mathewhe/aqua_rat huggingface dataset:
Question: What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
(A) Rs.2.04
(B) Rs.2.09
(C) Rs.2.06
(D) Rs.2.22
(E) Rs.2.08
Rationale: C.I. when interest is compounded yearly
= [5000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 5000 * 26/25 * 51/50 = Rs. 5304
C.I. when interest is compounded half-yearly
= [5000 * (1 + 2/100)2]
= (5000 * 51/50 * 51/50 * 51/50) = Rs. 5306.04 Difference = (5306.04 - 5304) = Rs. 2.04.
Answer:A
Answer: (A) Rs.2.04
Question: A certain company has budgeted $1380 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $400, how much was the company under budget or over budget?
(A) $55 under budget
(B) $30 under budget
(C) $30 over budget
(D) $55 over budget
(E) $90 over budget
Rationale: The budget for 3 months is (3/12)*$1380 = $345
The company is $55 over budget.
The answer is D.
Answer: (D) $55 over budget
Question: Smitha bought 8 Kg of kiwi fruit at an average rate of 360.If she returned 3.5kg to the retailer,at an average rate of remaining fruit was 202.5, Then what is the average price, of the returned 3.5 Kgs ?
(A) 41.5
(B) 43
(C) 42
(D) 45
(E) 47.3
Rationale: Total price of 8Kg kiwi fruit=8*45=360
Total price of 4.5Kg kiwi fruit=4.5*45=202.5
Total price of 3.5Kg kiwi fruit=360-202.5=157.5
Average price of 3.5 Kgs kiwi fruit= 157.5/3=45
Correct option Answer:D
Answer: (D) 45
Question: Suppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/2 of an ounce and one to measure exactly 1/3 of an ounce. You can pour precisely measured amounts into a beaker, which initially is empty. You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed. Which of the following represents, in ounces, a precise amount of distilled water you can transfer from the vat to the beaker?
I. 1/6
II. 1/7
III. 1/12
(A) 1/6 and 2/3
(B) III only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: 1/2-1/3=1/6 Choice III works
1/2+1/3=3+1/6 =4/6=2/3
Answer: A
Answer: (A) 1/6 and 2/3
Question: After 38 liters of petrol were poured into the tank, it was still 5% empty. How much petrol must be poured into the tank in order to fill it?
(A) 7 liters
(B) 4 liters
(C) 3 liters
(D) 2 liters
(E) 6 liters
Rationale: 95% ----------- 38
5% ------------ ?
=> 2 liters
Answer: D
Answer: (D) 2 liters
Question: The average age of 30 students in a class is 10years. If teacher's age is also included then average increases 1year then find the teacher's age?
(A) 59
(B) 55
(C) 61
(D) 41
(E) 36
Rationale: Total age of 50 students = 30*10 = 300
Total age of 51 persons = 31*11 = 341
Age of teacher = 341-300 = 41years
Answer is D
Answer: (D) 41
Question: If a^x = b^2y, then
(A) log a/b= x/y
(B) log a/ log b = x/y
(C) log a/ log b = 2y/x
(D) log b/a = x/y
(E) log b/a = y/x
Rationale: a^x = b^2y => log a^x = log b^2y => x log a = 2y log b
=> log a/ log b = 2y/x
ANSWER:C
Answer: (C) log a/ log b = 2y/x
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is ?
(A) 6 days
(B) 8 days
(C) 12 days
(D) 14 days
(E) 16 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days.
B)
Answer: (B) 8 days
Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 51% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
(A) 60%
(B) 50%
(C) 25%
(D) 16%
(E) 10%
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 51 - {both} + 40
{both} = 16%.
Answer: D.
Answer: (D) 16%
Question: Renee has a bag of 6 candies, 4 of which are sweet and 2 of which are sour. Jack picks two candies simultaneously and at random. What is the chance that exactly 1 of the candies he has picked is sour?
(A) 3/5
(B) 7/18
(C) 8/15
(D) 4/10
(E) 5/12
Rationale: Renee has a bag of 6 candies, 4 of which are sweet and 2 of which are sour.
Jack picks two candies simultaneously and at random. What is the chance
that exactly 1 of the candies he has picked is sour?
Here's what I did: I thought why not use combinatorics lol (too brave right? :roll: ). So I thought there are 6!/4!2! = 15 ways to pick 2 candies out of the 6.
I need exactly 1 sour so the chance of getting exactly 2 sour was 4/15. 1-4/15 = 11/15. This was SOOO WRONG !!
Here's the answer:
2/6 x 4/5 = 8/30 (sour fist and then sweet)
2/6 x 4/5 = 8/30 (sweet fist and then sour)
8/30 + 8/30 = 16/30 = 8/15.
C is the answer
Answer: (C) 8/15
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
(A) Rs.16000
(B) Rs.20000
(C) Rs.24000
(D) Rs.28000
(E) Rs.29000
Rationale: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
ANSWER:D
Answer: (D) Rs.28000
Question: How many seconds will a 600 m long train take to cross a man walking with a speed of 4 km/hr in the direction of the moving train if the speed of the train is 64 km/hr?
(A) 30
(B) 36
(C) 50
(D) 44
(E) 60
Rationale: Speed of train relative to man = 64 - 4 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 600 * 3/50 = 36 sec.
Answer: B
Answer: (B) 36
Question: Which of the following is true about 0<4x-|x|<5?
(A) -1<x<0
(B) 0<x<1
(C) 4<x<5
(D) 2<x<3
(E) 3<x<4
Rationale: when can be 4x-|x| be greater than 0..
NEVER when x is positive..
ONLY A is left..
you can also substitute any value within the given range to check for answer
Example - put x as -0.5 for A. 0<x<1..
so 4x-|x| = 4*(0.5)- |0.5|=2-0.5 = 1.5 and it satisfies 0<|x|-4x<5
B
Answer: (B) 0<x<1
Question: A shopkeeper sold an book offering a discount of 5% and earned a profit of 25%. What would have been the percentage of profit earned if no discount was offered?
(A) 131.6
(B) 120
(C) 130
(D) 110
(E) 150
Rationale: Let C.P. be $100.
Then, S.P. = $125
Let marked price be $x. Then, 95/100 x = 125
x = 12500/95 = $131.6
Now, S.P. = $131.6, C.P. = $100
Profit % = 31.6%.
A
Answer: (A) 131.6
Question: Let N = 18p, where p is a prime number greater than 2. How many odd numbers divide N?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: We start by factoring 18. 18 = 2*9 = 6*3 = 2*3*3. Since p is a prime number greater than 2 it must be odd. Therefore 3, 9, and p are the odd numbers that divide N. There are three odd divisors and the answer is therefore C.
Answer: (C) 3
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
(A) Rs.12828
(B) Rs.12800
(C) Rs.12829
(D) Rs.12297
(E) Rs.12819
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
Answer: B
Answer: (B) Rs.12800
Question: What is the units digit of (3^5)(4^13)?
(A) 2
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: -> The ones place of (~3)^n repeats after 4 times like 39713.
The ones place of (~4)^n repeats after 2 times like 464.
Then, 3^5=3^4*1+13^1.,
4^13=4^2*6+1=4^1=~4
which is (3^5)(4^13) (3^1)(~4)=(~3)(~4)=~2. Therefore, the answer is A.
Answer: (A) 2
Question: Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit integers are possible?
(A) 48
(B) 66
(C) 72
(D) 78
(E) 90
Rationale: Total number of 5 digit numbers that can be formed = 5! = 120.
Total number of 5 digit numbers in which 3 and 4 are adjacent = 48. This can be calculated by taking 3 and 4 as a pair and considering positions where they can appear.
Number of 5 digit numbers in which 3 and 4 are not adjacent = Total number of 5 digit numbers - Total number of 5 digit numbers in which 3 and 4 are adjacent.
Ans = 120 - 48 = 72
C
Answer: (C) 72
Question: If an integer n is to be chosen at random from the integers 1 to 88, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 33/44
Rationale: n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.
Thus when n is even, this whole expression will be divisible by 8.
from 1 to 88, there are 44 even integers.
Now when (n+1) is multiple by 8, we have 12 such values for (n+1)
probability that n(n+1)(n+2) will be divisible by 8
= (44 + 12)/88
= 66/88
= 33/44
Ans is E
Answer: (E) 33/44
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 620 m long?
(A) 86
(B) 89
(C) 277
(D) 278
(E) 291
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 620)/10 = 86 sec.
Answer: A
Answer: (A) 86
Question: A trader sells 40 metres of cloth for Rs.8200 at a profit of Rs.15 per metre of cloth. How much profit will the trder earn on 40 metres of cloth?
(A) Rs.950
(B) Rs.1500
(C) Rs.600
(D) Rs.1200
(E) None of these
Rationale: Explanation:
SP of 1 metre cloth = 8200/40 = Rs.205.
CP of 1 metre cloth = Rs.205 – 15 = Rs.190
CP on 40 metres = 190 x 40 = Rs.7600
Profit earned on 40 metres cloth = Rs.8200 – Rs.7600 = Rs.600.
Answer: Option C
Answer: (C) Rs.600
Question: A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. On arriving at the third station it is found to have 240 passengers. Find the no of passengers in the beginning?
(A) 264
(B) 180
(C) 192
(D) 144
(E) 168
Rationale: Let no of passengers in the beginning be X
After first station no passengers=(X-X/3)+280=2X/3 +280
After second station no passengers =1/2(2X/3+280)+12
1/2(2X/3+280)+12=240
2X/3+280=2*228 = 456 - 280 = 176
2X/3=176
X=264. So the answer is option A) 264.
Answer: (A) 264
Question: 3 no.'s A, B & C are in the ratio of 12:15:25. If sum of these no.'s is 312, find the ratio between the difference of B & A & the difference of C & B.
(A) 1 : 5
(B) 3 : 10
(C) 4 : 11
(D) 5 : 13
(E) 6 : 17
Rationale: We have, a = 12, b = 15, c = 25 and x = 312.
ax_ 12 X 312
a+b+c 12+15+25
— 72,
bx _ 15 X 312 B — — 90 a +b+c 12 + 15+ 25 cx 25 X 312 And, C =
a+b+c 12 + 15+ 25
...B-A=18 andC-B=60
- 150
Thus, their ratio = 18 : 60 or 3 : 10
B
Answer: (B) 3 : 10
Question: A certain pair of used shoes can be repaired for $11.50 and will last for 1 year. A pair of the same kind of shoes can be purchased new for $28.00 and will last for 2 years. The average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes?
(A) 20.8
(B) 21.46
(C) 21.74
(D) 22.3
(E) 21.4
Rationale: 1) Cost of repairing = 11.5 ( for one year ), Therefore for 2 years it would be$ 23.
2) Cost of new pair which will last for 2 years is$ 28.
Percentage change formula =( Final value - Initial value ) / ( Initial Value ) * 100. In this case the final value would be the price of new shoeinitial value would be the cost of repairing the old shoe.
I.e ( 28 - 23 ) / ( 23 ) * 100 = 21.74 %.
Ans is C
Answer: (C) 21.74
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 1 kmph, then the speed in downstream is?
(A) 16
(B) 77
(C) 20
(D) 99
(E) 71
Rationale: M = 15
S = 1
DS = 15 + 1 = 16
Answer: A
Answer: (A) 16
Question: Both the roots of the equation
(x - b)(x - c) + (x - b)(x - a) + (x - a)(x - b) = 0
(A) dependent on a, b, c
(B) always non real
(C) always real
(D) rational
(E) None of these
Rationale: Sol.(c) The equation is
3x2 - 2(a + b + c)x + (bc + ca + ab) = 0
The discriminant
D = 4(a + b + c)2 - 4.3.(bc + ca + ab)
= 4[a2 + b2 + c2 - ab - bc - ca]
= 2[(a2 - 2ab + b2) + (b2 - 2bc + c2) + (c2 - 2ca + a2)]
= 2[(a - b)2 + (b - c)2 + (c - a)2] ≥ 0
∴ Roots are always real.
Answer C
Answer: (C) always real
Question: Jacob is 16 years old. He is 2 times as old as his brother. How old will Jacob be when he is twice as old?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 24
Rationale: j=16;
j=2b;
b=16/2=8;
twice as old so b=8(now)+(8)=16;
jacob is 16+8=24
ANSWER:E
Answer: (E) 24
Question: Jaya can do a work in 10 days while Mahe can do the same work in 15days. Both of them finish the work together and get $300. What is the share of Jaya?
(A) $100
(B) $50
(C) $150
(D) $180
(E) $120
Rationale: Jaya's wages: Mahe's wages = 1/10 : 1/15 = 15:10 = 3:2
Jaya's share = 300*3/5 = $180
Answer is D
Answer: (D) $180
Question: A departmental store has 4 managers and 16 associates. The 4 managers have an average salary of $900. The 16 associates have an average salary of $10,000. What is the average salary for the departmental store?
(A) $8180
(B) $9190
(C) $4140
(D) $5150
(E) $6160
Rationale: Number of managers is 4
Their average salary is $900
Number of associates is 16
Their average salary is $10,000
Total salary of managers is 4*900=$3600
Total salary of associates is 16*10,000=$160,000
Total salary for the departmental store is 160,000+3600=163600
Average salary for the departmental store is 163600/20=8180
Answer is A
Answer: (A) $8180
Question: Ten years ago A was half of B’s Age. If ratio of their present ages is 3:4 then what is the total of their present ages?
(A) 30 years
(B) 08 years
(C) 35 years
(D) 20 years
(E) 25 years
Rationale: present age of A= 3x
present age of B= 4x
10 years ago A was half of B's age
3x-10=1/2(4x-10)
2x=10
x=5
total of their present age
A=3x=3*5=15
B=4x=4*5=20
toatal present age=35yrs
ANSWER:C
Answer: (C) 35 years
Question: There are two containers on a table. A and B. A is half full of wine, while B,which is twice A's size, is one quarter full of wine. Both containers are filled with water and the contents are poured into a third container C. What portion of container C's mixture is wine?
(A) 11.33%
(B) 22.33%
(C) 33.33%
(D) 44.33%
(E) 55.33%
Rationale: Let the size of container A is "x"
then B's size ll be "2x"
A is half full of wine -- >x/2
So remaining "x/2" of A contains water
B is quarter full of win --> 2x/4 --> x/2
So remaining ==> 2x - x/2 = 3x/2
3x/2 of B contains water
Totally C has A's content + B's Content = x + 2x =3x
Wine portion in C = x/2 of "A" + x/2 of "B"
==> x portion of wine
Water portion in C = x/2 of "A" + 3x/2 of "B"
==> 4x/2 ==> 2x portion of water
So portion of wine in C is
x/3x =1/3 portion of wine
if v expressed in %
1/3 * 100 = 33.33%
ANSWER:C
Answer: (C) 33.33%
Question: Fill in the missing number:
18 14 12 11 10.5 ?
(A) 10.1
(B) 10.4
(C) 10.2
(D) 10.25
(E) 10.3
Rationale: D
10.25
Divide each number by 2 and then add 5 to it.
Answer: (D) 10.25
Question: What is the number of 7-element subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9}
for which the sum of those 7 elements is a multiple of 3 ?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: We describe 2 solutions. Let S = {1, 2, . . . , 9}. Observe that the sum of the elements of S
is divisible by 3. So the problem is the same as asking for the number of ways that 2 elements
of S can be chosen so that their sum is divisible by 3 (the other 7 elements of S correspond to a
7-element set as in the problem). Choosing 2 elements of S with sum divisible by 3 corresponds
to either choosing 2 numbers divisible by 3 (which can be done in 3 ways) or choosing 1 number
that is one more than a multiple of 3 and 1 number that is one less than a multiple of 3 (which can
be done in 3 · 3 = 9 ways). Hence, the answer is 3 + 9 = 12.
correct answer C
Answer: (C) 12
Question: For what value of x, is |x – 3| + |x + 1| + |x| = 10?
(A) 0
(B) 3
(C) -3
(D) 4
(E) -2
Rationale: There are 3 transition points: -1, 0, 3
When x > 3,
|x−3|+|x+1|+|x|=10|
x−3+x+1+x=10
x = 4
Satisfies
When 0 < x < 3
|x−3|+|x+1|+|x|=10
−(x−3)+(x+1)+x=10
x = 6 (Not possible since 0 < x < 3)
When -1 < x < 0
|x−3|+|x+1|+|x|=10
−(x−3)+−(x+1)+x=10
x = -8 (Not possible since -1 < x < 0)
When x < -1
|x−3|+|x+1|+|x|=10
-(x - 3) - (x+1) - x = 10
x = -8/3
Satisfies
ANSWER:D
Answer: (D) 4
Question: Two dice are rolled. What is the probability the sum will be greater than 7?
(A) 1/9.
(B) 1/12.
(C) 5/36.
(D) 1/6.
(E) 7/36.
Rationale: Combinations possible: (6,6) , (5,6) , (6,5) , (5,5), (5,4) , (4,5), (4,4) = 7
Total combinations possible: 6*6=36
Answer = 7/36 Option E.
Answer: (E) 7/36.
Question: A train 150m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
(A) 75kmph
(B) 85kmph
(C) 95kmph
(D) 105kmph
(E) 115kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
150/[(x+5)*5/18] = 6
30(x+5) = 2700
x = 85kmph
Answer is B
Answer: (B) 85kmph
Question: What number is missing?
27, 54, ?, 108, 135, 162, 189, 216
(A) 81
(B) 95
(C) 104
(D) 137
(E) 158
Rationale: A
81
Add 27 each time.
Answer: (A) 81
Question: A ferry can transport 50 tons of vehicles. Automobiles range in weight from 1,600 to 3,200 pounds. What is the greatest number of automobiles that can be loaded onto the ferry?
(A) 23
(B) 41
(C) 48
(D) 62
(E) 86
Rationale: to get maximum vehicles we must take into consideration the minimum weight i.e 1600 pounds here
since , 1 ton = 2000 pounds
50 tons will be 100,000 pounds
from the answer choices:
let max number of vehicles be 62
total weight will be = 62*1600 = 99200 pounds , which is lesser than the maximum weight allowed .
Ans: D
Answer: (D) 62
Question: The average of first 10 natural numbers is?
(A) 9:3
(B) 5.5
(C) 2:2
(D) 5.2
(E) 5.9
Rationale: Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5
Answer: B
Answer: (B) 5.5
Question: The sector of a circle has radius of 28 cm and central angle 135o. Find its perimeter?
(A) 122 cm
(B) 92.2 cm
(C) 28.9 cm
(D) 29.2 cm
(E) 98.2 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 28) + 2(28)
= 66 + 56 = 122 cm
Answer:A
Answer: (A) 122 cm
Question: In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling price was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $5,500. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June?
(A) 1. $15,600
(B) 2. $15,750
(C) 3. $17,500
(D) 4. $18,100
(E) 5. $19,200
Rationale: Edited the question as there was a typo.
Range = Highest Value - Lowest Value.
Range in May was 15,000 and the lowest price in May was 4,500, thus the highest price in May was 15,000+4,500=19,500.
Range in June was 16,500 and the lowest price in June was 5,500, thus the highest price in June was 16,500+5,500=22,000.
Lowest price of a car in May-June was 4,500 (May) and the highest price of a car in May-June was 22,000, thus the range for May-June is 22,000-4,500=17,500.
Answer: C.
Answer: (C) 3. $17,500
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22
(B) 27
(C) 48
(D) 99
(E) 12
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer: C
Answer: (C) 48
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
(A) 5568
(B) 6369
(C) 5460
(D) 5635
(E) 6734
Rationale: 5000 * 104/100 * 105/100
=> 5460
Answer:C
Answer: (C) 5460
Question: What will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, 216, x
(A) 24
(B) 28
(C) 36
(D) 42
(E) 44
Rationale: Go on dividing by 6 to the next number
C)
Answer: (C) 36
Question: Two trains are moving in opposite direction @ 60 kmph and 90 kmph.Their lengths are 1.10 km and 0.9 km respectively.The time taken by the slower train to cross the faster train in seconds is
(A) 36
(B) 45
(C) 48
(D) 49
(E) 50
Rationale: R.S = (60+90)kmph => (150*5/18)m/sec => (125/3)m/sec
Distance covered = (1.10 + 0.9) km = (2*1000) = 2000 m.
Required time = (2000 * 3/125) = 48sec.
ANSWER:C
Answer: (C) 48
Question: In a certain city, 70 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 80 percent of the registered voters who are Democrats and 30 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
(A) 65%
(B) 52%
(C) 85%
(D) 69%
(E) 75%
Rationale: Say there are total of 100 registered voters in that city. Thus 70 are Democrats and 30 are Republicans.
70*0.80=56 Democrats are expected to vote for Candidate A;
30*0.30=9 Republicans are expected to vote for Candidate A.
Thus total of 56+9=65 registered voters are expected to vote for Candidate A, which is 65% of the total number of registered voters.
Answer: A
Answer: (A) 65%
Question: Find large number from below question The difference of two numbers is 1380. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1245
(B) 1345
(C) 1455
(D) 1577
(E) 1653
Rationale: Let the smaller number be x. Then larger number = (x + 1380).
x + 1380 = 6x + 15
5x = 1365
x = 273
Large number = 273+1380 = 1653
E
Answer: (E) 1653
Question: If X = the product of seven distinct prime numbers, how many factors does X have besides 1 and itself?
(A) 108
(B) 114
(C) 120
(D) 126
(E) 132
Rationale: Since X has 7 distinct prime factors, X has a total of 2^7 = 128 factors.
Besides 1 and itself, X has 126 factors.
The answer is D.
Answer: (D) 126
Question: If k^3 is divisible by 336, what is the least possible value of integer k?
(A) 56
(B) 70
(C) 84
(D) 96
(E) 120
Rationale: k^3 = 336*x = 2^4*3*7*x
The factors of k must at minimum include 2^2*3*7 = 84.
The answer is C.
Answer: (C) 84
Question: Set #1 = {A, B, C, D, E}
Set #2 = {K, L, M, N, O}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
(A) 13/6
(B) 13/5
(C) 13/25
(D) 2/3
(E) 5/6
Rationale: So Not a vowel in Set-1 : 3/5
And not a vowel in Ser-2:4/5
Now,
3/5∗4/5=12/25
This is for not a vowel.
Then for at least one vowel will be = 1−12/25=13/25
Answer will be C.
Answer: (C) 13/25
Question: 3 boys and 7 girls can complete John work in 10 days. 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?
(A) 20 days
(B) 30 days
(C) 40 days
(D) 60 days
(E) 70 days
Rationale: Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
Answer: (C) 40 days
Question: Which of the following CANNOT be a value of 7/(x–7)?
(A) -1
(B) -1/2
(C) 0
(D) 2
(E) 7
Rationale: The question doesn't ask for the value of x here, but for the possible results of the equation.
If 7/(x-7) = 0, then the numerator must be 0. But since the numerator is 7, the fraction can not be equal to 0.
The answer is C.
Answer: (C) 0
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
(A) 15
(B) 88
(C) 44
(D) 54
(E) 23
Rationale: Let the average after 7th inning = x
Then average after 16th inning = x - 3
16(x-3)+87 = 17x
x = 87 - 48 = 39
ANSWER=B
Answer: (B) 88