mathewhe/aqua_rat huggingface dataset:
Question: The salaries of A and B together amount to $5000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary?
(A) $1000
(B) $1250
(C) $2500
(D) $3500
(E) $3750
Rationale: Let A's salary is x
B's salary = 5000-x
(100-95)% of x = (100-85)% of (5000-x)
x = $3750
Answer is E
Answer: (E) $3750
Question: In a candy dish the ratio of red to yellow candies is 2:5, the ratio of red to green candies is 3:8, and the ratio of yellow ot blue candies is 9:2.what is the maximum total number Q of yellow and green candies combined if the maximum combined number of red and blue candies is fewer than 85?
(A) 144
(B) 189
(C) 234
(D) 279
(E) 309
Rationale: Given that Red is to yellow is 2:5, Red is to green is 3:8 and Yellow is to blue is 9:2.
Therefore, the total number of red, yellow, blue and green balls will be 18x, 45x, 10x and 48x respectively, where x is a constant.
If the combined number of red and blue balls is fewer than 85, i.e. max 84 balls, then the maximum number of yellow and green balls will be 279.
(10x+18x) < 85.
28x < 85, i.e. 28x <= 84 (Since number of balls cannot be in fraction). Thus, x<=3.
(45x+48x) = 93x.
Max (93x) Q= 279.
Answer is D.
Answer: (D) 279
Question: Which of the following could be the value of x, if 2|9x – 2| = 158?
(A) 77/9
(B) 0
(C) 9
(D) 3
(E) -2
Rationale: 2|9x – 2| = 158
=> |9x – 2| = 79
=>9x - 2 = 79
or 9x - 2 = -79
=> 9x = 81 or 9x = -77
=> x = 9 or x = -77/9
Answer C
Answer: (C) 9
Question: (128.5 x 4) + (13.8 x 5) = ? x 10
(A) 524.48
(B) 556.02
(C) 58.3
(D) 585.64
(E) 595.46
Rationale: Explanation :
? = (128.5 x 4) + (13.8 x 5)/10
=514 + 69/10 = 58.3
Answer : Option C
Answer: (C) 58.3
Question: If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have?
(A) 10 sides
(B) 8 sides
(C) 12 sides
(D) 9 sides
(E) None of these
Rationale: Explanatory Answer
Step 1: Compute sum of all interior and exterior angles
The sum of an exterior angle and an interior angle of a polygon = 180o.
The sum of all the exterior angles of a polygon = 360o.
From the question stem: sum of all interior angles of the given polygon = 1440o.
Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o.
Step 2: Compute number of sides
If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o.
Therefore, n = 10.
Alternative Approach : Using formula
Sum of all interior angles of a convex polygon = (n - 2)* 180
So, (n - 2) * 180 = 1440
n - 2 = 8
n = 10
Choice A
Answer: (A) 10 sides
Question: At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 80 customers per day, what is the value of x?
(A) 2
(B) 5
(C) 7
(D) 8
(E) 20
Rationale: WITHOUTusing the formula, we can see that today the restaurant served 40 customers above the average. The total amount ABOVE the average must equal total amount BELOW the average. This additional 40 customers must offset the “deficit” below the average of 80 created on the x days the restaurant served only 75 customers per day.
40/5 = 8 days.Choice (A).
WITHthe formula, we can set up the following:
80 = (75x + 120)/(x + 1)
80x + 80 = 75x + 120
5x = 40
x = 8Answer Choice (D)
Answer: (D) 8
Question: A boat covers a certain distance downstream in I hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph. what is the speed of the boat in still Water?
(A) 12kmph
(B) 13kmph
(C) 15kmph
(D) 16kmph
(E) 18kmph
Rationale: suppose it travels 1 km downstream in 1 hr and upstream in 1.5 hrs.
speed of boat in still water is x, then
1= 1/(x+3)
1.5= 1/(x-3)
solving we get
x= 15 kmph
ANSWER:C
Answer: (C) 15kmph
Question: The speed of a car is 98 km in the first hour and 70 km in the second hour. What is the average speed of the car?
(A) 76 kmph
(B) 75 kmph
(C) 87 kmph
(D) 56 kmph
(E) 84 kmph
Rationale: S = (98 + 70)/2
= 84 kmph
Answer: E
Answer: (E) 84 kmph
Question: 15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container S?
(A) A:45
(B) B:25
(C) C:37.5
(D) D:36
(E) E:42
Rationale: If you have a 37.5 liter capacity, you start with 37.5 L of A and 0 L of B.
1st Replacement
After the first replacement you have 37.5-15=22.5 L of A and 15 L of B. The key is figuring out how many liters of A and B, respectively, are contained in the next 15 liters of mixture to be removed.
The current ratio of A to total mixture is 22.5/37.5; expressed as a fraction this becomes (45/2) / (75/2), or 45/2 * 2/75. Canceling the 2s and factoring out a 5 leaves the ratio as 9/15. Note, no need to reduce further as we're trying to figure out the amount of A and B in 15 L of solution. 9/15 of A means there must be 6/15 of B.
Multiply each respective ratio by 15 to get 9 L of A and 6 L of B in the next 15L removal.
Final Replacement
The next 15L removal means 9 liters of A and 6 liters of B are removed and replaced with 15 liters of B. 22.5-9=13.5 liters of A. 15 liters of B - 6 liters + 15 more liters = 24 liters of B.
Test to the see if the final ratio = 9/16; 13.5/24 = (27/2) * (1/24) = 9/16. Choice C is correct.
Answer: (C) C:37.5
Question: When 1/20% of 4,000 is subtracted from 1/10 of 4,000, the difference is
(A) 50
(B) 200
(C) 380
(D) 398
(E) 400
Rationale: (1/10)*4000 - (1/20*100)*4000
=400 - 2
= 398
Answer D
Answer: (D) 398
Question: Which of the following are/is prime?
I. 143
II. 147
III. 157
(A)  II only
(B)  III only
(C)  III
(D)  IIII
(E)  I, II,III
Rationale: 1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice
which leaves us with 2 ) and 3) as possible answers
From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution
D
Answer: (D)  IIII
Question: A committee of 5 is to be selected from among 3 boys and 6 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?
what is the answer choice and how?
(A) 105
(B) 225
(C) 230
(D) 350
(E) 55
Rationale: I'm sure there is some problem with the question.
R U sure its atleast one boy and not atleast 1 boy and 1 girl?
if its 1 boy and 1 girl
3C1*5C4 + 3C2*5C3 + 3C3*5C2
3*5 + 3*10 + 1*10
15 + 30 + 10
55
E
Answer: (E) 55
Question: 1401 x 1401 = ?
(A) 1962800
(B) 1962801
(C) 1960000
(D) 1951611
(E) 1951613
Rationale: 1401 x 1401	= (1401)2
= (1400+1)2
= (1400)2 + (1)2 + (2 x 1400 x 1)
= 1960000 + 1 + 2800
= 1960001+ 2800
= 1962801.
B)
Answer: (B) 1962801
Question: If the number 90x8 is divisible by 8,then what will be the value of x?
(A) 0
(B) 4
(C) A and B
(D) None
(E) 1
Rationale: If Last three number are divisible by 8,then the number is divisible by 8.
So,X is replaced by either 0 or 4
Answer is A and b
Option C
Answer: (C) A and B
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 277
(B) 2678
(C) 287
(D) 108
(E) 277
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer: D
Answer: (D) 108
Question: If Jake loses 20 pounds, he will weigh twice as much as his sister. Together they now weigh 224 pounds. What is Jake’s present weight, in pounds?
(A) 131
(B) 135
(C) 156
(D) 177
(E) 188
Rationale: Lets say J is the weight of Jack and S is the wt of his sister.
If he loses 20 pounds, he s twice as heavy as his sister.
J-20=2*S
Also, together they weight 224 pounds
J+S=224
solvong the 2 equation ,we get J=156 pounds !
C
Answer: (C) 156
Question: An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third & 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?
(A) 0.6976
(B) 0.7543
(C) 0.8753
(D) 0.9864
(E) 1.2245
Rationale: Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976=0.6976
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
P=1−probability of not hitting the targetP=1−probability of not hitting the target
=1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)
=1−0.3024=1−0.3024
=0.6976
A
Answer: (A) 0.6976
Question: Calculate the circumference of a circular field whose radius is 5 centimeters.
(A) 30 π cm
(B) 80 π cm
(C) 70 π cm
(D) 50 π cm
(E) 10 π cm
Rationale: Circumference C is given by
C = 2πr = 2π*5 = 10 π cm
correct answer E
Answer: (E) 10 π cm
Question: A bullet train 160 m long is running with a speed of 70 kmph. In what time will it pass a man who is running at 8 kmph in the direction opposite to that in which the bullet train is going?
(A) 23 sec
(B) 15 sec
(C) 7.38 sec
(D) 6.92 sec
(E) 16 sec
Rationale: C
7.38 sec
Speed of the bullet train relative to man = (70 + 8) kmph
= 78*5/18 m/sec = 65/3 m/sec.
Time taken by the bullet train to cross the man = Time taken by it to cover 160 m at (65/3) m / sec
= (160 *3/65) sec = 7.38 sec
Answer: (C) 7.38 sec
Question: A factory produces 3400 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
(A) 575 toys
(B) 375 toys
(C) 680 toys
(D) 475 toys
(E) 675 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.
3400 / 5 = 680 toys
correct answer C
Answer: (C) 680 toys
Question: If the price of an article went up by 30%, then by what percent should it be brought down to bring it back to its original price?
(A) 25%
(B) 23 1/13%
(C) 16 7/3%
(D) 16 6/3%
(E) 16 2/3%
Rationale: Let the price of the article be Rs. 100.
30% of 100 = 30.
New price
= 100 + 30 = Rs. 130
Required percentage
= (130 - 100)/130 * 100
= 30/130 * 100
= 23 1/13%
Answer:B
Answer: (B) 23 1/13%
Question: ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 8. How many different 5-digit numbers areSvennumbers?
(A) 20
(B) 80
(C) 160
(D) 220
(E) 250
Rationale: ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 5-digit numbers areSvennumbers?
4/9*5/10*2/10*2/10*2/10=160/9000
D. 220
Answer: (D) 220
Question: 5^20+5^7/7=? Reminder is…………
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 5^20 mod 7 + 5^7 mod 7
Since 5 nd 7 are co-primes, we can use Euler's theorem
E(7) = 6
So 5^E(7) = 1
5^20 mod 7 => (5^6)^3 * 5^2 mod 7
1 * 25 mod 7 = 4
Similarly 5^7 mod 7 => 5^6 * 5 mod 7
1 * 5 mod 7 = 5
Now 4 + 5 mod 7
9 mod 7 = 2
ANSWER:B
Answer: (B) 2
Question: A barrel contains 12 oranges, 8 grapefruit, and 5 apples for a total of 25 pieces of fruit. As a game, several friends took turns randomly extracting a single piece of fruit from the barrel blindfolded. If the extracted piece of fruit was not an apple, it was returned to the bin. This process was repeated until an apple was drawn. What is the probability that an apple will be extracted on the third extraction or later?
(A) 5/25
(B) 8/25
(C) 12/25
(D) 16/25
(E) 4/5
Rationale: Favorable case = an apple is picked in the third extraction or later.
Unfavorable case = an apple is picked in either the first or second extraction.
Probability = Favorable outcomes / Total out comes
Also probability = 1-(Unfavorable outcomes / Total out comes)
Unfavorable case 1: probability of apple picked in first extraction = 5/25
Unfavorable case 2: probability of apple picked in second extraction (i.e., 2nd extraction not an apple)= (20/25)*(5/25) =(4/5)*(1/5)= 4/25
Total Unfavorable Probability = (5/25)+(4/25) = 9/25
i.e., Favorable Probability = 1 - (9/25) = 16/25
Answer Option: D
Answer: (D) 16/25
Question: Walking 7/6 of his usual rate, a boy reaches his school 7 min early. Find his usual time to reach the school?
(A) 22
(B) 28
(C) 99
(D) 49
(E) 66
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
7--------- ? 49 m
Answer:D
Answer: (D) 49
Question: A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 42 adults have their meal, find the total number of children that can be catered with the remaining food.
(A) 33
(B) 54
(C) 36
(D) 17
(E) 01
Rationale: Explanation:
As there is meal for 70 adults and 42 have their meal, the meal left can be catered to 28 adults.
Now, 70 adults = 90 children
7 adults = 9 children
Therefore, 28 adults = 36 children
Hence, the meal can be catered to 36 children.
ANSWER: C
Answer: (C) 36
Question: Four machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.
So 3/2* 4 = 6
So we need 6-4= 2 more machines.
Answer : A
Answer: (A) 2
Question: Speed of a man with current measures 15 km/hr. Speed of current is 2.5 km/hr. What is the speed of man against the current?
(A) 20 kmph
(B) 18 kmph
(C) 10 kmph
(D) 16 kmph
(E) 13 kmph
Rationale: Explanation:
Let the speed of man in still water be x km/hr
Now, speed with current=15 km/hr
Speed of current: 2.5 km/hr
Speed of man with current: Speed of man in still water+Speed of current
=>15=x+2.5
=>x=12.5
Speed of man against the current: Speed of man in still water-Speed of current
=>12.5-2.5
=>10 km/hr
ANSWER:C
Answer: (C) 10 kmph
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 3 1/2 hours
(B) 4 1/3 hours
(C) 6 1/3 hours
(D) 9 3/5 hours
(E) 2 1/2 hours
Rationale: Required time
= (5 1/4)/3 + (5 1/4)/7
= 2 1/2 hours.
Answer:E
Answer: (E) 2 1/2 hours
Question: What is the remainder when 49^74 - 5^74 is divided by 24?
(A) 2
(B) 1
(C) 0
(D) 3
(E) None of these
Rationale: easiest way for me: 49^74 - 5^74 = (49)^37-25^37 = (24*2+1)^37 - (24+1)^37 -> remainder is 1^37 - 1^37 = 0
Ans : C
Answer: (C) 0
Question: For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 72, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.
(A) K+36
(B) 2K+36
(C) (72+K)/2
(D) (72-K)/2
(E) 2(72-K)
Rationale: Let y be the years of service at the company.
After y years of service, Sue's age will be K + y.
Sue can retire when (K+y) + y = 72
y = (72 - K)/2
Then Sue's age will be K + y = K + (72 - K)/2 = (72+K) / 2
The answer is C.
Answer: (C) (72+K)/2
Question: Reduce
368/575
to the lowest terms
(A) 30/25
(B) 16/25
(C) 28/29
(D) 28/19
(E) None of these
Rationale: Explanation:
We can do it easily by in two steps
Step1: We get the HCF of 368 and 575 which is 23
Step2: Divide both by 23, we will get the answer 16/25
Answer: Option B
Answer: (B) 16/25
Question: If the area of a square with sides of length 8 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
(A) 4
(B) 8
(C) 12
(D) 16
(E) 18
Rationale: Let length of rectangle = L
8^2 = L*4
=> L = 64/4 = 16
Answer D
Answer: (D) 16
Question: When two coins are tossed, Find the probability of getting all tails?
(A) 1/3
(B) 3/4
(C) 1/8
(D) 3/8
(E) P(E) =1/4
Rationale: When two coins are tossed,
S = {HH, HT, TH, TT} where H = Head and T = Tail
Let E = event of getting all tails
Then E = {TT}
so, P(E) = n(E)/n(S) =1/4
Answer: (E) P(E) =1/4
Question: The fourth proportional to 5, 8, 15 is:
(A) 20
(B) 22
(C) 24
(D) 21
(E) 23
Rationale: Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x
= 5x = (8 x 15)
x = (8 x 15)/5= 24.
Answer is C.
Answer: (C) 24
Question: A committee of three people is to be chosen from four teams of two. What is the number of different committees that can be chosen if no two people from the same team can be selected for the committee?
(A) 20
(B) 22
(C) 26
(D) 30
(E) 32
Rationale: the amount of combinations of 3 person teams from a pool of 8. C(3/8) = 8!/5!*3! = 56 ways
Next I find the number of ways we CAN make a 3 person team using two from the same group, so
We take 2 people from a 2 person group C(2/2) and mutiply that by taking any 1 person from the remaining 6 C(1/6)
C(2/2)*C(1/6) = 6
This is the number of combinations by taking both parties from pair A. As we have a four pairs we must multiply this by 4 (4x6 = 24)
So there are 24 ways in which two people from the same pair can work together.
Finally we subtract this from the total number of combinations to find the number of groups where pairs do NOT work together....
56 - 24 = 32!
ANSWER:E
Answer: (E) 32
Question: How many words can be formed by using all letters of the word 'SCOUNDREL' ?
(A) 192870
(B) 324880
(C) 462880
(D) 362880
(E) 123880
Rationale: The word SCOUNDREL contains 9 different letters
Required number of words = 9P9 = 9! = 5*4*3*2*1 = 120
Answer is D
Answer: (D) 362880
Question: A train running at the speed of 70 km/hr crosses a pole in 36 seconds. What is the length of the train?
(A) 700
(B) 770
(C) 707
(D) 710
(E) 720
Rationale: Speed=(70 * 5/18) m/sec = (175/9) m/sec Length of the train = (Speed x Time) = (175/9 * 36) m
= 700 m.
Answer: A
Answer: (A) 700
Question: Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum Q of their ages will be 51, how old is Stephanie ?
(A) 6
(B) 10
(C) 14
(D) 20
(E) 24
Rationale: 1) take C (14y.o.), so mean that S=14, J=28, their sum itself is 42+10 years from now is 52, it is over the 51,
so eliminate C,D,E
2) take B (10y.o.), Q=meaning S=10,J=20, so 20+10+10=40 and for K=10-4/3=2+9=11, finally 40+11=51. It is correct
B
Answer: (B) 10
Question: If t is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of t ?
(A)  10
(B)  12
(C)  14
(D)  16
(E)  18
Rationale: Answer is C.
numbers in format of 3^k in the series from 1 to 30 inclusive t are: 3*1, 3*2, 3*3, 3*4, 3*5, 3*3*2, 3*7, 3*8, 3*3*3, 3*10. Total number of 3 = 13. So k=14.
Answer: (C)  14
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.90 per glass on the first day, what was the price per glass on the second day?
(A) $0.15
(B) $0.20
(C) $0.30
(D) $0.40
(E) $0.6
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.9=3*x --> x=$0.6.
Answer: E.
Answer: (E) $0.6
Question: In a single throw of a die, what is the probability of getting a number greater than 4?
(A) 1/2
(B) 1/3
(C) 2/3
(D) 1/4
(E) None
Rationale: Solution
When a die is thrown, we have S= {1,2,3,4,5,6}.
Let E = event of getting a number greater than 4= {5, 6}.
•P(E)= n(E) / n(S)
= 2/6
= 1/3.
Answer B
Answer: (B) 1/3
Question: A data set with a mean of 60 has a standard deviation of 4.5. Which of the following is the smallest number that falls within one standard deviation of the mean?
(A) 55
(B) 56
(C) 59
(D) 63.5
(E) 65
Rationale: One standard deviation of the mean is from{mean}-{deviation}=60-4.5=55.5 to{mean}+{deviation}=60+4.5=64.5. The smallest number within this range from the options is 55.
Answer: A.
Hope this helps.
Answer: (A) 55
Question: If a, b are the two roots of a quadratic equation such that a + b = 24 and a – b = 8, then the quadratic equation having a and b as its roots is :
(A) x2 + 2x + 8 = 0
(B) x2 - 4x + 8 = 0
(C) x2 - 24x + 128 = 0
(D) 2x2 + 8x + 9 = 0
(E) None of these
Rationale: Sol.(c) a + b = 24 and a – b = 8
=> a = 16 and b = 8 => ab = 16 × 8 = 128
A quadratic equation with roots a and b is
x2 - (a + b)x + ab = 0 or x2 - 24x + 128 = 0
Answer C
Answer: (C) x2 - 24x + 128 = 0
Question: A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 7. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used.
The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
(A) 7000
(B) 1000
(C) 1011
(D) 1101
(E) 1110
Rationale: The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 7*10*10*10=9*10^3
The difference = 10^4 - 7*10^3 = 10^3(10-7) = 7*10^3.
Answer: A.
Similar questions to practice:
Hope it helps.
Answer: (A) 7000
Question: A certain class of students is being divided into teams. The class can either be divided into 10 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
(A) 6
(B) 36
(C) 120
(D) 60
(E) 72
Rationale: Let total no of students in the class be N
So, we are told that N is divisible by both 10 24
So, Lets find the least common multiple of 10 24 , ie 120
So our answer is (C) 120
Answer: (C) 120
Question: A bag contains 12 white &18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 31/113
(B) 36/145
(C) 30/117
(D) 31/213
(E) 1/412
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145