mathewhe/aqua_rat huggingface dataset:
Question: 12x − 12 = 12y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?
(A) More than three
(B) Exactly three
(C) Exactly two
(D) Exactly one
(E) None
Rationale: => 12x - 12y = 12
=> x- y =1 -- 1
5y + 5x = 15
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 2
=> x=1
y=1
Therefore , the given system will have Exactly one solution
Answer : D
Answer: (D) Exactly one
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor
(A) 12
(B) 14
(C) 16
(D) 18
(E) 19
Rationale: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
A)
Answer: (A) 12
Question: 12, 24, 16, 32, 24, 48, ?
(A) 31
(B) 32
(C) 36
(D) 37
(E) 40
Rationale: E
40
This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8.
Answer: (E) 40
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3 Answer:A
Answer: (A) 3
Question: A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?
(A) 2/91
(B) 1/81
(C) 1/8
(D) 2/81
(E) 3/40
Rationale: Total number of balls = 4 + 5 + 6 = 15
Let S be the sample space.
n(S) = Total number of ways of drawing 3 balls out of 15 = 15C3
Let E = Event of drawing 3 balls, all of them are yellow.
n(E) = Number of ways of drawing 3 balls, all of them are yellow
= Number of ways of drawing 3 balls from the total 5 = 5C3
(∵ there are 5 yellow balls in the total balls)
P(E) = n(E)/n(S)
=5C3/15C3=5C2/15C3 [∵ nCr = nC(n - r). So 5C3 = 5C2. Applying this for the ease of calculation]
=(5×4/2×1)/(15×14×13/3×2×1)=5×4/(15×14×13/3)=5×4/5×14×13=4/14×13=2/7×13=2/91
ANSWER:A
Answer: (A) 2/91
Question: Which of the following is equal to (n – 3)2*square* if
n = 11?
(A) (n + 6)(n – 6)
(B) (n + 5)(n – 7)
(C) (n + 4)(n – 8)
(D) (n + 3)(n – 9)
(E) (n + 2)(n – 10)
Rationale: If n = 11, then:
(n – 3)2 = (11 – 3)2 = 82 = 64
Substitute 11 for n into each answer until you find one that equals 64:
(n + 6)(n – 6) = (17)(5) = 85
(n + 5)(n – 7) = (16)(4) = 64 You’ve found a match
correct answer B)(n + 5)(n – 7)
Answer: (B) (n + 5)(n – 7)
Question: Rs. 5000 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/5:1/5:1/10?
(A) 1000
(B) 992
(C) 772
(D) 552
(E) 312
Rationale: 1/5:1/5:1/10 = 2:2:1
1/5*5000 = 1000
2000-1000 = 1000
Answer: A
Answer: (A) 1000
Question: a, b are positive integers. The remainder of a to be divided by 7 is 6 and the remainder of b to be divided by 8 is 5.
Which is possible to be the remainder of a*b to be divided by 52
(A) a) 2
(B) b) 6
(C) c) 8
(D) d) 12
(E) e) 30
Rationale: Two ways to do it...
a=7x+6..
b=8y+5..
1) convenient way..
Take x and y as 0, and you will get a*b as 6*5=30
Answer : E
Answer: (E) e) 30
Question: The ratio of the ages of Maala and Kala is 4 : 3. The total of their ages is 2.8 decades. The proportion of their ages after 0.8 decades will be [1 Decade = 10 years]
(A) 4:3
(B) 12:11
(C) 7:4
(D) 6:5
(E) 6:7
Rationale: Explanation:
Let, Maala’s age = 4A and Kala’s age = 3A
Then 4A + 3A = 28
A = 4
Maala’s age = 16 years
and Kala’s age = 12 years
Proportion of their ages after 8 is = (16 + 8) : (12 + 8)
= 24 : 20
= 6 : 5 .. Answer: D
Answer: (D) 6:5
Question: It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(A) (2 16 + 1)
(B) (2 16 - 1)
(C) (7 x 2 23)
(D) (2 96 + 1)
(E) None of these
Rationale: Explanation:
Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
ANSWER IS D
Answer: (D) (2 96 + 1)
Question: A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 5?
(A) 2 / 3
(B) 1 / 6
(C) 3 / 3
(D) 4 / 5
(E) 2 / 4
Rationale: Only 6 so, 1 / 6
correct answer B
Answer: (B) 1 / 6
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 12 seconds. Find the length of the faster train?
(A) 270
(B) 288
(C) 266
(D) 120
(E) 126
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 12 sec = 27 * 10 = 270 m.
The length of the faster train = 120 m.
Answer: D
Answer: (D) 120
Question: The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is
(A) 16 cm
(B) 25 cm
(C) 30 cm
(D) 35 cm
(E) 40 cm
Rationale: Explanation:
So by now, you must be knowing this is a question of HCF, right.
H.C.F. of (700 cm, 385 cm, 1295 cm) = 35 cm.
Option D
Answer: (D) 35 cm
Question: What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 7?
(A) 70,592
(B) 64,850
(C) 64,749
(D) 149,700
(E) 156,720
Rationale: Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 7
Seeing the Options After Dividing an Finding the Reminder of 2
My Answer was A
Answer: (A) 70,592
Question: A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 4 km, if the person completes half of the distance by walking and the other half by running?
(A) 0.25
(B) 0.5
(C) 0.75
(D) 1
(E) 1.25
Rationale: time = 2/4 + 2/8 = 6/8 = 0.75 hours
The answer is C.
Answer: (C) 0.75
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
(A) 1/13
(B) 2/13
(C) 1/26
(D) 1/52
(E) 1/67
Rationale: Explanation:
Total number of cases = 52
Favourable cases = 2
Probability = 2/56 = 1/26
Answer: Option C
Answer: (C) 1/26
Question: What is the remainder when the number Q=14^2 * 15^8 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: 14^2 has units digit 6
15^8 has units digit 5
Thus Q=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero
Answer: (A)
Answer: (A) 0
Question: In an electric circuit, three resistors with resistances 2 ohms, 5 ohms and 6 ohms are connected in parallel. In this case, if R is the combined resistance of these three resistors, then the reciprocal of R is equal to the sum of the reciprocals resistors. What is R value?
(A) 13/15 ohms
(B) 15/13 ohms
(C) 5/8 ohms
(D) 3/7 ohms
(E) 45/18 ohms
Rationale: The wording is a bit confusing, though basically we are told that 1/R = 1/2 + 1/5 + 1/6, from which it follows that R=13/15ohms
Option: A
Answer: (A) 13/15 ohms
Question: An amount of Rs.3120 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of A?
(A) 1320
(B) 1196
(C) 1210
(D) 1440
(E) 1050
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of A = 6/13 * 3120 = Rs. 1440
Answer: D
Answer: (D) 1440
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio Q of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
(A) 8:3
(B) 3:2
(C) 4:3
(D) 2:3
(E) 3:8
Rationale: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio Q of Ann's time to Bob's time is 3:2.
Answer: B.
Answer: (B) 3:2
Question: The sum of four consecutive even numbers is 292. What would be the smallest number?
(A) 33
(B) 88
(C) 70
(D) 123
(E) 12
Rationale: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 292 => x = 37
Smallest number is: 2(x - 2) = 70.
Answer: C
Answer: (C) 70
Question: The sum R of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Rn = (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 aswe 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 R 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: A batsman scored 140 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(A) 45(4/11) %
(B) 45 %
(C) 45(5/11) %
(D) 57(1/7) %
(E) None of these
Rationale: Explanation :
Total runs scored = 140
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 140 - 60 = 80
Required % = (80/140) × 100 = 400/7 = 57(1/7)%
Answer : Option D
Answer: (D) 57(1/7) %
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 288
(B) 266
(C) 500
(D) 277
(E) 211
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters.Answer:C
Answer: (C) 500
Question: During a clearance sale, a retailer discounted the original price of its TVs by 20% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?
(A) 40%
(B) 45%
(C) 55%
(D) 60%
(E) 64%
Rationale: VERITAS PREPOFFICIAL SOLUTION:
D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 80% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 80% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 80% sale price. Using fractions, that means they pay: 4/5*(4/5) of the original price, which nets to 0.64 of the original price, or 64%.
E
Answer: (E) 64%
Question: The speed at which a man can row a boat in still water is 9 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 16 seconds
(B) 34 seconds
(C) 14 seconds
(D) 18 seconds
(E) 15 seconds
Rationale: Speed of the boat downstream = 9 + 3 = 12 kmph
= 12 * 5/18 = 10/3 m/s
Hence time taken to cover 60 m = 60*3/10
= 18 seconds.
Answer: D
Answer: (D) 18 seconds
Question: If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?
(A) $33.95
(B) $47.47
(C) $28.40
(D) $60.60
(E) $72.85
Rationale: The tip is 20% of what he paid for lunch. Hence
tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10
Total spent
50.50 + 10.10 = $60.60
correct answer D
Answer: (D) $60.60
Question: A large no. N =1234567891011121314…99899100. What will be the remainder when 1st 100 digits of N is divided by 9?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 8
Rationale: Hence the first 100 digits of N goes like this 1234567891011121314.......5253545
We need to find the sum of the above number to check for divisibility by 9.
From 1 to 50, each of the digits 1 to 4 occurs 14 times, digit 5 occurs 6 times and each of 6 to 9 occurs 5 times
Sum of digits from 1 to 4 = 10
Sum of digits from 6 to 9 = 30
Therefore, sum of digits from 1 to 50 = 10 * 15 + 5 * 6 + 30 * 5 = 330
Sum of digits from 51 to 54 plus a 5 = 5 * 4 + ( 1 + 2 + 3 + 4) + 5 = 20 + 15 = 35
Total sum = 330 + 35 = 365
When 365 is divided by 9, we get 5 as the remainder!
Correct Answer: 5
C
Answer: (C) 5
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
(A) 1/6
(B) 1/2
(C) 1/9
(D) 1/1
(E) 1/5
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then
= 18/36 = 1/2
P(E) = 1 - 1/2 =1/2.
Answer: B
Answer: (B) 1/2
Question: Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 10 machines produce in 6 minutes?
(A) 1344
(B) 4200
(C) 8400
(D) 50400
(E) 67200
Rationale: 8 machines produce 560 in 1 min
8 machines produce 560* 6 in 6 min
10 machine produce 560*6*(10/8) in 6 minutes
560*6*10/8=4200 answer is B.
Answer: (B) 4200
Question: Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.526. If Sanoop returned 3 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts?
(A) 560
(B) 561
(C) 562
(D) 563
(E) 564
Rationale: Total price of 8 t-shirts= 8*526=4208
Total price of 5 t-shirts=5*505=2525
Total price of 3 t-shirts=4208-2525=1683
Average price of 3 t-shirts=1683/3=561
Correct option Answer:B
Answer: (B) 561
Question: If a function f is defined by f(x)= 2x/(x-1) for all non zero numbers x. If f(a) = 4 and f(ab) = 6 then b= ?
(A) 3/2
(B) 1/2
(C) 7/2
(D) 3/4
(E) 1/4
Rationale: Given that f(x) =2x/(x-1) and f(a) = 4, then f(a) =2a/(a-1)=4 ===> 2a = 4a -4 => a =2, then backsolve using the answer choices:
f(ab) = f(2b) = 6
A) 3/2 ===> f(2*3/2) = f(3) = 2*3/(3-1) = 6/ 2 = 3
B) 1/2 ===> f((2*1/2) = f(1) = 2*1/(1-1) = undefined
C) 7/2 ===> f(2*7/2) = f(7) = 2*7/(7-1) = 14/6 = 7/3
D) 3/4 ===> f(2*3/4) = f(3/2) (2*3/2)/(3/2-1) = 3/(1/2) = 6 WINS
E) 1/4 ===> f(2*-1/4) = f(1/2) = (2*1/2)/(1/2-1) = 1/-1/2 = -2
Answer: D
Answer: (D) 3/4
Question: Train X and train Y pass one another traveling in opposite directions. Twenty four minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?
(A) 28
(B) 40
(C) 56
(D) 72
(E) 80
Rationale: Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30
d=100 and t = 24 min i.e 24/60 hr
using RTD table, (2R+30) * 24/60 = 100 ==> R= 110 miles/hr
So the rate of train X is 140 miles/hr (since R+30)
The distance traveled by Train X in 24 min is R*T = 140 * 24/60 = 56 miles (C)
Answer: (C) 56
Question: At a company, the average wage of male employees is $9.97 per hour, and the average wage of female employees is $10.37 per hour. If the average wage of all employees is $10.12 per hour, what is the ratio of the number of male employees to the number of female employees?
(A) 1 to 2
(B) 2 to 3
(C) 3 to 2
(D) 5 to 3
(E) 2 to 1
Rationale: Average hourly wage of male employees = 9.97 $
Average hourly wage of female employees = 10.37 $
Average hourly wage of all employees = 10.12 $
Let number of male employees = m
number of female employees = f
10.12 = (9.97m + 10.37f ) / m+f
=>10.12m + 10.12f = 9.97m + 10.37f
=> .15m = .25f
=> m/f = .25/.15 = 5/3
Answer D
Answer: (D) 5 to 3
Question: If the LCM of two integers X, Y (where Y> X and X>1) is X*Y, then which of the following can not be true?
(A) Both X and Y can be Prime Numbers.
(B) All Prime factors of X must be Prime factors of Y.
(C) Both X and Y can be consecutive integers.
(D) X and Y do not share any Prime factors.
(E) X and Y do not have a common factor
Rationale: If LCM of two numbers X and Y is the product XY then both numbers are Co- prime.
(Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).
Numbers that can be Co-Prime are :
1) Two consecutive natural numbers.
2) Two consecutive odd numbers.
3) Two prime numbers.
4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.
With above four statements it can be concluded that Options A, C, D and E are all true.
Only Option B cannot be true.
Hence answer is B
Answer: (B) All Prime factors of X must be Prime factors of Y.
Question: (3x + 2) (2x - 3) = ax^2 + kx + n . What is the value of a - n + k ?
(A) 5
(B) 7
(C) 9
(D) 10
(E) 11
Rationale: Expanding we have 6x^2 - 9x + 4x -6
6x^2 - 5x - 6
Taking coefficients, a = 6, k= -5, n = -6
Therefore a - n + k = 6 - (-6) - 5 = 12 - 5 = 7
The answer is B.
Answer: (B) 7
Question: If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 3720 , R will receive
(A) 720
(B) 700
(C) 800
(D) 900
(E) None of these
Rationale: Explanation :
Let P's capital = p, Q's capital = q and R's capital = r
Then
4p = 6q = 10r
=> 2p = 3q = 5r
=>q = 2p/3
r = 2p/5
P : Q : R = p : 2p/3 : 2p/5
= 15 : 10 : 6
R's share = 3720 * (6/31) = 120*6 = 720. Answer : Option A
Answer: (A) 720
Question: Two girls move in opposite directions, one from A to B and other from B to A. The girl from A reaches the destination in 16 hrs and girl from B reaches her destination in 25 hrs, after having met. If former's speed is 25 km/hr, what will be the speed of latter?
(A) 10 km/hr
(B) 12 km/hr
(C) 16 km/hr
(D) 20 km/hr
(E) 25 km/hr
Rationale: Hint: If two bodies A and B move from each other's starting point in opposite directions, they reach their destinations after having met, then their speeds Sa & Sb are given by,
Sa	/ Sb = √tb / √ta
where t is the time taken by them to cover the distance.
Sb	(25 x 4)	/ 5 = 20 km/hr
ANSWER IS D
Answer: (D) 20 km/hr
Question: The sub-duplicate ratio of 16:64 is
(A) 4:3
(B) 1:2
(C) 1:3
(D) 1:4
(E) 2:4
Rationale: root(16):root(64)=4:8=2:4
ANSWER:E
Answer: (E) 2:4
Question: In expressing a length of 11.482 km as nearly as possible with the three significant digits, find the percentage error
(A) 0.157%
(B) 0.207%
(C) 0.016%
(D) 0.021%
(E) None of these
Rationale: Explanation:
Error = (11.5 - 11.482) = 0.018
Required percentage =
0.018/ 11.482Ã—100=0.157
Option A
Answer: (A) 0.157%
Question: How can 0.1666 of 600 of 66.67 % can be written?
(A) 66.67
(B) 13.39
(C) 16.67
(D) 18.99
(E) 12.5
Rationale: 0.1666 = 1/6 of 600 = 100 of 66.67% = 100 of 2/3
100 * (2/3) = 66.67 ...... Ans - A
Answer: (A) 66.67
Question: In a fruit bucket total number of fruits is 99. If ratio of apple guava and mango is 17:9:7. Find the number of mangoes?
(A) 24
(B) 30
(C) 16
(D) 21
(E) 33
Rationale: Let the number of apple guava and mangoes are 17x, 9x, 7x
17x+9x+7x = 99
33x = 99
x = 3
Number of mangoes are = 3*7 = 21
Answer : D
Answer: (D) 21
Question: Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -5 then by what factors will the Mean,Variance and Standard Deviation respectively change ?
(A) -5,-5,-5
(B) -5,5,5
(C) 1,1,1
(D) -5,25,5
(E) 5,5,25
Rationale: Mean: If all values are multiplied by -5 then their sum will also be multiplied by -5 so Mean will also get -5
Variance:
Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values
When we multiply all the values by -5 then the difference between the mean and the individual values also gets multiplied by -5 and the square of that difference becomes 25. So, the variance gets multiplied by a factor of 25
SD:
Standard Deviation is the square root of variance so sqrt(25)=5. So SD gets multiplied by a factor of 5.
So, answer will be D.
Answer: (D) -5,25,5
Question: Which of the following equations has a solution in common with x^2 - 2x - 15 = 0?
(A) x^2 - 6x + 9 = 0
(B) x^2 + 2x - 15 = 0
(C) 2x^2 + 9x + 9 = 0
(D) 2x^2 + x - 3 = 0
(E) none of the above
Rationale: Given : x^2 - 2x - 15 => (x+3) (x-5) = 0 => 5 and -3 are the roots..
A. x^2 - 6x + 9 = 0 => (x-3) (x-3)
B. x^2 + 2x - 15 = 0 => (x+5) ( x-3)
C. 2 x^2 + 9x + 9 = 0 => (x+3) ( 2x+3)
D. 2 x^2 + x - 3 = 0 => (x-1) (2x+3).... no eq has same roots as per the parent eq..
Answer: C is correct answer
Answer: (C) 2x^2 + 9x + 9 = 0
Question: A man fell in a 30 meter deep well, in one day he climbs 4 meters up and slips 3 meters down. How many days would it take for him to come out of the well?
(A) 22
(B) 46
(C) 17
(D) 27
(E) 33
Rationale: D
I will take 27 days to come out of that well for that man,
He climbs 4 meter every day and slips 3 meter down that means he climbs 1 meter in total each day, so like this on 26th day he would have climbed 26 meter and on 27th day he will climb 4 meeter again so total 30 meter he will climb in 27 days.
Answer: (D) 27
Question: If a set consists of all positive digits less than or equal to 3 and of the squares of those digits, what is the mode of the set?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 9
Rationale: let set X= {1, 1.5, 2, 2.5, 3}
Set in question consists of even the squares of the digits contained in set X.
Hence required set = { 1, 1, 1.5, 2, 2.25, 2.5, 3, 4, 6.25, 9}
Mode of set= 1
ANSWER:A
Answer: (A) 1
Question: The ratio of the arithmetic mean of two numbers to one of the numbers is 5:8. What is the ratio of the smaller number to the larger number?
(A) 1:8
(B) 1:6
(C) 1:5
(D) 1:4
(E) 1:3
Rationale: For two numbers, the arithmetic mean is the middle of the two numbers.
The ratio of the mean to the larger number is 5:8, thus the smaller number must have a ratio of 2.
The ratio of the smaller number to the larger number is 2:8 = 1:4.
The answer is D.
Answer: (D) 1:4
Question: A scale 6 ft. 8 inches long is divided into 2 equal parts. Find the length of each part.
(A) 20 inches
(B) 77 inches
(C) 66 inches
(D) 97 inches
(E) 40 inches
Rationale: Explanation:
Total length of scale in inches = (6*12) + 8 = 80 inches
Length of each of the 2 parts = 80/2 = 40 inches
ANSWER:E
Answer: (E) 40 inches
Question: 15 litres of mixture contains 20% alcohol and the rest water. If 5litres of water be mixed with it, the percentage of alcohol in the new mixture would be?
(A) 16.67%
(B) 23%
(C) 15%
(D) 19.75%
(E) 21.23%
Rationale: Alcohol in the 15litres of mix. = 20% of 15litres = (20*15/100) = 3litres
water in it = 15-3 = 12litres
new quantity of mix. = 15+5 = 20 litres
Quantity of alcohol in it = 3litres
Percentage of alcohol in new mix. = 3*100/20 = 15%
Answer is C
Answer: (C) 15%
Question: During the first two weeks of January, the total rainfall in Springdale was 20 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January?
(A) 5 inches
(B) 6 inches
(C) 9 inches
(D) 10 inches
(E) 12 inches
Rationale: Total rainfall in 2 weeks = 20 inches.
Assume the rainfall in second week = 1.5x
Rainfall in first week = x
Total rainfall = 2.5x = 20 inches
x = 8 and 1.5x = 12
Rainfall during second week = 12 inches
Option E
Answer: (E) 12 inches
Question: Debbie had 5 1/2 yards of ribbon. She cut it into pieces that were each 1 1/2 yard long. How
many inches long is the leftover piece? Note that the fraction that indicates the leftover piece is a
fraction of a piece, not a fraction of the original amount.
(A) 22 inches
(B) 36 inches
(C) 48 inches
(D) 37 inches
(E) 17 inches
Rationale: 5 1/2 ÷ 1 1/2 = 11/2 x 2/3 = 22/6 =
3 4/6 = 3 2/3 pieces
1 1/2 yds. x 36 in. = 54 in. length of one piece
2/3 x 54 = 36 in. length of left over piece
correct answer B
Answer: (B) 36 inches