lit,
New quantity of water = 4/10*76 = 30.4 Lit
Water present initially = (30.4-6) = 24.4 Lit
Ratio = 45.6/24.4 =9/x There for x = 4.81 approx 5
Answer: E
Answer: E
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 54 years now, the son's age 8 years back was?
Options:
A)12yr
B)19yr
C)14yr
D)10yr
E)20yr
Rationale: Let the son's present age be x years
Then, 54-x = x
x = 27
Son's age 8 years back = 27-8= 19years
Answer is B
Answer: B
Question: If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'8" tall, which of the following is the median height of the children?
Options:
A)2'8"
B)2'6"
C)3'3"
D)3'4"
E)4'3
Rationale: Total number of children in class = 20
so median must be between 10th and 11th child when they are arranged in ascending order.
When arranged in ascending order 5th and 6th child will have the height of 3'4"
so required median height = (2'8"+2'8")/2 = 2'6"
Ans:Option A
Answer: A
Question: Mother,her daughter and her grand child weighs 130 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?
Options:
A)46
B)47
C)48
D)49
E)50
Rationale: mother + daughter + child = 130kg
daughter + child = 60kg
mother = 130 - 60 = 70kg
child = 1/5th of mother = (1/5)*70 = 14kg
So now daughter = 130 -(mother + child) = 130 - (70+14) = 46kg
ANSWER:A
Answer: A
Question: If 6 (A's capital) = 8 (B's capital) = 14 (C's capital). Then the ratio of their capitals is?
Options:
A)20:15:16
B)20:15:68
C)28:21:12
D)28:15:11
E)28:15:19
Rationale: 6A = 8B = 14 C
A:B:C = 1/6:1/8:1/14
= 28:21:12
Answer: C
Answer: C
Question: Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price?
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Taking the prices of products in ascending order(already arranged)
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239
we see that median value is the 6th value as there in total 11 values given
Arithmetic mean = total/number of entries = 1428/11 =129.8181
We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price
as we can clearly see that there is one value between $120 and $129.81, answer is 1 unit
Correct Answer - B
Answer: B
Question: What is the sum of all remainders obtained when the first 200 natural numbers are divided by 9?
Options:
A)397
B)401
C)403
D)405
E)399
Rationale: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=401.
Answer: B.
Answer: B
Question: 40 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 6 like all. How many people like apple?
Options:
A)47
B)49
C)54
D)58
E)62
Rationale: orange+mango-apple=7
mango+apple-orange=10
apple=40
orange+mango+apple=6
40+10+6-7=49 like apple
ANSWER:B
Answer: B
Question: If 20% of a number = 100, then 120% of that number will be?
Options:
A)20
B)120
C)360
D)600
E)820
Rationale: Let the number x. Then,
20% of x = 100
x = (100 * 100)/20 = 500
120% of x = (120/100 * 500) = 600.
ANSWER:D
Answer: D
Question: A bag contains 5 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
Options:
A)8/15
B)2/5
C)3/5
D)11/15
E)19/39
Rationale: Drawing two balls of same color from five green balls can be done in 5C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = 5C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 19/39
ANSWER:E
Answer: E
Question: FOG + FOG + FOG + FOG = 1448.
If F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: given,FOG + FOG + FOG + FOG = 1448
4(FOG)=1448
=>FOG=362
Face value of F is:3
Face value of O is:6
Face value of G is:2
so F+O+G=3+6+2=11
ANSWER:A
Answer: A
Question: what will be the unit value of 0!*1!*6!-5!?
Options:
A)4
B)3
C)0
D)1
E)2
Rationale: 1*1*5!*6-5!
5!(6-1)
5!*5
4!*5*5
it will be 0 because 5*4 with 0 at unit place so with any no. you multiply who have 0 unit place the product also have 0 at unit place.
answer C
Answer: C
Question: Find the area of a parallelogram with base 12 cm and height 18 cm.
Options:
A)200
B)216
C)345
D)244
E)242
Rationale: Area of a parallelogram = base * height = 12 * 18 = 216 cm2
Answer: Option B
Answer: B
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 184 hats in this group, how many of these hats are not blue?
Options:
A)28
B)42
C)48
D)128
E)76
Rationale: Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be
7x+4x+12x=184 or 23x=184...here 7x,4x and 12x represent hats of each type
23x=184 so x=8...Blue hats =7*8=56...Not blue will be 184-56=128.
Ans D
Answer: D
Question: Find the L.C.M of 32,84,126
Options:
A)2000
B)2018
C)5032
D)1008
E)2016
Rationale: 32=2^5 84=2^2*3*7 126=2*3^2*7
L.C.M=2^5*3^2*7=2016
Answer=(E)
Answer: E
Question: A hostel had provisions for 250 men for 40 days. If 50 men left the hostel, how long will the food last at the same rate?
Options:
A)48 days
B)50 days
C)45 days
D)60 days
E)None of these
Rationale: Explanation :
A hostel had provisions for 250 men for 40 days
If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.
Let the required numer of days = x days
More men, Less days (Indirect Proportion)
⇒Men250:200}::x:40
⇒250 × 40 = 200x
⇒ 5 × 40 = 4x
⇒ x = 5 × 10 = 50. Answer : Option B
Answer: B
Question: Barbara has 8 shirts and 5 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
Options:
A)41
B)24
C)36
D)70
E)56
Rationale: 8 shirts
9 pants
we can combine 2 shirts with (5-3) pants
2*2=4
we can combine the other shirts (6) with any pants (9)
4*5=20
Thus total :20+4=24ANS:B
Answer: B
Question: Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?
Options:
A)8
B)9
C)6
D)4
E)1
Rationale: Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.
x(2/75 + 1/45) + (30- x) 2/75 = 1
11x + 180 - 6x = 225 => x = 9
Answer:B
Answer: B
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)2000
B)2778
C)2299
D)2778
E)2771
Rationale: Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.
Answer:A
Answer: A
Question: Of the three-digit integers greater than 600, how many have two digits that are equal to each other and the remaining digit different from the other two?
Options:
A) 90
B) 82
C) 80
D) 75
E) 36
Rationale: Let the three digit number be represented as X Y Z.
There are 3 cases:
Case I.[ X=Y ]Z is not equal to XY :XXZorYYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 1 way
After XY are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(1)
[example numbers: 774,779,882,993 etc]
Case II.[ X=Z ]Y is not equal to XZ:XYXorZYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Z can be chosen in 1 way
After XZ are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (9 ways) * (1 way) = 27 ....(2)
[example numbers: 747,797,828,939 etc]
Case III.[ Y =Z ]X is not equal to YZ :XYYorXZZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 9 ways
After Y is chosen, Z can have 1 way
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(3)
[example numbers: 744,799,822,933 etc]
Therefore, total numbers of possible digits [sum of Case (1), (2)(3) above] = 27 + 27 + 27 - 1 = 80
One digit is subtracted from total number of possible digits to eliminate one possibility of XYZ = 700 to satisfy the condition that digit > 600.
Answer:(D)
Answer: D
Question: At a local appliance manufacturing facility, the workers received a 15% hourly pay raise due to extraordinary performance. If one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged, by approximately what percent would he reduce the number of hours that he worked?
Options:
A)13%
B)80%
C)20%
D)17%
E)12%
Rationale: Let's say he works usually 10 hours and earns 100 per hour.
10 * 100 = 1000
10 * 115 = 1150 (this are the new earnings after the raise)
To figure out how much he needs to work with the new salary in order to earn the original 1000:
1000/115 = 8.7
So he can reduce his work by 1.3 hours. Which is >13%.
Answer A
Answer: A