Free Algebra MCQs with Answers

• A. B4
• B. E25
• C. D16
• D. I91
• E. F36

Explanation: The number after each letter should be the square of its alphabet position: B is 2 and 2² = 4, E is 5 and 5² = 25, and F is 6 and 6² = 36.

• A. 1P6
• B. 2Y4
• C. 2T0
• D. 1R8
• E. 1M3

Explanation: The digits on either side of each letter represent the first and last digits of its alphabet position: P is 16, T is 20, R is 18, and M is…

• A. YCAEC
• B. KOMQO
• C. PTRUT
• D. GKIMK
• E. DHFJH

Explanation: In the valid groups, the alphabet positions follow the changes +4, -2, +4, -2, using alphabet positions such as G=7, K=11, I=9, M=13…

• A. OQMS
• B. UAWY
• C. NPLR
• D. BDZF
• E. FHDJ

Explanation: Most groups have alphabet-position changes of +2, -4, +6: OQMS gives 15, 17, 13, 19, and NPLR gives 14, 16, 12, 18.

• A. KMNL
• B. PRSQ
• C. VWYZ
• D. JLMK
• E. WYZX

Explanation: KMNL, PRSQ, JLMK and WYZX each follow alphabet-position changes of +2, +1, -2.

• A. GFI
• B. QOR
• C. LKN
• D. YXA
• E. TSV

Explanation: The first letter is followed by the previous letter and then the letter three positions after the first: GFI gives 7, 6, 9, and LKN gives…

• A. PMS
• B. ROU
• C. GDJ
• D. KIM
• E. EBH

Explanation: In PMS, ROU, GDJ and EBH, the second letter is three positions before the first and the third is six positions after it.

• A. A
• B. R
• C. E
• D. I
• E. O

Explanation: A, E, I and O are vowels, whereas R is a consonant. Therefore R is the only letter that does not belong.

• A. 104
• B. 110
• C. 108
• D. 112
• E. 116Preparing For College Admissions Tests

Explanation: The numbers 104, 108, 112 and 116 are all divisible by 4: 104 ÷ 4 = 26, 108 ÷ 4 = 27, 112 ÷ 4 = 28 and 116 ÷ 4 = 29.

• A. 11
• B. 28
• C. 327
• D. 416
• E. 5125Islamic Studies Quiz

Explanation: The intended pattern is a number followed by its square: 2 followed by 8 is not consistent with this wording, but the displayed forms…

• A. 525
• B. 39
• C. 24
• D. 426
• E. 636

Explanation: Each valid number places a digit beside its square: 5² = 25 gives 525, 3² = 9 gives 39, 2² = 4 gives 24, and 6² = 36 gives 636.

• A. 358
• B. 246
• C. 134
• D. 862

Explanation: In 358, 3 + 5 = 8; in 246, 2 + 4 = 6; and in 134, 1 + 3 = 4. In 862, 8 + 6 = 14, not 2, so it breaks the digit-sum pattern.

• A. 508
• B. 328
• C. 608
• D. 148

Explanation: The digit sums are 5 + 0 + 8 = 13, 3 + 2 + 8 = 13, 6 + 0 + 8 = 14, and 1 + 4 + 8 = 13.

• A. 30
• B. 630
• C. 10
• D. 520

Explanation: 630 is the only option divisible by 9 because its digit sum is 6 + 3 + 0 = 9, whereas the digit sums of 30, 10, and 520 are 3, 1, and 7.

• A. 20
• B. 42
• C. 58
• D. 72

Explanation: Three numbers are products of consecutive even numbers: 20 = 4 x 5, 42 = 6 x 7, and 72 = 8 x 9.

• A. 4422
• B. 2442
• C. 4242
• D. 2244

Explanation: 4422, 2442, and 2244 each contain a pair of identical adjacent digits, namely 44 or 22.

• A. 30
• B. 27
• C. 36
• D. 45

Explanation: 27, 36, and 45 are all multiples of 9: 27 = 9 x 3, 36 = 9 x 4, and 45 = 9 x 5.

• A. 35
• B. 48
• C. 75
• D. 84

Explanation: 48, 75, and 84 are divisible by 3 because their digit sums are 12, 12, and 12 respectively.

• A. 343
• B. 121
• C. 1331
• D. 2197Downloading Digital Educational Resources

Explanation: 343 = 7 x 7 x 7, 1331 = 11 x 11 x 11, and 2197 = 13 x 13 x 13, so these are perfect cubes.

• A. 41
• B. 43
• C. 53
• D. 57

Explanation: 41, 43, and 53 are prime numbers because each has no divisor other than 1 and itself. 57 is composite because 57 = 3 x 19.