# Data Sufficiency - Vikas Saini - Part 2

• A ) Statement I alone is sufficient.
B ) Statement II alone is sufficient.
C ) Both statement taken together are sufficient to answer this question.
D ) Each statement alone is sufficient.
E ) Both statements together are not sufficient.

Q1. Is X = 3Y ?
I. X^2 – 9Y^2 = 0.
II. (X – 3Y)^2 = 0.

Solution :-
From statement I, X^2 = 9Y^2
X = 3Y / -3Y
Not Sufficient.

From statement II, X – 3Y = 0.
X = 3Y
Sufficient.

Hence B.

Q2. Line xy is of length 8 cm and point z divides line xy. What is the length of xz ?
I. length of yz is 5 cm.
II. point z divides line xy externally.

Solution :-
From statement I, we can’t say about division that it’s external or internal.
From statement II, it’s given z divides line externally.
If both statements are taken together, length of xz can be find.

Hence C.

Q3. Is x^2 + y^2 > 100 ?
I. 2xy < 100.
II. (x + y)^2 > 200.

Solution :-
From statement I, 2xy < 100.
A.M. > G.M.
X^2 + y^2 / 2 > root (x^2.y^2)
X^2 + y^2 > 2xy.
By this statement either x^2 + y^2 < 100 or x^2 + y^2 > 100.
Not sufficient.

From statement II,
(x + y )^2 > 200.
X^2 + y^2 + 2xy > 200.
Therefore, x^2 + y^2 > 100 ( x^2 + y^2 > 2xy )
Sufficient.

Hence B.

Q4. X & y are positive integers such that x = 8y + 12, what is the greatest common divisor of x & y ?
I. x = 12 u, where u is an integer.
II. y = 12 z, where z is an integer.

Solution :-
From statement I, 12y = 8y + 12.
Can’t speculate about value of y.
Not sufficient.
From statement II, x = 8(12 z) + 12.
x = 12(8z + 1).
Sufficient.

Hence B.

Q5 . what is the value of a^3 + b^3 + 2.a^2.b^2 ?
I. a/b = 2.
II. b = 5.

Solution :-
From statement I alone not sufficient.
From statemnt II also alone not sufficient.

By taken together above both statements.
b = 5, a= 10.
Now value can be easily find.

Hence C.

Q6. If a,b,c are odd numbers and 1 < a < b < c, then what is the value of b ?
I. c < 9.
II. a < 5.

Solution : -
From statement I, 1 < a < b < c < 9
Only possibility 1 < 3 < 5 < 7 < 9.
Sufficient.

From statement II, a = 3 only.
Therefore 1 < 3 < 5 < 7
Sufficient.

Hence D.

Q7. Is the positive integer N a perfect square?
(1) The number of distinct factors of N is even.
(2) The sum of all distinct factors of N is even.

Solution :-
We know, to be a perfect square for any integer, it’s no of factors has to be odd.
It’s reverse is also true.

From statement I, no of distinct factors of N is even.
Hence it can’t be a perfect square.
Sufficient.

From statement II,
Let N = a^k x b^k.
odd + even is not equal to even.
Hence N can’t be perfect square.
Sufficient.

Hence D.

Q8. If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?
(1) The range of the n integers is 14
(2) The greatest of the n integers is 17.

Solution :-
x1 + x2 / 2 = 10.
X1 + Xn = 20.
X1 = ?

From statement I, Xn = X1 + 14.
X1 + X1 + 14 / 2 = 10.
2 X1 = 6.
X1 = 3.

From statement II, Xn = 17.
X1 + Xn / 2 = 10.
X1 + 17 / 2 = 10.
X1 = 3.

Hence D.

Q9. If n is an integer greater than 1, is 3^n - 2^n divisible by 35?
(1) n is divisible by 15.
(2) n is divisible by 18.

Solution :-
From statement I, n = 15 k.
3^(15k) – 2^(15k) mod 35
27^5k – 8^5k mod 35
We know (a^n – b^n) mod (a+b) = 0.
27^5k – 8^5k mod (8+27) = 0.
Sufficient.

From statement II, n = 18k.
3^18k – 2^18k mod 35
27^6k – 8^6k mod 35 = 0.
Sufficient.

Hence D.

Q10. If x is a positive integer,is x prime ?
I. x^5 has exactly six distinct natural factors.
II. x^2 -10x+21 = 0.

Solution :-
We know if N = a^k
And no of factors = (k+1)
Then x is a prime numeber.
From statement I, x is a prime number.
Sufficient.

From statement II, x^2 – 10x +21 = 0.
X = 3,7.
Then x is a prime number.
Sufficient.

Hence D.

Q11. If a and b are both positive, what is the value of b root(a).
I. ab = 25.
II. b^2 . a = 80.

Solution :-
From statement I it’s obvious that it is insufficient.
From statement II, b^2 . a = 80.
b. root (a)= root (80).
Sufficient.

Hence B.

Q.12. How many books are on the bookshelf ?
I. The bookshelf is 12 feet long.
II. The average weight of each book is 1.2 pounds.

Solution :-
From statement I, we know how long bookshelf is, but not given width of each book.
Therefore it’s insufficient.
From statement II, it’s given only weight of each book. It is also not sufficient.

Hence E.

• Q4. X & y are positive integers such that x = 8y + 12, what is the greatest common divisor of x & y ?I. x = 12 u, where u is an integer.II. y = 12 z, where z is an integer.

why is statement 1 not sufficient?
we come to conclusion y = 3(u-1) similar to x = 12(8z + 1)

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