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GMAT - Data Sufficiency - Algebra

If x = 2t and y = t/3, what is the value of x^2 – y^2? (more)

If x = 2t and y = t/3, what is the value of x^2 – y^2?

(1) t^2 – 3 = 6
(2) t^3 = −27

Given:

x = 2t and y = t/3

x2 - y2 = (2t)2 - (t/3)2 = 4t2 - t2/9 ... required value

Statement 1:

t2 - 3 = 6

t2 = 9

required value = 4t2 - t2 / 9 = 4*9 - 9/9 = 36 - 1 = 35

sufficient

Statement 2

t3 = - 27

t = - 3 (only Real Value)

t2 = 9

Required value = 35 (same as statement 1)

Sufficient

 

 

Is rst = 1 ? (more)

Is rst = 1 ?

(1) rs = 1
(2) st = 1

Statement 1:

rs = 1

doesn't say anything about t. Insufficient

Statement 2:

st = 1

doesn't say anything about r. Insufficient

 

Combined:

rs= 1

st = 1

Example to  prove insufficiency, r = 1/2, s = 2, t = 1/2

it satisfies both the statements but rst = 1/2

so E.

 

If n + k = m, what is the value of k ? (more)

If n k = m, what is the value of k ?

(1) n = 10
(2) m 10 = n

(1) n = 10

given n + k = m

=> 10 + k = m

=> k = m - 10

k is dependent on the value of m

Insufficient

(2) m + 10 = n

given n + k = m

adding 10 to both sides

n + k + 10 = m + 10

since m + 10 = n

n + k + 10 = n

k = -10

Sufficient

If x is an integer, is x|x|<2^x ? (more)

If x is an integer, is x|x|<2x ?

(1) x < 0
(2) x = -10

Statament 1:

x < 0

also we know |x| > 0

since positive x negative = negative

x |x| < 0 ... 1

also,

2x for real x is always positive

i.e. 2x > 0 ...2

from 1 and 1

x |x| < 2x

Sufficient

Statement 2:

x = -10

since x < 0 we can invoke statement 1 and say statement 2 is also sufficient