Quantitative Reasoning

Linear Equation

Medium

If $2^{(x+y)} = 64$ and $128^{(x-y)} = 2$ , then what is the value of x?

41/14

43/14

21/7

22/7

✅ Correct Option: 2

Converting to base 2:

$64 = 2^6$

$128 = 2^7$

$2 = 2^1$

Rewriting the first equation:

$2^{(x+y)} = 64$

$2^{(x+y)} = 2^6$

Since the bases are equal, the exponents must be equal:

$x + y = 6$ ... (Equation 1)

Rewriting the second equation:

$128^{(x-y)} = 2$

$(2^7)^{(x-y)} = 2^1$

$2^{7(x-y)} = 2^1$

Since the bases are equal, the exponents must be equal:

$7(x - y) = 1$

$x - y = \dfrac{1}{7}$ ... (Equation 2)

Solving the system of equations by adding Equation 1 and Equation 2:

$x + y + x - y = 6 + \dfrac{1}{7}$

$2x = 6 + \dfrac{1}{7}$

$2x = \dfrac{42}{7} + \dfrac{1}{7}$

$2x = \dfrac{43}{7}$

$x = \dfrac{43}{14}$

Therefore, the value of $x = \dfrac{43}{14}$ .

2026: 22 May Shift 2

Which of the following pair of linear equations has no solution?

(A) $2x + 3y - 1 = 0$ and $4x + 6y - 4 = 0$

(B) $x - 2y = 0$ and $3x + 4y - 20 = 0$

(D) $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$

Choose the correct answer from the options given below:

2026: 26 May Shift 1

System of linear equations 2x + 4y +1 = 0 and 4x + 8y + 2 = 0 has/ have :

2026: 21 May Shift 1

Which one of the following pairs of linear equations is/are inconsistent?

(A) 7 x + 2 y = 3, 14 x + 4 y = 5

(B) 2 x - 3 y = 7, 4 x - 6 y = 12

(D) 2 x - 2 y = 2, 4 x - 4 y = 5

Choose the correct answer from the options given below:

2026: 21 May Shift 2

Which one of the following pair of linear equations is/are inconsistent?

A. x − y = 6, x − y = 13

B. 2x − 10y = 15, 7x − 35y =25

C. x − y = 15, 5x - 5y = 75

D. 7x − 9y − 3 = 0, 14x − 18y − 8 = 0

Choose the correct answer from the options given below:

2025: 29 May Shift 2

The system of equations $4x + 14y = 18$ and $6x + 21y = 33$ has

2026: 18 May Shift 2

Which of the following pairs of linear equations is/are consistent?

A. $x + y = 5, 2x + 2y = 10$

B. $2x + y - 6 = 0, 4x - 2y - 4 = 0$

C. $x - y = 8, 3x - 3y = 16$

D. $x - 2y = 0, 3x + 4y - 20 = 0$

Choose the correct answer from the options given below:

If 2(x+y)=642^{(x+y)} = 642(x+y)=64 and 128(x−y)=2128^{(x-y)} = 2128(x−y)=2, then what is the value of x?

Solution

Related questions:

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CUET General Test Past Year Questions (Topic-Wise)

If $2^{(x+y)} = 64$ and $128^{(x-y)} = 2$ , then what is the value of x?