IPMAT Indore 2026 · Quantitative Ability · Question 27

IPMAT Indore 2026 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.

Averages, Mixture and AlligationArithmeticMultiple choiceMedium
The possible values of x in the set \{1,5,13\} for which the mean of eight observations 5,\,8,\,3x+2,\,15,\,27,\,29,\,36,\,5x-2 equals their median are
  1. A
    only 13
  2. B
    5 and 13
  3. C
    only 5
  4. D
    only 1
Pick an option, then check.
Answer & solution

Answer: Option B

With only three candidates, test each.

Step 1 — the mean, in general. The fixed numbers 5,8,15,27,29,36 sum to 120, and the two variable ones add \left( 3x+2 \right)+\left( 5x-2 \right)=8x:

\text{Mean}=\frac{120+8x}{8}=15+x

A pleasingly simple result — the mean is just 15+x.

Step 2 — test x=1. Observations: 5,8,5,15,27,29,36,3. Sorted: 3,5,5,8,15,27,29,36.

\text{Median}=\frac{8+15}{2}=11.5, \text{Mean}=16 ✗

Step 3 — test x=5. Observations: 5,8,17,15,27,29,36,23. Sorted: 5,8,15,17,23,27,29,36.

\text{Median}=\frac{17+23}{2}=20, \text{Mean}=20 ✓

Step 4 — test x=13. Observations: 5,8,41,15,27,29,36,63. Sorted: 5,8,15,27,29,36,41,63.

\text{Median}=\frac{27+29}{2}=28, \text{Mean}=28 ✓

Answer: Option 2 — 5 and 13

Shortcut. Derive the mean once as 15+x — then each test is just “sort eight numbers and average the middle two”. Since two options claim “only”, finding a second success immediately settles it.

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