Secret Operator

A secret operator combines two numbers by an unknown rule. Work out the rule from the examples, then apply it.

🎯 Try it yourself

Tap an answer. You'll see if it's right, and why. Easy ones come first.

1. Q1Medium

   If 3 ◆ 2 = 3 and 7 ◆ 4 = 21, find 3 ◆ 2.

   1. A7
   2. B3
   3. C1
   4. D8
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   Answer: B. 3

   💡 a ◆ b = a × b − a, so 3 ◆ 2 = 3.

2. Q2Medium

   If 8 @ 3 = 32 and 4 @ 3 = 16, find 3 @ 2.

   1. A11
   2. B15
   3. C25
   4. D9
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   Answer: D. 9

   💡 a @ b = a × b + a, so 3 @ 2 = 9.

3. Q3Medium

   If 3 # 2 = 8 and 8 # 7 = 23, find 4 # 2.

   1. A8
   2. B10
   3. C14
   4. D36
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   Answer: B. 10

   💡 a # b = 2a + b, so 4 # 2 = 10.

4. Q4Medium

   If 9 ★ 7 = 54 and 4 ★ 2 = 4, find 4 ★ 3.

   1. A28
   2. B8
   3. C1
   4. D7
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   Answer: B. 8

   💡 a ★ b = a × b − a, so 4 ★ 3 = 8.

5. Q5Hard

   If 8 ★ 5 = 39 and 11 ★ 9 = 40, find 8 ★ 2.

   1. A60
   2. B24
   3. C18
   4. D8
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   Answer: A. 60

   💡 a ★ b = a² − b², so 8 ★ 2 = 60.

6. Q6Hard

   If 7 ▲ 2 = 53 and 11 ▲ 3 = 130, find 8 ▲ 2.

   1. A80
   2. B100
   3. C68
   4. D88
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   Answer: C. 68

   💡 a ▲ b = a² + b², so 8 ▲ 2 = 68.

7. Q7Hard

   If 10 # 9 = 1 and 8 # 7 = 1, find 8 # 7.

   1. A0
   2. B1
   3. C225
   4. D63
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   Answer: B. 1

   💡 a # b = (a − b)², so 8 # 7 = 1.

8. Q8Hard

   If 5 ◆ 2 = 49 and 4 ◆ 2 = 36, find 8 ◆ 2.

   1. A100
   2. B24
   3. C36
   4. D109
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   Answer: A. 100

   💡 a ◆ b = (a + b)², so 8 ◆ 2 = 100.