Quantitative Reasoning

Number System

Hard

Match the LIST-I with LIST-II

LIST-I (For given Euclidean Algorithm, a = bq + r, Where a & b are real) LIST-II Values of q and r
A. a = -112, b = -7 I. q = -13, r = 1
B. a = 118, b = -9 II. q = 14, r = 3
C. a = -109, b = 6 III. q = -19, r = 5
D. a = 115, b = 8 IV. q = 16, r = 0

Choose the correct answer from the options given below:

LIST-I (For given Euclidean Algorithm, a = bq + r, Where a & b are real)	LIST-II Values of q and r
A. a = -112, b = -7	I. q = -13, r = 1
B. a = 118, b = -9	II. q = 14, r = 3
C. a = -109, b = 6	III. q = -19, r = 5
D. a = 115, b = 8	IV. q = 16, r = 0

A-III, B-I, C-IV, D-II

A-III, B-II, C-IV, D-I

A-IV, B-I, C-III, D-II

A-IV, B-II, C-III, D-I

✅ Correct Option: 3

Use $a = bq + r$ with $0 \le r < |b|$ .

A: $-112 = (-7)(16) + 0$ , so $q=16$ , $r=0$ (IV).

B: $118 = (-9)(-13) + 1$ , so $q=-13$ , $r=1$ (I).

C: $-109 = 6(-19) + 5$ , so $q=-19$ , $r=5$ (III).

D: $115 = 8(14) + 3$ , so $q=14$ , $r=3$ (II).

2024

The difference of the greatest and the smallest of the fractions $\frac{1}{2}$ , $\frac{8}{11}$ , $\frac{7}{8}$ , $\frac{7}{9}$ , $\frac{5}{6}$ is:

2026: 12 May Shift 2

Select the missing number from given options.

12	7	95
14	8	132
16	9	?

2022: 20 Aug Shift 1

$296 \times 296 - 204 \times 204 = ?$

2022: 20 Aug Shift 1

The greatest length of the scale that can measure exactly 20 cm, 90 cm, 1 m 25 cm and 1 m 30 cm length is:

2026: 25 May Shift 2

In a number system $\sqrt{3}$ is:

2022: 20 Aug Shift 1

$-224 + (-314) \times 9 = ?$

Solution