mathewhe/aqua_rat huggingface dataset:
Question: Some of the workers at a hedge fund are analysts; the others are not analysts. There are a total of 2x/3 analysts at the hedge fund. A total of x hedge fund workers have an MBA. Furthermore, x/3 analysts have an MBA, y/4 of the hedge fund workers are neither analysts nor have an MBA, and 40 workers are not analysts. If there are y total workers at the hedge fund, x is equal to which of the following?
(A) 36
(B) 50
(C) 60
(D) 75
(E) 80
Rationale: AnalystsNot AnalystsTotal
MBAx/32x/3x
No MBAy/4
Total2x/350y
We are asked for the value of x.
From the table: 2x/3 = y - 40
y - 40 + (y/4) = 40
5y/4 = 80
y = 64
2x/3 = 64 - 40 = 24
x = 72/2 = 36
Answer: A
Answer: (A) 36
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 3/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
(A) 20
(B) 25
(C) 15
(D) 30
(E) 35
Rationale: answer of 1st
just add the given probabilities p(blue)+p(red)+p(green) i.e
1/8+1/5+3/10=5+8+12/40 =25/40
now we know p(blue)+p(red)+p(green)+p(yellow)=1
25/40+p(yellow)=1
p(yellow)=15/40
i.e why yellow balls are 15.
C
Answer: (C) 15
Question: An article is bought for Rs.600 and sold for Rs.550, find the loss percent?
(A) 8.33%
(B) 16 7/3%
(C) 16 2/8%
(D) 16 2/3%
(E) 76 2/3%
Rationale: 600 ---- 50
100 ---- ? =>8.33%
Answer:A
Answer: (A) 8.33%
Question: The capacity of a cylindrical tank is 246.4 litres. If the height is 4 metres, what is the diameter of the base?
(A) 1.4 metres
(B) 2.8 metres
(C) 28 metres
(D) 14 metres
(E) none of these
Rationale: Capacity (volume) of a cylindrical tank = πr2h
(Here r = radius and h = height of the tank)
Now, from the question, 246.4 × 0.001 = 22⁄7 × r2 × 4
[∵ 1 litre = 1000 cm3 = 0.001 m3]
or, 0.2464×7/22×4 = r2
or,r = 0.14 m
or,diameter = 2r = 0.28 m
Answer E
Answer: (E) none of these
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
(A) 2/5
(B) 7/9
(C) 3/11
(D) 8/5
(E) 9/1
Rationale: Explanation:
The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.
ANSWER IS C
Answer: (C) 3/11
Question: Ram purchased a flat at Rs. 1 lakh and Prem purchased a plot of land worth Rs. 1.1 lakh. The respective annual rates at which the prices of the flat and the plot increased were 10% and 5%. After two years they exchanged their belongings and one paid the other the difference. Then
(A) Ram paid Rs. 275 to Prem
(B) Ram paid Rs. 475 to Prem
(C) Ram paid Rs. 375 to Prem
(D) Prem paid Rs. 475 to Ram
(E) None of these
Rationale: Explanation :
After 2 years the price of the flat will be (1)(1.10)2 = Rs. 1.21 lakh.
Correspondingly the price of the land will be (1.1)(1.05)2 = Rs. 1.21275 lakh.
Hence, the price of the plot is Rs. (1.21275 – 1.21) lakh = Rs. 275 more than that of the flat. Hence, if they exchange, Ram will have to pay Prem this amount.
Answer : A
Answer: (A) Ram paid Rs. 275 to Prem
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 50 percent butterfat to obtain milk that is 20 percent butterfat?
(A) 6
(B) 12
(C) 14
(D) 24
(E) 28
Rationale: Equate the fat:
0.1x + 0.5*8 = 0.2(x + 8) --> x = 24.
Answer: D.
Answer: (D) 24
Question: If x and y are positive odd integers, then which of the following must also be an odd integer? I. x^(y+2) II. x(y+4) III. (y+1)^(x-1) + 2
(A) II,III only
(B) I,II only
(C) I only
(D) II only
(E) III only
Rationale: let x= 5, y= 3
I. 5^5 = > Odd
II. 5*7 = > Odd
III. 4^4 +2= > Even
Answer : B
Answer: (B) I,II only
Question: The present worth of Rs.1404 due in two equal half-yearly instalments at 8% per annum. Simple interest is:
(A) 1320
(B) 1300
(C) 1325
(D) 120
(E) None of these
Rationale: Explanation:
Required Sum = PW of Rs.702 due 6 months hence +PW of Rs.702 due 1 year hence
=Rs.[100×702/100+(8×12)+100×702/100+(8×1)]
= Rs. 1325
Answer: C
Answer: (C) 1325
Question: A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
(A) 62 m
(B) 54 m
(C) 50 m
(D) 55 m
(E) 56 m
Rationale: Explanation:
Let x is the length of the train in meter and v is its speed in kmph
x/9 = ( v-2)(10/36) ---(1)
x/10 =( v-4) (10/36) --- (2)
Dividing equation 1 with equation 2
10/9 = (v-2)/(v-4)
=> 10v - 40 = 9v - 18
=> v = 22
Substituting in equation 1, x/9 = 200/36 => x = 9×200/36 = 50 m
Answer: Option C
Answer: (C) 50 m
Question: If Q = {1, 7, 18, 20, 29, 33}, how much less is the mean of the numbers in Q than the median of the numbers in Q?
(A)  1.0
(B)  1.5
(C)  2.0
(D)  2.5
(E)  3.0
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (1 + 7 + 18 + 20 + 29 + 33)/6 = 18
Median = (18 + 20)/2 = 19
Difference = 1
Option A
Answer: (A)  1.0
Question: 4 persons a, b, c, d are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?
(A) 12
(B) 36
(C) 48
(D) 72
(E) 144
Rationale: firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..
total 4 are there..
take a,b, and c as one,so total =2..
these 2 can be arranged in 2! ways..
a,b, and c can be arranged within themselves in 3! ways ..
TOTAL = 2!*3!=12
A
Answer: (A) 12
Question: At Company X, senior sales representatives visit the home office once every 20 days, and junior sales representatives visit the home office once every 15 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?
(A) 10%
(B) 25%
(C) 33%
(D) 50%
(E) 67%
Rationale: Each 60-day period, senior representatives visit the home office 3 times while junior representatives visit 4 times, thus 33% more.
The answer is C.
Answer: (C) 33%
Question: Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 10 miles apart. One and a half hours later, they are again 10 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?
(A) a) 13.33-x
(B) b) 40-x
(C) c) 80-2x
(D) d) 120-x
(E) e) 40-x/2
Rationale: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.
Here, the two cars approach a distance 10 mi, then move away from each other another distance of 10 miles. That's a total distance of 20 miles in 1.5 hr, which gives a rate of:
R = (20 mi)/(1.5) = 13.33 mph
That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.
One of the speeds is x, and let's call the other y. We want y.
x + y = 13.33
y = 13.33 - x
Answer =(A)
Answer: (A) a) 13.33-x
Question: At 11:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 3:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
(A) 6:00 p.m.
(B) 7:00 p.m.
(C) 8:00 p.m.
(D) 9:00 p.m.
(E) 10:00 p.m.
Rationale: By the time Jim starts, Tom has already covered = 4 hr * 10 mph = 40 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 40 miles which can be covered in = 40/10= 4 hours
If Jim leaves at 3 pm, he will catch Tom at 7 pm
Answer: B
Answer: (B) 7:00 p.m.
Question: A train 125 m long pass a telegraph pole in 5 seconds. Find the speed of the train
(A) 90 km/hr
(B) 68.4 km/hr
(C) 72 km/hr
(D) 79.2 km/hr
(E) None
Rationale: Sol.
Speed = [125/5] m/sec = [25 * 18/5] km/hr = 90 km/hr.
Answer A
Answer: (A) 90 km/hr
Question: Express 25 mps in kmph?
(A) 77 kmph
(B) 55 kmph
(C) 90 kmph
(D) 56 kmph
(E) 17 kmph
Rationale: 25 * 18/5 = 90 kmph
Answer: C
Answer: (C) 90 kmph
Question: How many shots of 1cm radius can be prepared from a sphere of 3cm radius?
(A) 33
(B) 88
(C) 27
(D) 88
(E) 99
Rationale: 4/3 π * 3 * 3 * 3 = 4/3 π * 1 * 1 * 1 * x
x = 27
Answer: C
Answer: (C) 27
Question: If a quarter kg of potato costs 60 paise, how many paise does 200 gm cost?
(A) 65 paise
(B) 70 paise
(C) 52 paise
(D) 48 paise
(E) None of these
Rationale: Explanation :
Let 200 gm potato costs x paise
Cost of ¼ Kg potato = 60 Paise
=> Cost of 250 gm potato = 60 Paise (∵ 1 Kg = 1000 gm => ¼ Kg = 1000/4 gm = 250 gm)
More quantity, More Paise (direct proportion)
Hence we can write as
Quantity200:250}::x:60
⇒200×60=250×x⇒4×60=5×x⇒4×12=x⇒x=48 . Answer : Option D
Answer: (D) 48 paise
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
(A) 120
(B) 145
(C) 166
(D) 170
(E) 189
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: (C) 166
Question: If m is an odd integer and n an even integer, which of the following is definitely odd?
(A) (2m+n)(m-n)
(B) (m+n2)+(m+n2)
(C) m2+mn+n2
(D) m +n
(E) None
Rationale: m+n because the sum of an even and an odd number is always an odd number.
Ex: 3 is an odd number and 6 is an even number. Now, 3+6=9, is an odd number.
ANSWER:D
Answer: (D) m +n
Question: Daniel is playing a dice game in which a dice is rolled 5 times. If a number turns up exactly 3 times then the game is won. Daniel has thrown the dice two times and got number 4 both times. What is the probability that Daniel will win the game ?
Note: the dice is an unbiased die with numbers 1 to 6
(A) 1/216
(B) 75/216
(C) 80/216
(D) 90/216
(E) 100/216
Rationale: Probability of any number from 1 to 6 = 1/6.
Given that you already have 2 4s , leaving you with 3 more slots to determine if you will win or not.
2 scenarios for a win:
Scenario 1: 4 4 T N N , with T= 4 , N= not 4
Probability of this scenario = 1*1*(1/6)*(5/6)*(5*6)*3!/2!=75/216 .... (3!/2! to show the arrangement of TNN in 3 slots)
Scenario 2: 4 4 N N N , with N = any particular number but 4 and in this case for a 'win' all 'N's are the same number.
Probability of this scenario = 1*1*(5/6)*(1/6)*(1/6) = 5/216 ...(with 1/6 shows the probability of choosing that same number out of 6 possible)
Thus the final probability = 75/216 + 5/216 = 80/216
C is the correct answer.
Answer: (C) 80/216
Question: The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 70 cents more than the commodity Y?
(A) 2010
(B) 2011
(C) 2012
(D) 2013
(E) 2014
Rationale: The cost of commodity X increases by 10 cents per year relative to commodity Y.
The price of X must gain 20 + 70 = 90 cents on commodity Y, which will take 9 years.
The answer is A.
Answer: (A) 2010
Question: In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 30,870,000, how many red beads were removed?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 30,870,000
= 2^4 * 5^4 * 3087
= 2^4 * 3 * 5^4 * 1029
= 2^4 * 3^2 * 5^4 * 343
= 2^4 * 3^2 * 5^4 * 7^3
The answer is C.
Answer: (C) 3
Question: In the xy-coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (4, 6) and Q = (6, 2)?
(A) 0.8
(B) 1.0
(C) 1.2
(D) 1.4
(E) 1.6
Rationale: First, get the middle coordinate between (4,6) and (6,2).
x = 4 + (6-4)/2 = 5
y = 2 + (6-2)/2 = 4
Second, get the slope of (5,4) and (0,0). m = 4-0 / 5-0 = 4/5 = 0.8
Answer: A
Answer: (A) 0.8
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
(A) 2.8%
(B) 3.6%
(C) 4.4%
(D) 5.2%
(E) 6.0%
Rationale: Let amount spent by Jill = 100
Clothing=50, Food=20, others=30
Tax on clothing= 2
Tax on others=2.4
Percentage= 4.4/100 4.4%
Answer: C
Answer: (C) 4.4%
Question: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 51, what is the value of a?
(A) 24
(B) 25
(C) 28
(D) 32
(E) 34
Rationale: Let a=2k, b=3k, and c=4k.
a+b+c = 2k+3k+4k = 9k
Since the average is 51:
9k/3 = 51
3k = 51
k=17
Then a=34.
The answer is E.
Answer: (E) 34
Question: Two pipes can fill a tank in 12 minutes and 20 minutes respectively. Both pipes are opened together and after some time the first pipe is closed and the tank is full in totally 10 minutes. For how many minutes was first pipe open?
(A) 8 minutes
(B) 6 minutes
(C) 7 minutes
(D) 10 minutes
(E) 9 minutes
Rationale: Second pipe is opened for 10 minutes. So , part of tank filled by the second pipe = 10/20=1/2.
So, 1 -1/2 = 1/2 tank is filled by first pipe.
First pipe can fill 1/2 of tank in 1 * 12/2 = 6minutes.
So, the first pipe is opened for 6minutes.
ANSWER:B
Answer: (B) 6 minutes
Question: If Rani earns a raise of between 5% and 11%, non-inclusive, by what fraction could her salary have increased?
(A) 1/4
(B) 1/5
(C) 1/70
(D) 1/10
(E) 1/20
Rationale: Perhaps it is also easy to just translate the % into fractions:
6%: 6/100 = 3/50
7%: 7/100
8%: 8/100 = 4/50 =2/25
9%: 9/100
10%:10/100=1/10
Only 1/10 exists in the answer choices, so ANS D
Answer: (D) 1/10
Question: How many days will there be from 29th January,1996 to 15th May,1996(both days included)?
(A) 102
(B) 103
(C) 111
(D) 120
(E) 108
Rationale: Explanation:
Number of days from 29-Jan-1996 to 15-May-1996 (both days included)
= 3(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 108
Answer: Option E
Answer: (E) 108
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.
(A) 488
(B) 776
(C) 481
(D) 480
(E) 412
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.Answer:D
Answer: (D) 480
Question: There are 36 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
(A) 4
(B) 7
(C) 17
(D) 21
(E) 27
Rationale: let's find the range of Both and hence the range of x. Minimum value of Both: Say there is no overlap in the two sets. 36 = x + 2xx = 12In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.36 = 2xx = 18 So Both lies between 0 and 18 Only option (C) satisfies this condition. ANSWER:C
Answer: (C) 17
Question: Spanish Language Broadcast records last 90 min on each of two sides. If it takes 3 hours to translate one hour of broadcast, how long will it take to translate 16 full records?
(A) 144 hours
(B) 124 hours
(C) 134 hours
(D) 154 hours
(E) 164 hours
Rationale: Records last 90 min on each of 2 sides,
==> record last 90*2 = 180 min = 3 hours
16 full records--> 16*3 = 48 hour broadcast
Given, 3 hours to translate 1 hour of broadcast
Let x be the time required to translate 48 hour broadcast(16 full records)
x = 48*3
=144 hours
ANSWER:A
Answer: (A) 144 hours
Question: In a race where 12 cars are running, the chance that car X will win is 1/6, that Y will win is 1/10 and that Z will win is 1/8. Assuming that a dead heat is impossible, find the chance that one of them will win.
(A) 1/140
(B) 1/180
(C) 27/410
(D) 47/120
(E) 57/120
Rationale: Required probability = P(X) + P(Y) + P(Z) (all the events are mutually exclusive).
= 1/6 + 1/10 + 1/8
= 47/120
ANSWER:D
Answer: (D) 47/120
Question: I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 71 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
(A) 8715
(B) 0152
(C) 3581
(D) 5041
(E) 9126
Rationale: D
5041
n^1
71 * 71 = 5625 (sum of first 71 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).
Answer: (D) 5041
Question: A can do a piece of work in 10 days, while B alone can do it in 15 days. They work together for 5 days and the rest of the work is done by C in 2 days. If they get 450 for the whole work, how should they divide the money ?
(A) 225, 150, 75
(B) 250, 100, 100
(C) 200, 150, 100
(D) 175, 175, 100
(E) None of these
Rationale: Work done by A and B in 5 days = (1⁄10 + 1⁄15) × 5 = 5⁄6
Work remaining = 1 - 5⁄6 = 1⁄6
∴ C alone can do the work in 6 × 2 = 12 days
Ratio of their share work = 5⁄10 : 5⁄15 : 2⁄12 = 3 : 2 : 1
Share of wages = 225, 150, 75
Answer A
Answer: (A) 225, 150, 75
Question: The average of 8 numbers is 25, that of the first 2 is 20 and of the next three is 26. The sixth number is less than the seventh by 4, and less than the eighth by 6. The last number is
(A) 30
(B) 32
(C) 40
(D) 36
(E) 38
Rationale: Explanation :
Sum of all the numbers = 25*8 = 200
Sum of first two numbers = 40
Sum of next three numbers(i.e., 3rd, 4th and 5th) = 78
So, sum of first five numbers = 118 and sum of 6th, 7th and 8th number = 82
Assuming sixth number to be x, we get 7th number = x+4 and 8th number = x+6.
So, x + (x+4) + (x+6) = 82
=> x = 24.
Hence, last number(8th number) = 30.
Answer : A
Answer: (A) 30
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) 54888
(B) 2777
(C) 5400
(D) 1278
(E) 2881
Rationale: 100x + 400 = 12(x – 5)
x = 50
100 * 50 + 400 = 5400
Answer: C
Answer: (C) 5400
Question: Find number which is 80% less than 80.
(A) 18
(B) 22
(C) 28
(D) 26
(E) 16
Rationale: Explanation:
80% less is 20% of the given number
Therefore, 20% of 80 is 16.
ANSWER: E
Answer: (E) 16
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
(A) 2266
(B) 2987
(C) 2678
(D) 6725
(E) 2677
Rationale: CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725.
Answer: D
Answer: (D) 6725
Question: By using the numbers 1, 3, 4, 6 and 9 only once, how many five digit numbers can be made that are divisible by 8?
(A) 3
(B) 12
(C) 6
(D) 18
(E) 42
Rationale: A number to be divisible by 8 must end with 08, 16, 24,32 ,40 or 72.
So, there are the following cases possible:
349-16 --> the first three digits can be arranged in 3=6 ways.
Total = 6 = 6.
Answer: C.
Answer: (C) 6
Question: In certain year in Country C, x sets of twins and y sets of triplets were born. If there were z total babies born in Country C in this year, and x and y were both greater than 0, which of the following represents the fraction Q of all babies born who were NOT part of a set of twins or triplets?
(A) z - 2x - 3y
(B) (2x+3y)/z
(C) (x+y)/z
(D) 1 - (2x+3y)/z
(E) 1 - (x+y)/z
Rationale: X set of twins implies 2x babies of twin category.
Y set of triplets means 3y babies of triplet category.
Let K be the babies other than twin or triplet category.
Total babies = z = 2x+3y+k.
or K=Z-(2x+3y)
=> Fraction of babies other than twin or triplet categories = K/Z = Z-(2x+3y)/Z.
Q= 1- (2x+3y)/Z. Hence answer is D.
Answer: (D) 1 - (2x+3y)/z
Question: Diane find 1 can of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?
(A) 5
(B) 7 and a half
(C) 10
(D) 12 and a half
(E) 15
Rationale: She will need 2 cans to paint the rest of this room and 3 for the next room for a total of 5 cans.
A
Answer: (A) 5
Question: The sum of two numbers is 216 and their H.C.F. is 27. The number are:
(A) 27, 189
(B) 81,189,
(C) 108, 108
(D) 154, 162
(E) none of these
Rationale: Let the required numbers be 27a and 27b.Then, 27a+27b=216
a+b=8
Now, co-primes with sum 8 are(1, 7)and(3,5).
required numbers are (27*1*, 27*7) and (27*3,27*5)
i.e., (27, 189)and (81,135)
out of these, the given one in the answer is the pair(27,189).
correct Option:A
Answer: (A) 27, 189
Question: A committee has 6 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 127
(B) 300
(C) 882
(D) 272
(E) 323
Rationale: The number of ways to select two men and three women
= 6C₂ * ⁶C₃
= (6*5)/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 300
Answer: B
Answer: (B) 300
Question: The sum E of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by En = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
(A) 4345
(B) 4302
(C) 4258
(D) 4214
(E) 4170
Rationale: a method to do it under one minutes is to take advantage of the choices given...
lets work on the last digit as we have different units digit in each choice...
total sum of 1 to 100 inclusive will have 0 as the last digit..
this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...
now for single digit in sum E of even number from 25 to 63..
25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..
here too the units digit is 0, but 64 has to be excluded from the total..
two ways from here on..
1) we are subtracting 0 from 0
so units digit should be 0, but we have to add 64..
so last/units digit =4..
2)we subtract 64 from sum of even int..
so units digit=80-4=76..
or units digit =6...
so our answer should have units digit as 10-6=4..
only D has 4 as units digit..
ans D
Answer: (D) 4214
Question: In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?
(A) 24
(B) 48
(C) 56
(D) 72
(E) 96
Rationale: These 5 people can be arranged in 5! ways. These are the total number of ways you get.
Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.
Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72
ANSWER:D
Answer: (D) 72