CAT TUTORIALS (Win vote of thanks and a token of appreciation )

birendra.trivedi

birendra.trivedi

Birendra Trivedi
hi GUYS this is a forum where i gonna come out with the chapters which are required to be studies if you are preapring for CAT.


here any doubt on any questions you can place your questions and we will try to find the solutions to it .

so put up your questions and any one who answeres the question or solves the doubt of the aspirants will win a a vote of thanks and appreciation from this forum . so guys are you all ready to play question answere round
 

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here comes my first question (CAT Preparation)

Question

If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?


121
3267
363
33


pls tell me the answere


any one out there
 
Why dont you team up with tribhu who has started initiative like GET 10 WORDS DAILY ON UR MOBILE FR FREE

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hey Cat guys i dont think guys you all are energetic .you should be a complete hunters as IIM's guys are and that what makes them have edge over others.


i am giving some cat question, i have formed some maths question do practise and if you all have any question do let me know i will help you ok all though i am not an expert but ya i can say together we gonna solve it ok


come on cat guys wake up from the sleep and get ready for preparing for cat.

here comes the question




</SPAN>Question 1: If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?
</SPAN>
Question 2: Find the remainder when the polynomial x4 - 3x2 + 7x - 10 is divided by x - 2.
​
  1. Question 3:If one of the roots of the quadratic equation 2x2 - 7x + q = 0 is 3, then find the other root.



    Question 4:A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and whatisthereservationcharge?



    Question 5:If p and q are the roots of the equation x2 - bx + c = 0, then what is the equation if the roots are (pq + p + q) and (pq - p - q)?
    ​
    Question 6:If (x + 2) 2 = 9 and (y + 3) 2 = 25, then the maximum value of x / y is.



    Question 7:For what values of 'm' is y = 0, if y = x2 + (2m + 1)x + m2 - 1? X is a real number.





  1. Question 8 - If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of 'a'?
    Question9 -Find the greatest number of five digits, which is exactly divisible by 7, 10, 15, 21 and 28.



    Question10-Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?



    Question 11-Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?



    Question 12 -When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?



    Question 13:The sum of the first 100 numbers, 1 to 100 is divisible by



    Question 14 -How many different factors are there for the number 48, excluding 1 and 48?



    Question 15- 1025 - 7 is divisible by​

  2. Question 16-Find the G.C.D of 12x2y3z2, 18x3y2z4, and 24xy4z3​

  3. Question 17 -What is the value of M and N respectively? If M39048458N is divisible by 8 & 11; Where M & N are single digit integers?


    ​
 
I was able to solve some of the questions. here are the answers

4. First class fare is 210 and Reservation price is 6
8. 363
9. The number is 99960
10. 1590
12. 7
14. 8
16. 6xy2z2
17. M is 6 and N is 4




In question nos 11, 13, 15..options are missing..can u post them.
Click to expand...

plz post the answers for remaining ?s
 
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i am extremely sorry for forgetting to post the options for 11,13,15.

ya sure i am posting the options for the following questions
 
11Question:
Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

(1) (x-z)2 y is even
(2) (x-z)y2 is odd
(3) (x-z)y is odd
(4) (x-y)2z is even


13Question
The sum of the first 100 numbers, 1 to 100 is divisible by

(1) 2, 4 and 8
(2) 2 and 4
(3) 2 only
(4) None of these



15Question:
1025 - 7 is divisible by
1.2
2.3
3.9
4.Both (2) and (3)






good all the answeres you have answered are absolutely correct.


i appreciate you for your dedication and the interest that you have shown in solving this CAT Sums .

can you comment on this thread in a true manner how is it an what more should we can do so that more CAT Aspirants get benifitted .and hey i have thanked you also as my thread has a rule that i will thank all those who atleast attempts those questions .
 
1) Question
If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?
1.-22.5
2.16
3.-10.5
4.-17.5
Correct Answer is -17.5. Correct Choice is (4)

Explanatory Answer

We know that the product of the roots of a quadratic equation ax2 + bx + c = 0 is

In the given equation, x2 + mx + 24 = 0, the product of the roots = = 24.
The question states that one of the roots of this equation = 1.5.
If x1 and x2 are the roots of the given quadratic equation and let x1 = 1.5.
Therefore, x2 == 16.
In the given equation, m is the co-efficient of the x term.
We know that the sum of the roots of the quadratic equation ax2 + bx + c = 0 is = -m
Sum of the roots = 16 + 1. 5 = 17 = -17.5.
Therefore, the value of m = -17.5
 
2)Question
Find the remainder when the polynomial x4 - 3x2 + 7x - 10 is divided by x - 2

(1) 8
(2) -20
(3) 18
(4) 0
Correct Choice is (1) and Correct Answer is 8

Explanatory Answer

By remainder theorem: If a polynomial in one variable 'x' is divided by (x - a), where 'a' is any real number, then the remainder is the value of the polynomial at x = a.

Therefore, remainder = (2)4 - 3(2)2 + 7(2) - 10 = 8
 
3)Question
If one of the roots of the quadratic equation 2x2 - 7x + q = 0 is 3, find the other root

(1) -3
(2) -1/2
(3) 1/2
(4) 1/4

Correct Choice is (3) and Correct Answer is 1/2

Explanatory Answer

Substituting x = 3 in the given equation we get
2(32) - 7 (3) + q = 0. Therefore, q = 3

Now, the given equation becomes 2x2 - 7x + 3 = 0

By solving this we get (x - 3) (2x - 1) = 0
i.e., x = 3 & 1/2. The second root is 1/2.
 
4)Question
A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge?
1.Rs. 105 and Rs. 6
2.Rs. 216 and Rs. 12
3.Rs. 210 and Rs. 12
4.Rs. 210 and Rs. 6
Correct Answer is Rs. 210 and Rs. 6. Correct Choice is (4)

Explanatory Answer

Let half of the full basic fare be Rs. X.
Therefore, full basic fare is Rs. 2X.

Let the reservation charge be Rs. Y per ticket.
Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge)
2X + Y = 216*** --- (1)

The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y.
Hence, 3X + 2Y = 327*** --- (2)

Solving (1) and (2) we get,
X = 105 and Y = 6

Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6
 
5) If p and q are the roots of the equation x2 - bx + c = 0, then what is the equation if the roots are (pq + p + q) and (pq - p - q)?

(1) x2 - 2cx + (c2 - b2) = 0
(2) x2 - 2bx + (b2 + c2) = 0
(3) Bcx2 - 2(b+c)x + c2 = 0
(4) x2 + 2bx - (c2 - b2) = 0

Correct Choice is (1). Correct Answer is x2 - 2cx + (c2 - b2) = 0

Explanatory Answer

In the given quadratic equation x2 - bx + c = 0,
The sum of the roots p + q = b --- (1)
And the product of the roots pq = c --- (2)

We have to formulate a quadratic equation whose roots are (pq + p + q) and (pq - p -q).

The sum of the two roots = pq + p +q + pq - p - q = 2pq
But from eqn (2), we know that pq = c
Therefore, the sum of the roots = 2c

The product of the roots = (pq + p + q)(pq - p - q)= (pq)2 - (p+q)2
From equation (1) and (2), we know that pq = c and p + q = b
Therefore, the product of the roots = c2 - b2

We know the sum of the roots and the product of the roots.
Therefore, the quadratic equation is x2 - (sum of the roots)x + product of the roots =

=> x2 - 2cx + c2 - b2 = 0
 
6)Question
If (x + 2) 2 = 9 and (y + 3) 2 = 25, then the maximum value of x / y is

(1) 1 / 2
(2) 5 / 2
(3) 5 / 8
(4) 1 / 8

Correct Answer is 5 / 8. Correct Choice is (3)

Explanatory Answer

(x + 2) 2 = 9
=> x + 2 = ± 3
=> x = 1 or -5
and (y + 3) 2 = 25
=> y + 3 = ± 5
=> y = 2 or -8
Therefore, maximum value of x / y = -5 / -8 = 5 / 8.
 
7)Question
For what values of 'm' is y = 0, if y = x2 + (2m + 1)x + m2 – 1? x is a real number.

(1) m -2
(2) m < 0
(3) m = 0
(4) m -1.25

Correct Answer is m -1.25 . Correct Choice is (4)

Explanatory Answer


When x is real, then the discriminant of a quadratic equation (ax2 + bx + c = 0) 0.
i.e. D = b2 - 4ac 0

In this case, (2m + 1)2 4(m2 - 1)
4m2 + 4m + 1 4(m2 - 1)
Solving for m, we get m - 1.25
 
8)Question

If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?
1.121
2.3267
3.363
4.33
Correct choice (3). Correct Answer - (363)

Explanatory Answers


112 is a factor of the given number. The number does not have a power or multiple of 11 as its factor. Hence, "a" should include 112

33 is a factor of the given number. 62 is a part of the number. 62 has 32 in it. Therefore, if 33 has to be a factor of the given number a * 43 * 62 * 1311, then we will need at least another 3.

Therefore, if "a" should be at least 112 * 3 = 363 if the given number has to have 112 and 33 as its factors.
 
9)Question
Find the greatest number of five digits, which is exactly divisible by 7, 10, 15, 21 and 28.

(1) 99840
(2) 99900
(3) 99960
(4) 99990

Correct Choice is (3) and the correct answer is 99960

Explanatory Answers

The number should be exactly divisible by 15 (3, 5), 21 (3, 7), 28 (4, 7).
Hence, it is enough to check the divisibility for 3, 4, 5 and 7.

99960 is the only number which satisfies the given condition.
 
10)Question
Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?

(1) 1050
(2) 540
(3) 1440
(4) 1590

Correct choice is (4) and Correct Answer is 1590

Explanatory Answers

Let the number that Anita wanted to multiply be 'X'.
She was expected to find the value of 35X.
Instead, she found the value of 53X.

The difference between the value that she got (53X) and what she was expected to get (35X), according to the question, is 540.

i.e., 53X - 35X = 540
or (53 - 35) * X = 540
X = 30

Therefore, new product = 53 * 30 = 1590
 
11)Question
Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

(1) (x-z)2 y is even
(2) (x-z)y2 is odd
(3) (x-z)y is odd
(4) (x-y)2z is even

Correct Choice is (1) and Correct Answer is (x-z)2 y is even

Explanatory Answer

x and y are odd and positive and z is even and positive

(x - z)2 y is even cannot true

x - z is odd and y is odd
Therefore, (x - z)2 will be odd and (x - z)2 y will be odd
 
12)Question
When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?

(1) 10
(2) 7
(3) 192
(4) None of these

Correct Choice is (2) and Correct Answer is 7

Explanatory Answer

Let the number be 'a'.

When 'a' is divided by 36, let the quotient be 'q' and we know the remainder is 19

i.e., and remainder is 19

or a = 36q + 19

when a is divided by 12, we get

or

36q is perfectly divided by 12

Therefore, remainder = 7
 
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