mathewhe/aqua_rat huggingface dataset:
Question: If x^5y^4z^2 <0 , which of the following must be true?
I. xy <0
II. yz <0
III. xz <0
(A) I
(B) II
(C) III
(D) I and II
(E) None
Rationale: Ans:- x^5y^4z^2 <0
x must be negative. x<0 ; y and z can be either negative or positive as even powers is always positive.
I. xy <0 :- x<0 but y can be - or + hence xy < 0 when y>0 or xy >0 when y <0. So not always true.
II. yz <0 :- As both y and z can be + or - ; yz < 0 or yz >0 are possible
II. xz <0 :- x<0 but z can be - or + hence xz < 0 when z>0 or xz >0 when z <0. So not always true.
Ans :- E
Answer: (E) None
Question: The smallest value of n, for which 2n+3 is not a prime number, is
(A) 4,5
(B) 3,4
(C) 2,6
(D) 5,6
(E) 2,3
Rationale: (2Ã—1 + 3) = 5.
(2Ã—2 + 3) = 7.
(2Ã—3 + 3) = 9.
(2Ã—4 + 3) = 15.
which is not prime , n=3,4.
ANSWER:B
Answer: (B) 3,4
Question: The workforce of Company X is 60% female. The company hired 24 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?
(A) 160
(B) 220
(C) 288
(D) 360
(E) 420
Rationale: Let's xx be total quantity of employees
0.6x=females before adding men
0.55(x+24)=females after adding men
as quantity of women doesn't change we can make an equation:
0.6x=0.55(x+24)
0.05x=13.2
x=264 - this is quantity of employees before adding 24 men
So after adding it will be 288
Answer is C
Answer: (C) 288
Question: On the number line, the number p is twice as many units from -2 as -2 is from 7. If p is less than –2, what is the value of p ?
(A) –20
(B) –10
(C) –6
(D) 10
(E) 14
Rationale: Distance between -2 and 7 = 9
Since number p is twice as many units from -2 as -2 is from 7
, therefore p can be -20 Since , p is less than -2 ,
the value of p = -20
Answer A
Answer: (A) –20
Question: There are 4 boys and 2 girls. In how many ways can they be seated in a row so that all the 4boys do not sit together?
(A) 450
(B) 330
(C) 576
(D) 712
(E) 496
Rationale: Total number of persons = 4+2 = 6
they can be seated in a row in 6! ways
Treat 4boys as 1 so we have 3 people can be arranged in 3! ways
4boys can be arranged among themselves in 4! ways
Required number of ways = 6!-4!*3! = 576
Answer is C
Answer: (C) 576
Question: Meg and Bob are among the 7 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
(A) 24
(B) 30
(C) 2520
(D) 90
(E) 120
Rationale: Total # of ways the race can be finished is 7!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 7!/2=2520.
Answer: C.
Answer: (C) 2520
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 978
(C) 267
(D) 166
(E) 199
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer:A
Answer: (A) 270
Question: A man bought 10 crates of mangoes for $40 total. If he lost 2 of the crates, at what price would he have to sell each of the remaining crates in order to earn a total profit of 20 percent of the total cost?
(A) $6
(B) $8
(C) $10
(D) $12
(E) $14
Rationale: As given, after lost, the remaining 8 crates total cost = $40
So, 1 crate cost = 40/8 = 5
To get 20% profit, 1 crate cost should be = 5+5*20/100 =$6
Answer : A
Answer: (A) $6
Question: An even positive integer 'x' has 'y' positive integral factors including '1' and the number itself. How many positive integral factors D does the number 4x have?
(A) 4y
(B) 3y
(C) 16y
(D) 5y
(E) Cannot be determined
Rationale: I tried for x=2,4 and 6. The integral factors D for x and 4x did not have any specific relation.
My answer is E.
Answer: (E) Cannot be determined
Question: One ton has 2100 pounds, and one pound has 16 ounces. How many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons?
(A)  1680
(B)  1700
(C)  2350
(D)  2500
(E)  8000
Rationale: 16 pounds and 4 ounces= 16*16 + 4 = 260 ounces.
13 tons = 13*2100 pound = 13*2100*16 ounces.
Hence the answer is (13*2100*16)/260 = 1680.
Answer: A.
Answer: (A)  1680
Question: When positive integer N is divided by positive integer J, the remainder is 12. If N/J = 204.06, what is value of J?
(A) 100
(B) 500
(C) 600
(D) 800
(E) 200
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 204.06
Here 204 is the quotient.
Given that Remainder = 12
So, 204.06= 204 + 12/J
So, J = 200
Answer: E
Answer: (E) 200
Question: The average of first 10 even numbers is?
(A) 226
(B) 27
(C) 27
(D) 11
(E) 99
Rationale: Sum of 10 even numbers = 10 * 11 = 110
Average = 110/10 = 11
Answer: D
Answer: (D) 11
Question: If a rectangular billboard has an area of 117 square feet and a perimeter of 44 feet, what is the length of each of the shorter sides?
(A) 4
(B) 7
(C) 8
(D) 9
(E) 26
Rationale: This question can be solved algebraically or by TESTing THE ANSWERS.
We're told that a rectangle has an area of 117 and a perimeter of 44. We're asked for the length of one of the SHORTER sides of the rectangle.
Since the answers are all INTEGERS, and the area is 117, the shorter side will almost certainly be less than 10 (since 10x10 = 100, but we're NOT dealing with a square). Answer B (7) does NOT divide evenly into 117, so the correct answer is
Let's TEST Answer D: 9
IF...
The shorter side = 9...
The area = 117....117/9 = 13 = the longer side
Perimeter = 9+9+13+13 = 44
D
Answer: (D) 9
Question: A certain sum becomes Rs. 20720 in four years and 24080 in six years at simple interest. Find sum and rate of interest?
(A) 14%
(B) 12%
(C) 11%
(D) 22%
(E) 14%
Rationale: Let the interest for one year be x.
As amount = Principal + Interest, we have
P + 4x = 20720 --- (1) ; P + 6x = 24080 --- (2)
Solving the equations (1) and (2), we can get
P = Rs. 14000 and x = Rs. 1680
Interest for one year on Rs. 14000 is Rs. 1680
So, R = (100 * 1680)/(14000 * 1) = 12% p.a.
Answer:B
Answer: (B) 12%
Question: The distance between Delhi and Mathura is 120 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 40.00 a.m.
(B) 10.13 a.m.
(C) 12.00 a.m.
(D) 18.00 a.m.
(E) 19.00 a.m.
Rationale: Explanation:
D = 120 â€“ 20 = 100
RS = 20 + 25 = 45
T = 100/45 = 2 hours 13 minutes
8 a.m. + 2 hours 13 minutes = 10:13 a.m.
Answer: Option B
Answer: (B) 10.13 a.m.
Question: A tyre has two punctures. The first puncture alone would have made the tyre flat in 8 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
(A) 3 1/5min
(B) 3 2/5min
(C) 3 3/7min
(D) 3 4/5min
(E) 3 min
Rationale: Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(1/8+1/6)=(7/24)
So both punctures will make the type flat in
(24/7)mins=3 3/7mins
Option C
Answer: (C) 3 3/7min
Question: Jack and Lee walk around a circular track. It takes Jack and Lee respectively 6 and 10 minutes
to finish each lap. They start at the same time, at the same point on the track, and walk in the
same direction around the track. After how many minutes will they be at the same spot again
(not necessarily at the starting point) for the first time after they start walking?
(A) 15
(B) 16
(C) 30
(D) 32
(E) 60
Rationale: Experimenting with the numbers in turn, dividing 6 into 15 and 10 into 15, we get
answers one whole number apart, so they are together again at 15 minutes.
correct answer A
Answer: (A) 15
Question: Husband has prepared for a candle light dinner on the honeymoon for his wife. While they were having the dinner, a strong breeze flew through the open window and four candles out of ten were extinguished. After that, the husband closed the window.
How many candles were left in the end?
(A) 4
(B) 6
(C) 8
(D) 2
(E) 9
Rationale: A
Four
As the window was closed it is obvious that the six candles that were not extinguished were lit till they melted away entirely. Thus only four candles that were extinguished remain at the end.
Answer: (A) 4
Question: A part of certain sum of money is invested at 9% per annum and the rest at 15% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
(A) 4:6
(B) 4:9
(C) 5:3
(D) 4:1
(E) 4:2
Rationale: 15:9
= 5:3
Answer: C
Answer: (C) 5:3
Question: A pair of articles was bought for $50 at a discount of 30%. What must be the marked price of each of the article?
(A) $25
(B) $17.50
(C) $29.65
(D) $35.95
(E) $45.62
Rationale: S.P. of each of the article = 50/2 = $25
Let M.P = $x
70% of x = 25
x = 25*.7 =$17.50
Answer is B
Answer: (B) $17.50
Question: A completes a work in 4 days and B complete the same work in 8 days. If both of them work together, then the number of days required to complete the work will be
(A) 8 days
(B) 9 days
(C) 2.67 days
(D) 12 days
(E) 13 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
Therefore, here, the required number of days = 4 × 8/ 12 = 2.67 days.
Answer : C
Answer: (C) 2.67 days
Question: A shopping cart contains only apples, oranges, and pears. If there are three times as many oranges as apples, and four times as many pears as oranges, then the apples are equivalent to what fraction of the pears?
(A) 1/6
(B) 1/8
(C) 1/12
(D) 1/4
(E) 3/4
Rationale: O = 3A
P = 4O = 12A
A = P/12
The answer is C.
Answer: (C) 1/12
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 120 metres?
(A) 18
(B) 24
(C) 17
(D) 12
(E) 13
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 120 m = 120/5 = 24 seconds.
Answer: B
Answer: (B) 24
Question: John works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 1,000 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 216,000. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?
(A) 72,000
(B) 48,000
(C) 50,000
(D) 36,000
(E) 40,000
Rationale: let the rate be x, then population of the bacteria after each hour can be given as 1000, 1000x, 1000(x^2), 1000(x^3)
now population at 4pm =216,000
thus we have 1000(x^3) = 216,000 =216
thus x=6
therefore population at 3pm = 1000(36) = 36,000
Answer : D
Answer: (D) 36,000
Question: A boat moves downstream at the rate of 1 km in 5 mins & upstream at the rate of 4 km/hour. What is the velocity of the current?
(A) 2 km/hr
(B) 4 km/hr
(C) 8 km/hr
(D) 10 km/hr
(E) 12 km/hr
Rationale: Speed downstream = 1(560)=12 km/hr
Speed upstream =41 = 4 km/hr
velocity of the current =12(12−4)=4 km/hr
B
Answer: (B) 4 km/hr
Question: A boy has 9 trousers and 10 shirts. In how many different ways can he select a trouser and a shirt?
(A) 100
(B) 102
(C) 104
(D) 108
(E) 90
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 * 10 = 90 ways.
E
Answer: (E) 90
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
(A) 18 kmph
(B) 17 kmph
(C) 24 kmph
(D) 19 kmph
(E) 12 kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph
Answer:C
Answer: (C) 24 kmph
Question: In how many ways can the letters of the word UWPIS be arranged in a row so that the vowels appear in alphabetic order?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: three letters can be arranged in 2! ways.
only one combination AEI is required.
5 letters can be arranged in 5! ways.
thus 5!/ 2! * 1 = 60.
E
Answer: (E) 60
Question: In each of the following numbers, what should be the missing digit in the indicated place such that the number is a multiple of 11?
945678?
(A) 7
(B) 6
(C) 8
(D) 5
(E) 2
Rationale: Explanation:
Divisibility of 11: If the difference of the sum of the digits at odd places and the sum of the digits at even places of a number is zero or a multiple of 11, then that number is divisible by 11.
As per divisibility rule of 11, difference = (x + 21) - 18 = x + 3
=> x + 3 = 11 => x = 8
ANSwer: C
Answer: (C) 8
Question: To hail means to praise and acclaim and this is contrary to what has been proposed in the passage. Ask doubt using Question Id: 6305
(A) 22
(B) 99
(C) 82
(D) 27
(E) 26
Rationale: Answer:A
Answer: (A) 22
Question: A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a plce and come back, how far is the place?
(A) 2 km
(B) 2.4 km
(C) 2.5 km
(D) 3.4 km
(E) None
Rationale: Sol.
Speed downstream = (5+1) kmph = 6 kmph; Speed upstream = (5 - 1)kmph = 4 kmph. Let the required distance be x km.
Then, x/6 + x/4 = 1 ⇔ 2x + 3x = 12 ⇔ 5x = 12 ⇔ x = 2.4 km.
Answer B
Answer: (B) 2.4 km
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
(A) 81:121
(B) 81:128
(C) 81:118
(D) 81:107
(E) 81:189
Rationale: Ratio of the sides = ³√729 : ³√1331
= 9 : 11
Ratio of surface areas = 92 : 112
= 81:121
Answer: A
Answer: (A) 81:121
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
(A) 12:15:18
(B) 12:15:16
(C) 12:15:19
(D) 12:15:11
(E) 12:15:12
Rationale: Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16.Answer: B
Answer: (B) 12:15:16
Question: The average of five integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 69, what is the least possible value of one of the other two integers?
(A) 5
(B) 8
(C) 20
(D) 21
(E) 30
Rationale: When it comes to averages, we know thataverage value = (sum of n values)/n
We can rewrite this into a useful formula:sum of n values = (average value)(n)
The average of five integers is 63
So, the sum of ALL 5 integers = (63)(5) =315
The average of three of the integers is 65
So, the sum of the 3 integers = (69)(3) =207
So, the sum of the 2 REMAINING integers =315-207=108
If the sum of the 2 REMAINING integers =108, and we want to minimize one value, we must MAXIMIZE the other value.
100 is the maximum value so let 1 integer = 100, which means the other must equal 8
Answer: B
Answer: (B) 8
Question: Fill in the sequence:
1 5 9 15 ?
(A) 11
(B) 41
(C) 51
(D) 21
(E) 31
Rationale: D
21
Position of the vowels a e i o u.
Answer: (D) 21
Question: Find the odd man out. 2, 3, 5, 9, 12, 17, 23
(A) 12
(B) 9
(C) 23
(D) 2
(E) 3
Rationale: Explanation :
2
2 + 1 = 3
3 + 2 = 5
5 + 3 = 8
8 + 4 = 12
12 + 5 = 17
17 + 6 = 23
ie, 8 should have come in place of 9
Answer : Option B
Answer: (B) 9
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (3,3) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
(A) 0
(B) 2/5
(C) -2
(D) 1
(E) 7/4
Rationale: CONCEPT: The readers need to know that a rectangle can be divided into two equal area by a Straight line only when the straight line passes through the Centre of the Rectangle (Intersection of its two diagonals)Draw a figure and know it for yourself.
The point of Intersections of the diagonals will be the midpoint of any diagonal i.e. Midpoint of (0,0), and (7,4) OR Midpoint of (0,4) and (7,0)
i.e. Either [(0+7)/2, (0+4)/2] OR [(0+7)/2, (4+0)/2] =[3.5, 2]
Slope of line passing through points (3,3) and (3.5,2) = (2-3)/(3.5-3) = - 1/0.5= -2
C
Answer: (C) -2
Question: log√ 8 / log 8 is equal to
(A) 1/√8
(B) 1/4
(C) 1/2
(D) 1/8
(E) None
Rationale: Solution
log√ 8 / log 8	= log(8)1/2 / log 8
= 1/ 2 log 8 /log 8
= 1/ 2.
Answer C
Answer: (C) 1/2
Question: Three positive integers a, b, and c are such that their average is 40 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?
(A) 41
(B) 44
(C) 45
(D) 46
(E) 47
Rationale: Solution
Given Data
3 positive integers
Average of a, b, and c = 40.
So, a+b+c3a+b+c3 =120 or a + b + c = 120
a ≤ b ≤ c
Median = (a + 13)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 13
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 13) + (a + 13) = 120 (b and c are equal and b, the median, is a + 13)
Or 3a =94 or a = 31.33
So, b = c = 31.33 + 13 = 44.33
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 13) + (a + 14) = 120
Or 3a = 93 or a=31 The value of the numbers is an integer
If a = 31, b = 44 and c = 45.
The least value for c that satisfies all these conditions is 45.
Correct answer is choice C.
Answer: (C) 45
Question: The sum of two numbers is 22. Five times one number is equal to 6 times the other. The bigger of the two numbers is
(A) 10
(B) 12
(C) 14
(D) 15
(E) 60
Rationale: a:b 5:6
a+b=22
5x+6x=22
x=2
then two numbers are 10,12
ANSWER:B
Answer: (B) 12
Question: What is the difference between the local value of 3 and 2 in the number 2324?
(A) 430
(B) 377
(C) 280
(D) 277
(E) 112
Rationale: Explanation:
300 â€“ 20 = 280
Answer: C
Answer: (C) 280
Question: What type of switch is this?
(A) 2
(B) 7
(C) 6
(D) 8
(E) 9
Rationale: Answer:B
Answer: (B) 7
Question: What is 120% of 13/24 of 600?
(A) 320
(B) 390
(C) 440
(D) 480
(E) 510
Rationale: 120% * 13/24 * 360 = 1.2 * 13 * 25 = 390
The answer is B.
Answer: (B) 390
Question: How many integers between 100 and 150, inclusive, can be evenly
divided by neither 3 nor 5?
(A) 33
(B) 28
(C) 27
(D) 26
(E) 24
Rationale: Numbers divisible by 3 start from 102 and end at 150
so total numbers are (150-102)/3 + 1 = 17
Numbers divisible by 5 start from 100 and end at 150
So total numbers are (150-100)/5 + 1 = 11
Total Numbers divisible by 15 start from 105 and end at 150
So total numbers are (150-105)/15 + 1 = 4
So 17+11-4 = 24
Answer : E
Answer: (E) 24
Question: A square was given. Inside the square there are white tiles and black tiles. Black tiles was among the diagonal of the square and dimensions of both white as well as black tiles is 1cm x 1cm. If there are 81 black tiles in the square. Then find the no of white tiles in it.
(A) 2399
(B) 1600
(C) 2679
(D) 1697
(E) 1711
Rationale: In a square, number of squares on the diagonal is equal to the tiles on a single row. If there are even number of square on a side, then total squares on the diagonal is 2n - 1, otherwise 2n. As the total tiles on the diagonal are given as 81, then number of tiles on a side = 2n - 1 = 81 so n = 41.
So number of white tiles = 412−81=1681−81412−81=1681−81 = 1600
Answer:B
Answer: (B) 1600
Question: (23341379 × 72) = ?
(A) 1223441288
(B) 2142579288
(C) 2142339288
(D) 2142339277
(E) 1680579288
Rationale: 23341379 × 72
= 23341379(70 + 2)
= (23341379 × 70) + (23341379 × 2)
= 1633896530 + 46682758
= 1680579288
Answer is E.
Answer: (E) 1680579288
Question: If positive integer n is divisible by both 5 and 21, then n must be divisible by which of the following?
(A) 8
(B) 15
(C) 18
(D) 24
(E) 48
Rationale: A number divisible by both 5,21 is 105 which s divisible by 15.
IMO : Answer B 15
Answer: (B) 15
Question: The length of a rectangle is reduced by 25%. By what % would the width have to be increased to maintainthe original area?
(A) 15%
(B) 20%
(C) 25%
(D) 33%
(E) 40%
Rationale: Sol. Required change = (25*100)/(100-25)=25%
D
Answer: (D) 33%
Question: Natasha climbs up a hill, and descends along the same way she went up. It takes her 3 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 3 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?
(A) 1.5
(B) 2.5
(C) 3.75
(D) 5
(E) 7.5
Rationale: Lets assume distance to top as X, so the total distance travelled by Natasha = 2x
Total Time taken = 3+ 2 = 5 Hrs
Avg speed = Total Dist/Total time taken = 2x/5
Avg speed of complete journey is given as = 3 Hrs
2 x/5 = 3
X = 7.5 miles
Avg speed while climbing = Distance/Time = 7.5/3 = 2.5
Option B
Answer: (B) 2.5
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
(A) 1
(B) 6
(C) 5
(D) 6
(E) 8
Rationale: Let the duration of the flight be x hours. Then,
600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr.
Answer: A
Answer: (A) 1
Question: Half a number plus 5 is 15.What is the number?
(A) 8
(B) 20
(C) 10
(D) 11
(E) 12
Rationale: Let x be the number. Always replace "is" with an equal sign
(1/2)x + 5 = 15
(1/2)x = 15 - 5
(1/2)x = 10
x = 20
correct answer is B
Answer: (B) 20
Question: What is the probability of flipping a fair coin nine times and the coin landing on heads on at least two flips?
(A) 57/64
(B) 119/128
(C) 251/256
(D) 503/512
(E) 509/512
Rationale: The number of possible outcomes is 2^9=512.
0 heads: There is 1 way to have all tails.
1 head: There are 9 ways to have one head.
P(0 or 1 head)=10/512=5/256
P(at least 2 heads)=1 - 5/256 = 251/256
The answer is C.
Answer: (C) 251/256
Question: The sum of three consecutive even numbers is 48. Find the middle number of the three?
(A) 14
(B) 16
(C) 18
(D) 24
(E) 64
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 48
6P = 48 => P = 8.
The middle number is: 8P = 64.
ANSWER:E
Answer: (E) 64
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
(A) 1000
(B) 888
(C) 2889
(D) 2888
(E) 2881
Rationale: 100 * 100 = 10000
125 * 80 = 10000
No change
Answer:A
Answer: (A) 1000
Question: Find the fourth proportional to 2.4, 4.6 and 7.6?
(A) 14.56
(B) 14
(C) 15.34
(D) 16.2
(E) 17
Rationale: Formula = Fourth propotional = (b × c)/a
A = 2.4 , B = 4.6 and C = 7.6
(4.6 × 7.6)/2.4 = 14.56
A
Answer: (A) 14.56
Question: What is the greatest prime factor of 3^8 - 1?
(A) 29
(B) 31
(C) 37
(D) 41
(E) 43
Rationale: 3^8-1 = (3^4-1)(3^4+1) = 80*82 = 8*10*2*41
The answer is D.
Answer: (D) 41
Question: A man purchased 3 blankets @ Rs.100 each, 2 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) 278
(B) 900
(C) 278
(D) 450
(E) 772
Rationale: 10 * 150 = 1500
3 * 100 + 2 * 150 = 600
1500 – 600= 900
Answer:B
Answer: (B) 900
Question: Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 960 pounds of the seed mixture?
(A) 6
(B) 12
(C) 20
(D) 24
(E) 120
Rationale: If the mixture contains 2 pounds of timothy, the mixture must be 40 pounds.
Thus we need 40 pounds of mixture per acre.
960 / 40 = 24 acres
The answer is D.
Answer: (D) 24