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  1. Subjects ›
  2. DAT Quantitative Reasoning ›
  3. Question of the Day

DAT Quantitative Reasoning Question of the Day

DAT Quantitative Reasoning Question of the Day

Answer today's DAT Quantitative Reasoning question, reveal the full explanation, then keep the streak going with a new question every day.

If 2x+1+2x+2+2x+3=1122^{x+1} + 2^{x+2} + 2^{x+3} = 1122x+1+2x+2+2x+3=112, what is the value of xxx?

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Question of the Day

If 2x+1+2x+2+2x+3=1122^{x+1} + 2^{x+2} + 2^{x+3} = 1122x+1+2x+2+2x+3=112, what is the value of xxx?

  1. x=1x = 1x=1
  2. x=2x = 2x=2
  3. x=3x = 3x=3 (correct answer)
  4. x=4x = 4x=4
  5. x=5x = 5x=5

Explanation: Factor out 2x2^x2x from the left side: 2x+1+2x+2+2x+3=2x⋅21+2x⋅22+2x⋅23=2x(2+4+8)=2x⋅14=14⋅2x2^{x+1} + 2^{x+2} + 2^{x+3} = 2^x \cdot 2^1 + 2^x \cdot 2^2 + 2^x \cdot 2^3 = 2^x(2 + 4 + 8) = 2^x \cdot 14 = 14 \cdot 2^x2x+1+2x+2+2x+3=2x⋅21+2x⋅22+2x⋅23=2x(2+4+8)=2x⋅14=14⋅2x. So the equation becomes 14⋅2x=11214 \cdot 2^x = 11214⋅2x=112. Dividing both sides by 14: 2x=82^x = 82x=8. Since 8=238 = 2^38=23, we have 2x=232^x = 2^32x=23, which means x=3x = 3x=3. Verification: 24+25+26=16+32+64=1122^4 + 2^5 + 2^6 = 16 + 32 + 64 = 11224+25+26=16+32+64=112 ✓.