Exercise 26

 

Assessment started: undefined.

Item 1

Rachel, Chan, and Sue work at a grocery store that sells pens, erasers, and pencils. 

Rachel says, "Seven pens and five erasers cost the same as six pencils.

Chan says, "Four pens and nine pencils cost the same as five erasers.

Sue says, "Six pencils and three erasers cost the same as four pens.

Only one is lying. Can you tell us who?

• Rachel
• Chan
• Solution

  Let A$A$ equal the price of pens, B$B$ equal the price of erasers, and O$O$ equal the price of pencils.
  Rachel is saying that 7A+5B=6O$7A+5B=6O$. 
  Chan is saying that 4A+9O=5B$4A+9O=5B$. 
  Sue is saying that 6O+3B=4A$6O+3B=4A$.

  Combining Rachel's and Chan's statements, we get 11A=−3O$11A=-3O$. This is impossible.
  Combining Chan's and Sue's statements, we get 15O=2B$15O=2B$. This is possible.
  Combining Rachel's and Sue's statements, we get 8B=−3A$8B=-3A$. This is impossible.
  This means that either Rachel is lying, or Chan and Sue are both lying. But there can be only one liar.

  Hence, Rachel is the liar.

 

Math problem search

Have students practice their addition, subtraction, multiplication and division skills by searching for hidden math equations in a word search-style puzzle. It can be adapted to any skill you want students to practice, and promotes a solid understanding of basic math facts.

Maths puzzles for kids

 

Math Puzzles for Kids:

1. Math crossword puzzles

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Logic puzzles

 

Assessment started: undefined.

Item 1

In a toy store, there are 4$4$ dolls of different heights A, B, C$A,B,C$, and D$D$.

D$D$ is neither as tall as A$A$ nor as short as C$C$.

B$B$ is shorter than D$D$ but taller than C$C$.

If Kelly wants to purchase the tallest doll, which one should she purchase?

• A$A$
• B$B$
• C$C$
• D
• Solution

  D$D$ is not as tall as A$A$, which means D$D$ is shorter than A$A$, So D<A$D<A$.
  D$D$ is not as short as C$C$, D$D$ is taller than C$C$, So D>C$D>C$.
  B$B$ is shorter than D$D$ but taller than C$C$. So we get, C<B<D$C<B<D$.

  So A$A$ is the tallest.