mathewhe/aqua_rat huggingface dataset:
Question: A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 50 days starting with sunday is
(A) 280
(B) 285
(C) 171
(D) 295
(E) 275
Rationale: Explanation:
As the month begin with sunday, so there will be five sundays in the month. So result will be:
=(510×5+240×25/30)=(8550/50)=171
Answer: Option C
Answer: (C) 171
Question: A new savings account offers 9 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?
(A) $80.00
(B) $84.40
(C) $360.00
(D) $6,360.00
(E) $6,552.15
Rationale: The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.09) (1/2) = $270. (Note: the 6 months are “1/2” in the equation since 9% is a yearly rate, not a bi-yearly one).
Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,270. The interest earned during the final 6 months of the year is $6,270(.09)(1/2) = $282.15. Therefore, the total balance is the original amount ($6000) + $270 + $282.15 = $6,552.15.
The correct answer is E.
Answer: (E) $6,552.15
Question: A card board of size 34*14 has to be attached to a wooden box and a total of 35 pins are to
be used on the each side of the card box. find the total number of pins used.
(A) 135
(B) 136
(C) 137
(D) 138
(E) 139
Rationale: total 35 pins are there and 4 sides of card board...so 35X4=140
now in the rectangle 4 vertices have 4 pins which is common to the sides....so 140-4=136
ANSWER:B
Answer: (B) 136
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 32. Find the profit percentage?
(A) 80%
(B) 50%
(C) 59%
(D) 40%
(E) 60%
Rationale: L.C.M of 15 and 12
= 60
CP of 60 articles
= Rs. 100 (25 * 4)
SP of 60 articles
= Rs. 160 (32 * 5)
Profit percentage
= (160 - 100)/100 * 100 = 60%
Answer: E
Answer: (E) 60%
Question: A started a business with Rs. 21,000 and is joined afterwards by B with Rs. 36,000. After how many months did B join if the profits at the end of the year are divided equally?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Sol.
Suppose B joined after x months.
Then, 21000 * 12 = 36000 * (12 - x) ⇔ 36x = 180 ⇔ x = 5.
Hence, B joined after 5 months.
Answer B
Answer: (B) 5
Question: How many integers n are there such that 1< 5n +5 < 40?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
Rationale: Solution:
1< 5n + 5 < 40 is a compound inequality. Compound inequalities often need to be manipulated, and we can use the rules of algebra that we already know, to do this. Just as with equations, whatever we do to one part of a compound inequality, we must do to all parts of the compound inequality. Let’s first isolate n within the inequality.
1< 5n + 5 < 40
We first subtract 5 from all three parts of the inequality, and we obtain:
-4 < 5n < 35
Next, we divide both sides of the inequality by 5 and we get:
-4/5 < n < 7
The integers that are greater than -4/5 and less than 4 are 0, 1, 2, and 3. Thus, there are 4 integers that satisfy the inequality 1 < 5n + 5 < 40.
The answer is E
Answer: (E) 7
Question: 0---:-|---:--|-:--:-|--:---|-:----1
On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance A between any two of the tick marks?
(A) 1/70
(B) 1/35
(C) 2/35
(D) 1/12
(E) 1/7
Rationale: divisions are 0 1/7 2/7 3/7 4/7 5/7 6/7 1
1/5 2/5 3/5 4/5 5/5
expressing the same in terms of the lcm of 5,7 ,i.e 35
0 7/35 14/35 21/35 28/35 35/35
5/35 10/35 15/35 20/35 25/35 30/35
by comparing the divisions with each other we can see 1/35 is the shortest possible distance between any two selected divisions.
A=1/35
Answer is B.
Answer: (B) 1/35
Question: Which of the following triples of numbers have the same standard deviation as the numbers m, n and o?
I. m-2, n-2, o-2
II. 0, m-n, o-n
III. m-4, n+5, o-1
(A) I only
(B) II only
(C) I and III only
(D) II and I only
(E) I, II, and III
Rationale: If we add or subtract a constant to each term in a set the standard deviation will not change.
Set {m-2, n-2, o-2} is obtained by subtracting 2 from each term of {m, n, o}.
Set {0, m-n, o-n} is obtained by subtracting s from each term of {m, n, o}.
Set {m-4, n+5, o-1} is totally different from {m, n, o}.
Thus the answer is I and II only.
Answer: D.
Answer: (D) II and I only
Question: There are 11 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 11 points that contain the point A?
(A) 45
(B) 105
(C) 182
(D) 210
(E) 455
Rationale: Any 2 points out 10 points will create triangle with third point A, so the answer is 10C2=45.
Answer: A.
Answer: (A) 45
Question: Alice has a jar of juice, and she drank 1/6 of the juice for lunch. If Alice drank 2/5 of the remaining juice for dinner, what fraction of the juice was left after dinner?
(A) 1/2
(B) 2/3
(C) 1/4
(D) 2/5
(E) 3/5
Rationale: Let x be the amount of juice at the beginning.
After lunch, the remaining juice was (5/6)x.
After dinner, the remaining juice was (3/5)(5/6)x = (1/2)x.
The answer is A.
Answer: (A) 1/2
Question: A, B and C invests Rs.4000, Rs.2000 and Rs.6000 in a business. After one year A removed his money; B and C continued the business for two more year. If the net profit after 3 years be Rs.3300, then A's share in the profit is?
(A) 6000
(B) 4000
(C) 2000
(D) 600
(E) 300
Rationale: 4*12 : 2*36 : 4*36
2: 3: 6
2/11 * 3300 = 600
Answer: D
Answer: (D) 600
Question: A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 140, then how much amount should C pay as his share of rent?
(A) 35
(B) 45
(C) 25
(D) 36
(E) 55
Rationale: A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=140×9/35=4×9=36
Answer is D
Answer: (D) 36
Question: If mn represents a positive two digit number, where m and n are single digit integers, which of the following cannot be true?
(A) m+n =9
(B) (m)(n)=9
(C) m-n = 9
(D) n-m= 9
(E) m/n = 9
Rationale: (A) mn = 45 or 63 or 27
(B) mn = 33 or 19
(C) 90
(D) impossible
(E) mn = 91
(D) is impossible because 09 is not a valid two digit number --- if there's a zero in the ten's place, that's just 9, a single digit number. Therefore, no valid two digit number would satisfy (D).
ans D
Answer: (D) n-m= 9
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did C get in a profit of Rs.2430 ?
(A) s. 432
(B) s. 486
(C) s. 822
(D) s. 812
(E) s. 810
Rationale: Let the total amount in the partnership be 'x'.
Then A's share = x/3
B's share = x/4
C's share = x/5
D's share = x - (x/3 + x/4 +x/5) = 13x/60
A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13
A's share in the profit of Rs. 2430 = 12 (2430/60) = Rs. 486
Answer: B
Answer: (B) s. 486
Question: A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 10 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?
(A) 7% loss
(B) 13% loss
(C) 4% profit
(D) 13% profit
(E) 15% profit
Rationale: Total cost 60*($250/1.1)=54.54*250;
# of cameras sold is 60-6=54 total revenue is 54*250;
# of cameras returned is 6 total refund 6*(250/1.1)*0.5;
So, total income 54*250+ 6*(250/1.1)*0.5
The dealer's approximate profit is (54*250+ 6*(250/1.1)*0.5-54.54*250)/(54.54*250)*100=4%
Answer: C.
Answer: (C) 4% profit
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 30% on hers. If Mindy earned 2 times as much as Mork did, what was their combined tax rate?
(A)  32.5%
(B)  34%
(C)  22.5%
(D)  33.3%
(E)  37.5%
Rationale: Say Morks income is - 100
So tax paid will be 40
Say Mindys income is 2*100 = 200
So tax paid is 30% * 200 = 60
Total tax paid = 40+60 = 100.
Combined tax % will be 100/100+200 = 33.3%
Answer: (D)  33.3%
Question: Some persons can do a piece of work in 12 days. Two times the number of these people will do half of that work in?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: 12/ (2 * 2) = 3 days
Answer:A
Answer: (A) 3
Question: If two integers x,y (x>y) are selected from -6 to 6 (inclusive), how many cases are there?
(A) 70
(B) 74
(C) 78
(D) 82
(E) 86
Rationale: There are 13 integers from -6 to 6 inclusive.
13C2 = 78.
The answer is C.
Answer: (C) 78
Question: A and B can do a work in 18 day, B and C in 30 days, A and C in 22 (1/2) days. In how many days can A,B and C individually do the work?
(A) 60,90,128
(B) 60,90,120
(C) 60,90,127
(D) 60,90,118
(E) 60,90,121
Rationale: (A+B+C)'s two days work = 1/18 + 1/30 + 2/45
= (5 + 3 + 4)/90 = 2/15
(A+B+C)'s one day work = 2/15 * 1/2 = 1/15
A's one day's work = 1/15 - 1/30 = 1/30
B's one day's work = 1/15 - 2/45 = 1/45
C's one day's work = 1/15 - 1/18= 1/90
So, A,B and C can individually do the work in 30, 45 and 90 days.
Answer:B
Answer: (B) 60,90,120
Question: A train has a length of 150 meters . it is passing a man who is moving at 3 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.
(A) 182 km/hr
(B) 180 km/hr
(C) 152 km/hr
(D) 169 km/hr
(E) 183 km/hr
Rationale: Explanation:
Length of the train, l = 150m
Speed of the man , Vm= 3 km/hr
Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr
Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)
=> 180 = Vt - 3
=> Vt = 180 + 3 = 183 km/hr
Answer: Option E
Answer: (E) 183 km/hr
Question: In how many ways can the letters of word BISECTION be arranged such that NO two vowels appear together?
(A) 9!
(B) 5!*4!
(C) 4!*5!
(D) 5!*4!*2!
(E) 6!*4!
Rationale: No 2 vowels together = the only arrangement possible will be C V C V C V C V C (with V=vowel, C=consonant). This is true as we have 4 vowels and 5 consonants and any other combination will force us to pair 2 vowels together.
Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 4!*5! ----> C is the correct answer.
Answer: (C) 4!*5!
Question: If a, b, and c are consecutive even integers and a < b < c, all of the following must be divisible by 4 EXCEPT
(A) a + c
(B) b + c
(C) ac
(D) (bc)/2
(E) (abc)/4
Rationale: Let integers be a= x-2, b= x, c= x+2
Now by options
a+c = 2x (has to be divisible by 4 as x is an even no.)
b+c = 2x +2 = 2(x+1) as x is an even no. x+1 is odd, so eq. becomes 2 * odd hence cannot be divisible by 4
ANSWER:B
Answer: (B) b + c
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 3600 interest only for the period. The principal amount borrowed by him was:
(A) s. 2000
(B) s. 10,000
(C) s. 15,000
(D) s. 18,000
(E) s. 20,000
Rationale: Principal = Rs. (100 x 3600)/(12X3) = Rs. 10000. Answer: Option B
Answer: (B) s. 10,000
Question: To be eligible for retirement benefits at the Mankind Corporation, the sum of an employee's age, in years, and the number of years employment must be at least 60. If a, where a <60, is a certain employee's age when hired and b is the minimum number of years of employment required for the employee to be eligible for retirement benefits, which of the following equations represents the relationship between a and b?
(A) 2a+2b=60
(B) ab=60
(C) a+2b=60
(D) a+b=60
(E) 2a+b=60
Rationale: We are told that when a certain employee was hired he was a years old and that the he needed minimum b years to be eligible for benefits.
Now,after b years of employment, when the employee will be be eligible for benefits, the employee will be a+b years old and will have b years of employment, thus{age after b years}+{employment years}=(a+b)+b=a+2b=60
Answer: C
Answer: (C) a+2b=60
Question: The set X = {11,12,13,14,15}. The set Y = {2,3,4,5}. We will randomly choose one element x from set X and one element y from set Y. What is the probability that x / y will be an integer?
(A) 11/20
(B) 7/20
(C) 3/20
(D) 7/10
(E) 3/10
Rationale: The total number of x and y pairs is 5*4=20.
There are six pairs such that x / y is an integer.
The probability that x / y is an integer is 6/20=3/10.
The answer is E.
Answer: (E) 3/10
Question: A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?
(A) 180 km
(B) 127 km
(C) 178 km
(D) 188 km
(E) 111 km
Rationale: Explanation:
Speed in downstream = (14 + 4) km/hr = 18 km/hr;
Speed in upstream = (14 â€“ 4) km/hr = 10 km/hr.
Let the distance between A and B be x km. Then,
x/18 + (x/2)/10 = 19 â‡” x/18 + x/20 = 19 â‡’ x = 180 km.
Answer: A
Answer: (A) 180 km
Question: Find the area of the square field if a train 800 metres long passes the field with a speed of 120 kmph in one minute.
(A) 1.48 sq. km
(B) 2.44 sq. km
(C) 7.44 sq. km
(D) 1.45 sq. km
(E) 1.44 sq. km
Rationale: Explanation:
120 km/hr = 120 * 5/18 = 33.33 m/s
v = d/t ; 33.33 = d/60
d = 2000 m
Hence, in one minute the train travels 2000 m. But, as the train is 800 m long and it passes the field, the length of the field is 2000 – 800 = 1200 m.
Area = 1200 * 1200 = 1.44 sq. km
ANSWER: E
Answer: (E) 1.44 sq. km
Question: Two cars are driving toward each other. The first car is traveling at a speed of 90 km/h, which is 50% faster than the second car's speed. If the distance between the cars is 975 km, how many hours will it take until the two cars meet?
(A) 6
(B) 6.5
(C) 7
(D) 7.5
(E) 8
Rationale: The speed of the first car is 90 km/h.
The speed of the second car is 90 / 1.5 = 60 km/h.
The two cars complete a total of 150 km each hour.
The time it takes the cars to meet is 975 / 150 = 6.5 hours.
The answer is B.
Answer: (B) 6.5
Question: Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days?
(A) 20
(B) 10
(C) 50
(D) 40
(E) 60
Rationale: D
40
We have M1 D1 = M2 D2
So, 24 * 35 = M2 * 21 => M2 = 40.
Answer: (D) 40
Question: If a + b > 0 and a * b < 0, which of the following must be true?
I. a > 0 or b > 0
II. a < 0 or b < 0
III. a and b have the same sign
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: I. True, for the sum to be greater than 0, at least one of a or b has to be positive
II. True, for the product to be less than 0, one of a or b has to be negative
III. Not true, by the previous two, one of a or b has to be positive and the other has to be negative
D
Answer: (D) I and II only
Question: Three printing presses, P, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take P, working alone at its constant rate, to do the same job?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 20
Rationale: =1/4-1/5=1/20
P can do 1/20 job in 1 hour
P can do the whole job in 20 hours=E
Answer: (E) 20
Question: what is the value of y if the greatest common divisor of (e+5)!,(e-2)!, and (e+2)! is 24.
(A) 5
(B) 7
(C) 4
(D) 66
(E) 6
Rationale: GCD of (e+4)!,(e-2)!, and (e+2)! is 24. Find x.
Best way to find n is substitute each of the answer and find out the correct one.
Only option E gave the correct answer.
Try 6 and find GCD or 10!, 4! and 8!. 4! itself is 24 and 4! which is contained in the other two factorials. This satisfies the condition, hence answer is 6.
Answer is E.
Answer: (E) 6
Question: What is the sum of the different positive prime factors of 640?
(A) 5
(B) 7
(C) 10
(D) 15
(E) 17
Rationale: The prime factorization of 640
= 64 * 10
= 2^6 * 2*5
The sum of the different positive prime factors = 2+5 = 7
The answer is B.
Answer: (B) 7
Question: If two painters can complete two rooms in two hours, how many rooms painted if 10 painters work for 6 hours?
(A) 35
(B) 25
(C) 20
(D) 30
(E) 15
Rationale: Explanation:
Two painters can complete two rooms in two hours.So 30 rooms can be painted in 6 hrs by 10 painters
Answer: D) 10 painters
Answer: (D) 30
Question: A person travels equal distances with speeds of 3km/hr, 6km/hr, 9km/hr. and takes a total time of 11minutes. Find the total distance ?
(A) 1km
(B) 500mts
(C) 900mts
(D) 2km
(E) 250mts
Rationale: Let the each distance be x km
total distance = 3x
then total time,
(x/3)+(x/6)+(x/9) = 11/60
x=0.3
total distance = 3*0.3 = 0.9km = 900meters
correct option is C
Answer: (C) 900mts
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.45 only. Menâ€™s wages are?
(A) 6Rs
(B) 7Rs
(C) 8Rs
(D) 4Rs
(E) 3Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 45 Rs.
5M + 5M + 5M ----- 45 Rs.
15M ------ 45 Rs. => 1M = 3Rs.
Answer:E
Answer: (E) 3Rs
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 7.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1?
(A) $0.50
(B) $1.00
(C) $1.25
(D) $1.50
(E) $1.75
Rationale: OA is definitely wrong. The answer should be C.
Answer: (C) $1.25
Question: A student gets 50% in one subject, 70% in the other. To get an overall of 70% how much should get in third subject.
(A) 90%
(B) 25%
(C) 45%
(D) 55%
(E) 65%
Rationale: Let the 3rd subject % = x
50+70+x = 3*70
120+x =210
x = 210-120 = 90
Answer : A
Answer: (A) 90%
Question: A square is drawn inside a right-angled triangle with the two perpendicular sides as 12 cm and 8 cm. what is the side of the largest possible square that can be drawn?
(A) 4.8 cm
(B) 4.4 cm
(C) 4.9 cm
(D) 5.0 cm
(E) 5.2 cm
Rationale: Area of triangle is 1/2 * 12 * 8 = 48
Side of square = x
The entire triangle split into two right angled triangle and one square with dimensions as follows
i) square with side x
ii) Right angled triangle with perpendicular sides x and 12-x
iii) Right angled triangle with perpendicular sides 8-x and x
Sum of area of all three = 48
= x2 + 1/2*x*(12-x) + 1/2*x*(8-x) = 48
= x = 4.8 cm
answer : A
Answer: (A) 4.8 cm
Question: If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
(A) -10.0
(B) -0.5,
(C) -0.4
(D) -0.2,
(E) 10.0
Rationale: Solution:
(0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
Answer: C
Answer: (C) -0.4
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 11.1%
(B) 20%
(C) 45.8%
(D) 10.5%
(E) 31.6%
Rationale: Option E
Explanation:
100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer: (E) 31.6%
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in
(A) 3 days
(B) 4 days
(C) 5 days
(D) 6 days
(E) 7 days
Rationale: Answer: Option 'A'
That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
Answer: (A) 3 days
Question: On the number line, if x is halfway between -8 and 4, and if y is halfway between -2 and 6, what number is halfway between x and y?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: x= -2 and y = 2.
The answer is C.
Answer: (C) 0
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x
(A) 2980
(B) 2990
(C) 3000
(D) 3100
(E) 3158
Rationale: 12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
E
Answer: (E) 3158
Question: A car covers a distance of 624 km in 6 ½ hours. Find its speed?
(A) 104
(B) 376
(C) 1267
(D) 198
(E) 621
Rationale: 624/6 = 104 kmph
Answer: A
Answer: (A) 104
Question: The ratio 5:20 expressed as percent equals to
(A) 50 %
(B) 125 %
(C) 25 %
(D) None of above
(E) 30%
Rationale: Explanation:
Actually it means 5 is what percent of 20, which can be calculated as,
(5/20)*100 = 5 * 5 = 25
Option C
Answer: (C) 25 %
Question: A woman on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
(A) 71.11 km/hr.
(B) 68.11 km/hr.
(C) 44.11 km/hr.
(D) 88.11 km/hr.
(E) 31.11 km/hr.
Rationale: A
71.11 km/hr.
Total time taken = 160/64 + 160/80 = 9/2 hours
--> Average speed = 320 x 2/9 = 71.11 km/hr.
Answer: (A) 71.11 km/hr.
Question: The average (arithmetic mean) of the even integers from 24 to 48 inclusive is how much greater than the average (arithmetic mean) of the even integers from 12 to 24 inclusive?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: So, according to A mean of a set of even numbers from 24 to 48 =(24+48)/2=36 and mean of a set of even numbers from 12 to 24 =(12+24)/2=18
Difference=36-18=18
Answer: C.
Answer: (C) 18
Question: The following sets each have a mean of 10 and the standard deviations are given in variable form.
Set I = {7, 8, 9, 11, 12, 13}, standard deviation = A
Set II = {10, 10, 10, 10, 10, 10}, standard deviation = B
Set III = {6, 6, 6, 14, 14, 14}, standard deviation = C
Rank these three standard deviations from least to greatest.
(A) A, B, C
(B) A, C, B
(C) B, A, C
(D) B, C, A
(E) C, B, A
Rationale: SD is minimum when the terms are closer to the mean.
In set 2, we have all terms equal to mean. hence, its SD is 0.(The Lowest)
Comparing Set 1 and Set 3, Set 1 has terms more closer to mean than set 3. hence, Set 3 Sd is the highest.
So, Answer is C
Answer: (C) B, A, C
Question: There are 200 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%?
(A) 150
(B) 100
(C) 99
(D) 50
(E) 25
Rationale: There are 198 managers and 2 others. The 2 others would compose 2% of the total number of people if there were 100 people in the room. Thus 100 managers must leave.
The answer is B.
Answer: (B) 100
Question: welve children take sixteen days to complete a work which can be completed by 8 adults in 12 days. Sixteen adults left and four children joined them. How many days will they take to complete the remaining work?
(A) 3 days
(B) 4 days
(C) 6 days
(D) 8 days
(E) 10 days
Rationale: One child’s one day work = 1/192.
One adult’s one day’s work = 1/96.
Work done in 3 days = ((1/96) x 16 x 3) = 1/2
Remaining work = 1 – 1/2 = 1/2
(6 adults+ 4 children)’s 1 day’s work = 6/96 + 4/192 = 1/12
1/12 work is done by them in 1 day.
1/2 work is done by them in 12 x (1/2) = 6 days
ANSWER:C
Answer: (C) 6 days
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 38 years now, the son's age five years back was:
(A) 76 years.
(B) 14 years.
(C) 55 years.
(D) 45 years.
(E) 61 years.
Rationale: Let the son's present age be x years.
Then, (38 - x) = x
2x = 38 => x = 19
Son's age 5 years back = (19 - 5) = 14 years.
Answer: B
Answer: (B) 14 years.
Question: Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $5 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
(A) 8n + 2
(B) 8n + 4
(C) 9n + 2
(D) 9n + 3
(E) 9n + 4
Rationale: its C
n items for $8 each
total price $8n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [5+ (n-1)]
= $ n+4
total cost
8n+n+4 = 9n+4
E
Answer: (E) 9n + 4