KA-0056Place value and digit positions
4 points, difficulty 2 of 3Level 3–4about 90sThe two digits of a number are swapped and the number gets bigger by 36. Which of these could be the number?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Try swapping each one and see.
2The strategy
Swapping the digits of a two-digit number changes it by nine times the difference between the digits. For the number to grow, the second digit has to be the larger one.
3The full solution
Swapping changes the number by 9 times the digit difference, so a change of 36 needs a difference of 4 with the bigger digit second. 15 becomes 51, and 51 - 15 = 36.
Solution
The reliable way
Test each option by swapping. 13 becomes 31, a rise of 18. 15 becomes 51, a rise of 36 — that works. 24 becomes 42, a rise of 18. 41 becomes 14 and 62 becomes 26, both of which fall. So the number is 15. The transferable idea: check the direction of a change as well as its size.
The elegant way
Swapping the digits of a two-digit number changes it by 9 times the difference between the digits, so a rise of 36 means a digit difference of 4 with the larger digit second.
Why this is on the test: Digit-swap questions are pure place value, and the trap is a number whose digits are right but in the wrong order.