Elementary Algebra · Basic Numeracy · UPSC Civil Service

In the expression $5 * 4 * 3 * 2 * 1$, * is chosen from $+$, $-$, $\times$ each at most two times. What is the smallest non-negative value of the expression?

A father said to his son, "n years back I was as old as you are now. My present age is four times your age n years back". If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?

Let $p, q, r$ and $s$ be distinct positive integers. Let $p, q$ be odd and $r, s$ be even. Consider the following statements :

1. $(p - r) (qs)$ is even.

2. $(q - s) q^2 s$ is even.

3. $(q + r)^2 (p + s)$ is odd.

Which of the statements given above are correct?

If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?

The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples.

Consider the following statements:

1. The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples.

2. The total cost of one orange and one mango is equal to the cost of one apple.

Which of the statements given above is/are correct?

Let $p$ and $q$ be positive integers satisfying $p < q$ and $p + q = k$. What is the smallest value of $k$ that does not determine $p$ and $q$ uniquely?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:

Is $(x + y)$ an integer?

Statement-I:

$ (2x + y) $ is an integer.

Statement-II:

$ (x + 2y) $ is an integer.

Which one of the following is correct in respect of the above Question and the Statements?

In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q - S = 2S and T = R + S + 3, then what is the value of P + R - T?

Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following :

1. p + q + r - s - t is definitely even.

2. 2p + q + 2r - 2s + t is definitely odd.

Which of the above statements is/are correct?

Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements :

1. The number of possible values of p is 5.

2. The number of possible values of q is 6.

Which of the above statements is/are correct?

Question: Is (p + q - r) greater than (p - q + r), where p, q and r are integers ?

Statement-1: (p - q) is positive.

Statement-2: (p - r) is negative.

Which one of the following is correct in respect of the above Question and the Statements?

X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements:

1. 8 years ago, the age of X was five times the age of Y.

2. After 14 years, the age of X would be two times the age of Y.

Which of the above statements is/are correct?