Two friends, Rahul and Vikram, are managing a joint bank account. The balance of the account fluctuates each year, and they make decisions based on the relationship between the account balances each year. This year, the difference in their balances follows the equation 2x – y = 12, where x is Rahul’s balance and y is Vikram’s balance.

Question:
Given that 2x – y = 12, which of the following statements must be true for any values of x and y?
1. Both Rahul’s and Vikram’s account balances must always be positive.
2. If Rahul’s balance is positive, then Vikram’s balance must always be negative.
3. If Rahul’s balance is negative, then Vikram’s balance must always be positive.

Select the correct answer based on the statements above.
(a) Statement 1 only
(b) Statement 2 only
(c) Both Statements 1 and 2
(d) Neither Statement 1, 2, nor 3

Question

Two friends, Rahul and Vikram, are managing a joint bank account. The balance of the account fluctuates each year, and they make decisions based on the relationship between the account balances each year. This year, the difference in their balances follows the equation 2x &ndash; y = 12, where x is Rahul&rsquo;s balance and y is Vikram&rsquo;s balance.

Question:
Given that 2x &ndash; y = 12, which of the following statements must be true for any values of x and y?
1. Both Rahul&rsquo;s and Vikram&rsquo;s account balances must always be positive.
2. If Rahul&rsquo;s balance is positive, then Vikram&rsquo;s balance must always be negative.
3. If Rahul&rsquo;s balance is negative, then Vikram&rsquo;s balance must always be positive.

Select the correct answer based on the statements above.
(a) Statement 1 only
(b) Statement 2 only
(c) Both Statements 1 and 2
(d) Neither Statement 1, 2, nor 3

ONLiNE UPSC · Accepted Answer

Statement 1: This is not necessarily true. The equation 2x &ndash; y = 12, does not require both balances to be positive. For example, if Rahul&rsquo;s balance is 1 and Vikram&rsquo;s balance is -10, the equation holds.

Statement 2: This is not necessarily true. If Rahul&rsquo;s balance is positive, Vikram&rsquo;s balance doesn&rsquo;t have to be negative. For example, if Rahul&rsquo;s balance is 10 and Vikram&rsquo;s balance is 8, the equation 2x &ndash; y = 12 holds.

Statement 3: This is not necessarily true, if Rahul&rsquo;s balance is negative, Vikram&rsquo;s balance must be positive to maintain the equation 2x &ndash; y = 12. For example, if Rahul&rsquo;s balance is -1, then 2(&minus;1) &ndash; y = 12 leads to &minus;2 &ndash; y = 12, so Vikram&rsquo;s balance must be y = &minus;14 that is negative, to hold the equation 2x &ndash; y = 12.
So, none of the Statements are correct.
Hence, option d is correct.

Algebra

Linear Equations

Website Link

Test Your Knowledge

Student Resources


M Question 1	⏱ 0
Two friends, Rahul and Vikram, are managing a joint bank account. The balance of the account fluctuates each year, and they make decisions based on the relationship between the account balances each year. This year, the difference in their balances follows the equation 2x – y = 12, where x is Rahul’s balance and y is Vikram’s balance. Question: Given that 2x – y = 12, which of the following statements must be true for any values of x and y? 1. Both Rahul’s and Vikram’s account balances must always be positive. 2. If Rahul’s balance is positive, then Vikram’s balance must always be negative. 3. If Rahul’s balance is negative, then Vikram’s balance must always be positive. Select the correct answer based on the statements above. (a) Statement 1 only (b) Statement 2 only (c) Both Statements 1 and 2 (d) Neither Statement 1, 2, nor 3

Algebra

Linear Equations

Demo Session!

Demo Session Fill out the form below and hit the Join Session button to proceed.

Are you genious?

Demo Session
Fill out the form below and hit the Join Session button to proceed.